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Diffstat (limited to 'Engineering_Heat_Transfer')
| -rw-r--r-- | Engineering_Heat_Transfer/CHAPTER1.ipynb | 482 | ||||
| -rw-r--r-- | Engineering_Heat_Transfer/CHAPTER10.ipynb | 239 | ||||
| -rw-r--r-- | Engineering_Heat_Transfer/CHAPTER11.ipynb | 332 | ||||
| -rw-r--r-- | Engineering_Heat_Transfer/CHAPTER12.ipynb | 342 | ||||
| -rw-r--r-- | Engineering_Heat_Transfer/CHAPTER2.ipynb | 713 | ||||
| -rw-r--r-- | Engineering_Heat_Transfer/CHAPTER4.ipynb | 607 | ||||
| -rw-r--r-- | Engineering_Heat_Transfer/CHAPTER5.ipynb | 126 | ||||
| -rw-r--r-- | Engineering_Heat_Transfer/CHAPTER6.ipynb | 545 | ||||
| -rw-r--r-- | Engineering_Heat_Transfer/CHAPTER7.ipynb | 709 | ||||
| -rw-r--r-- | Engineering_Heat_Transfer/CHAPTER8.ipynb | 527 | ||||
| -rw-r--r-- | Engineering_Heat_Transfer/CHAPTER9.ipynb | 571 | ||||
| -rw-r--r-- | Engineering_Heat_Transfer/CHAPTER_3.ipynb | 339 | ||||
| -rw-r--r-- | Engineering_Heat_Transfer/README.txt | 10 | ||||
| -rw-r--r-- | Engineering_Heat_Transfer/screenshots/heat_transferred.png | bin | 0 -> 9126 bytes | |||
| -rw-r--r-- | Engineering_Heat_Transfer/screenshots/length_required.png | bin | 0 -> 13684 bytes | |||
| -rw-r--r-- | Engineering_Heat_Transfer/screenshots/wall_tempratures.png | bin | 0 -> 10804 bytes |
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diff --git a/Engineering_Heat_Transfer/CHAPTER1.ipynb b/Engineering_Heat_Transfer/CHAPTER1.ipynb new file mode 100644 index 00000000..d020ad30 --- /dev/null +++ b/Engineering_Heat_Transfer/CHAPTER1.ipynb @@ -0,0 +1,482 @@ +{
+ "metadata": {
+ "name": "CHAPTER1"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter1:Fundamental Concepts"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 1.1 Page No.7"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# determination of surface temperature on one side of a firewall\n",
+ "\n",
+ "#Given\n",
+ "k=9.4 # thermal conductivity in [BTU/hr.ft. \u02daRankine]\n",
+ "q=6.3 # heat flux in [BTU/s. sq.ft]\n",
+ "T1=350 # the outside surface temperature of one aide of the wall [\u02daF]\n",
+ "\n",
+ "#Calculation\n",
+ "# converting heat flux into BTU/hr sq.ft\n",
+ "Q=6.3*3600 # [BTU/hr.sq.ft]\n",
+ "dx=0.5 # thickness in [inch]\n",
+ "#converting distance into ft\n",
+ "Dx=0.5/12.0 # thickness in [ft]\n",
+ "# solving for temeprature T2\n",
+ "T2=T1-(Q*Dx/k) # [\u02daF]\n",
+ "\n",
+ "#Result\n",
+ "print\"The required temperature on the other side of the firewall is \",round(T2,1),\"F\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The required temperature on the other side of the firewall is 249.5 F\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 1.2 Page No.9"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# determination of thermal conductivity of aluminium\n",
+ "\n",
+ "#Given\n",
+ "k_ss=14.4 # thermal conductivity of stainless steel in [W/m.K]\n",
+ "dt_ss=40 # [K]\n",
+ "dt_al=8.65 # [K]\n",
+ "dz_ss=1 # [cm]\n",
+ "dz_al=3 # [cm]\n",
+ "\n",
+ "#calculation\n",
+ "k_al=k_ss*dt_ss*dz_al/(dt_al*dz_ss);# thermal conductivity of Al in [W/m.K]\n",
+ "\n",
+ "#result\n",
+ "print\"The thermal conductivity of aluminium is\",round(k_al,0),\"W/m.K\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The thermal conductivity of aluminium is 200.0 W/m.K\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 1.3 Page No.13"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# determination of heat transferred by convection\n",
+ "\n",
+ "#Given\n",
+ "h_c=3 # convective coefficient in [BTU/hr.ft**2\n",
+ "A=30*18 # Cross sectional area in ft**2\n",
+ "T_w=140 # Roof surface temperature in degree Fahrenheit\n",
+ "T_inf=85 # Ambient temperature in degree Fahrenheit\n",
+ "\n",
+ "#Calculation\n",
+ "dT= (T_w-T_inf)\n",
+ "Q_c=h_c*A*dT # Convective heat transfer in BTU/hr\n",
+ "\n",
+ "#Result\n",
+ "print\"The heat transferred by convection is\",round(Q_c,2),\"BTU/hr\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The heat transferred by convection is 89100.0 BTU/hr\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 1.4 Page No.14"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# determining average film conductance\n",
+ "\n",
+ "#Given\n",
+ "D=0.0243 # diameter in meter\n",
+ "L=0.2 # length in meter\n",
+ "A=3.14*D*L # cross-sectional area in sq.m\n",
+ "cp=4200.0 # specific heat of water in J/kg.K\n",
+ "T_b2=21.4 # temperature of bulk fluid in degree celsius\n",
+ "T_in=20.0 # temperature of inlet water in degree celsius\n",
+ "T_w=75.0 # temperature of wall in degree celsius\n",
+ "Q=500.0 # volumetric flow rate in cc/s\n",
+ "density=1000 # density of water in kg/cu.m\n",
+ "\n",
+ "#calculation\n",
+ "m=Q*density/10**6 # mass flowa rate in kg/s\n",
+ "# using definition of specific heat and Newton's law of cooling\n",
+ "hc=m*cp*(T_b2-T_in)/(A*(T_w-T_in))\n",
+ "\n",
+ "#result\n",
+ "print\"The average film conductance is \",round(hc,0),\"W/sq.m. K\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The average film conductance is 3503.0 W/sq.m. K\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 1.5 Page No.18"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# determination of heat loss rate by radiation\n",
+ "\n",
+ "#Given\n",
+ "W=14 # width in ft\n",
+ "L=30.0 # length in ft\n",
+ "A=W*L # area in ft**2\n",
+ "F_12=1 # view factor assumed to be 1\n",
+ "T1=120+460 # driveway surface temperature in degree Rankine\n",
+ "T2=0 # space temperature assumed to be 0 degree Rankine\n",
+ "\n",
+ "#Calculation\n",
+ "sigma=0.1714*10**(-8) # value of Stefan-Boltzmann's constant in BTU/(hr.ft**2.(degree Rankine)**4)\n",
+ "e=0.9 # surface emissivity\n",
+ "q=sigma*A*e*F_12*((T1)**4-(T2)**4);\n",
+ "\n",
+ "#result\n",
+ "print\"The heat loss rate by radiation is \",round(q,0),\"BTU/hr\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The heat loss rate by radiation is 73319.0 BTU/hr\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 1.6 Page No.19"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# determination of radiation thermal conductance\n",
+ "\n",
+ "#Given\n",
+ "A=420.0 # area in sq.ft\n",
+ "T1=580.0 # driveway surface temperature in degree Rankine\n",
+ "T2=0 # surface temperature assumed to be 0 degree Rankine\n",
+ "Qr=73320 # heat loss rate in BTU/hr\n",
+ "\n",
+ "#calculation\n",
+ "hr=Qr/(A*(T1-T2)) # radiation thermal conductance in BTU/(hr.ft**2.(degree Rankine)\n",
+ "\n",
+ "#result\n",
+ "print\"the radiation thermal conductance is \",round(hr,2),\"BTU/(hr. sq.ft R)\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "the radiation thermal conductance is 0.3 BTU/(hr. sq.ft R)\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 1.7 Page No. 21"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "%pylab inline"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Identification of all resistances and their values\n",
+ "# Estimation of heat transfer per unit area\n",
+ "# Determination of the inside and outside wall temperatures\n",
+ "\n",
+ "#Given\n",
+ "A=1.0 # assuming A=1 m**2 for convenience\n",
+ "hc1_avg=15.0 # taking average of extreme values for hc [W/m**2.K]\n",
+ "k=(0.38+0.52)/2.0 # thermal conductivity of common brick in W/M.k\n",
+ "L=0.1 #10 cm converted into m\n",
+ "Rk=(L/(k*A)) # resistance of construction material, assume common brick\n",
+ "\n",
+ "#calcultion\n",
+ "T_inf1=1000.0 # temperature of exhaust gases in K\n",
+ "T_inf2=283.0 # temperature of ambient air in K\n",
+ "Rcl=1/(hc1_avg*A) # resistance on left side of wall [K/W]\n",
+ "Rc2=Rcl \n",
+ "q=(T_inf1-T_inf2)/(Rcl+Rk+Rc2) # heat transferred per unit area\n",
+ "T_in=T_inf1-Rcl*q #inlet temprature \n",
+ "T_out=T_inf2+Rc2*q\n",
+ "\n",
+ "#result\n",
+ "print\"(b)\"\n",
+ "print\"The resistance on left side of wall is \",round(Rcl,2),\"K/W\"\n",
+ "print\"The resistance of construction material of wall is\",round(Rk,2),\"K/W\"\n",
+ "print\"The resistance on right side of wall is \",round(Rc2,2),\"K/W\"\n",
+ "print\"(c)The Heat transferred per unit area is \",round(q/1000,2),\"kw\"\n",
+ "print \"(d)\"\n",
+ "print\"The inside wall temperature is \",round(T_in,0),\"K\"\n",
+ "print\"The outside wall temperature is\",round(T_out,1),\"K\"\n",
+ "\n",
+ "#Plot\n",
+ "import matplotlib.pyplot as plt\n",
+ "fig = plt.figure()\n",
+ "ax = fig.add_subplot(111)\n",
+ "\n",
+ "x1=[5,5]\n",
+ "T1=[0,1000]\n",
+ "\n",
+ "x2=[8,8]\n",
+ "T2=[0,1000]\n",
+ "\n",
+ "x3=[1,4]\n",
+ "T3=[1000,1000]\n",
+ "\n",
+ "x4=[4,5]\n",
+ "T4=[1000,866]\n",
+ "\n",
+ "x5=[5,8]\n",
+ "T5=[866,417]\n",
+ "\n",
+ "x6=[8,9]\n",
+ "T6=[417,290]\n",
+ "\n",
+ "x7=[9,10]\n",
+ "T7=[290,283]\n",
+ "\n",
+ "xlabel(\"x\") \n",
+ "ylabel(\"T (K)\") \n",
+ "plt.xlim((0,11))\n",
+ "plt.ylim((0,1200))\n",
+ "\n",
+ "ax.plot([1], [1000], 'o')\n",
+ "ax.annotate('(1000K)', xy=(1,1020))\n",
+ "\n",
+ "ax.plot([5], [866], 'o')\n",
+ "ax.annotate('(T1)', xy=(5.5,866))\n",
+ "\n",
+ "ax.plot([8], [417], 'o')\n",
+ "ax.annotate('(T2)', xy=(7.5,417))\n",
+ "ax.plot([10], [283], 'o')\n",
+ "ax.annotate('(283K)', xy=(10.5,283))\n",
+ "\n",
+ "\n",
+ "\n",
+ "a1=plot(x1,T1)\n",
+ "a2=plot(x2,T2)\n",
+ "a3=plot(x3,T3)\n",
+ "a4=plot(x4,T4)\n",
+ "a5=plot(x5,T5)\n",
+ "a6=plot(x6,T6)\n",
+ "a7=plot(x7,T7)\n",
+ "show(a1)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(b)\n",
+ "The resistance on left side of wall is 0.07 K/W\n",
+ "The resistance of construction material of wall is 0.22 K/W\n",
+ "The resistance on right side of wall is 0.07 K/W\n",
+ "(c)The Heat transferred per unit area is 2.02 kw\n",
+ "(d)\n",
+ "The inside wall temperature is 866.0 K\n",
+ "The outside wall temperature is 417.4 K\n"
+ ]
+ },
+ {
+ "output_type": "display_data",
+ "png": 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IbWZZwcyaNQu73e74B5eUlER4eDh79+5l4MCBJCUlAZCVlcXy5cvJysoiLS2N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\nkIhbnvzxNPAAAAAASUVORK5CYII=\n"
+ }
+ ],
+ "prompt_number": 24
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 1.8 Page No.24"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# determination of surface temperature\n",
+ "\n",
+ "#Given\n",
+ "k=0.604 # [BTU/(hr.ft.degree Rankine)]\n",
+ "hc=3.0 # average value for natural convection in BTU/(hr.ft**2.degree Rankine)\n",
+ "ew=0.93 \n",
+ "f_wr=1.0 # shape factor\n",
+ "sigma= 0.1714*10**(-8) # BTU/(hr.ft**2.degree Rankine).\n",
+ "L=4/12.0 # length in ft\n",
+ "T1=80+460 # temperature of side-walk in degree Rankine\n",
+ "T_inf=20+460 # temperature of ambient air in degree Rankine\n",
+ "T_r=0 # assuming space temperature to be 0 degree Rankine\n",
+ "\n",
+ "#Calculation\n",
+ "# LHS of the form a*Tw+b*Tw**4=c\n",
+ "a=((k/L)+hc) #Coefficient of Tw in the equation\n",
+ "b=(sigma*ew*f_wr) #Coefficient of Tw**4 in the equation\n",
+ "c=(k*T1/L)+(hc*T_inf)+(sigma*f_wr*ew*T_r**4) #right hans side of the equation\n",
+ "#Soving by try and error\n",
+ "Tw1=470 #assumed first value of temprature\n",
+ "LHS1=a*Tw1+b*Tw1**4\n",
+ "Tw2=480 #assumed 2nd value of temprature\n",
+ "LHS2=a*Tw2+b*Tw2**4\n",
+ "Tw3=490 #assumed 3rd value of temprature\n",
+ "LHS3=a*Tw3+b*Tw3**4\n",
+ "Tw4=485 #assumed 4th value of temprature\n",
+ "LHS4=a*Tw4+b*Tw4**4\n",
+ "Tw5=484.5 #assumed fifth value of temprature\n",
+ "LHS5=a*Tw5+b*Tw5**4\n",
+ "\n",
+ "#result\n",
+ "print\"RHS\",round(c,1)\n",
+ "print\"LHS at surface Temprature 1=\",round(LHS1,1)\n",
+ "print\"LHS at surface Temprature 2=\",round(LHS2,1)\n",
+ "print\"LHS at surface Temprature 3=\",round(LHS3,0)\n",
+ "print\"LHS at surface Temprature 4=\",round(LHS4,1)\n",
+ "print\"LHS at surface Temprature 5=\",round(LHS5,1)\n",
+ "print\"\\nLHS is close enough to RHS at Temprature 484.5. So Surface Temprature is\",Tw5,\"R\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "RHS 2418.5\n",
+ "LHS at surface Temprature 1= 2339.4\n",
+ "LHS at surface Temprature 2= 2394.4\n",
+ "LHS at surface Temprature 3= 2450.0\n",
+ "LHS at surface Temprature 4= 2422.0\n",
+ "LHS at surface Temprature 5= 2419.2\n",
+ "\n",
+ "LHS is close enough to RHS at Temprature 484.5. So Surface Temprature is 484.5 R\n"
+ ]
+ }
+ ],
+ "prompt_number": 22
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Engineering_Heat_Transfer/CHAPTER10.ipynb b/Engineering_Heat_Transfer/CHAPTER10.ipynb new file mode 100644 index 00000000..f7b3f4b6 --- /dev/null +++ b/Engineering_Heat_Transfer/CHAPTER10.ipynb @@ -0,0 +1,239 @@ +{
+ "metadata": {
+ "name": "CHAPTER10"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 10: Condensation and Vaporization Heat Transfer"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 10.1 Page NO.527"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "%pylab inline"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Calculation of the heat-transfer rate and the amount of steam condensed\n",
+ "\n",
+ "#Given\n",
+ "# properties of engine oil at (328 + 325)/2 = 326.5 degree F = 320\u00b0F from appendix table C11\n",
+ "rou_f=0.909*62.4 # density in lbm/ft**3 \n",
+ "cp=1.037 # specific heat BTU/(lbm-degree Rankine) \n",
+ "v_f=0.204e-5 # viscosity in ft**2/s \n",
+ "kf=0.393 # thermal conductivity in BTU/(lbm.ft.degree Rankine) \n",
+ "a=6.70e-3 # diffusivity in ft**2/hr \n",
+ "Pr=1.099 # Prandtl Number \n",
+ "V_v=4.937 # specific volume in ft**3/lbm from superheated steam tables\n",
+ "rou_v=1/V_v # vapour density\n",
+ "g=32.2\n",
+ "hfg=888.8 # from saturated steam tables\n",
+ "Tg=327.81\n",
+ "Tw=325\n",
+ "L=2.0 # length in ft\n",
+ "W=3.0 # width in ft\n",
+ "z=0.204*10**-5 # distance from entry of plate in ft\n",
+ "\n",
+ "#Calculation\n",
+ "# film thickness is given as follows\n",
+ "y=((4*kf*v_f*(Tg-Tw)/3600.0)/(rou_f*g*hfg*(1-(rou_v/rou_f))))**(1/4.0) #let y=delta/z**(1/4)\n",
+ "hz=1665 #From Table 10.1\n",
+ "hL=(4/3.0)*hz # at plate end\n",
+ "mf=(hL*L*W*(Tg-Tw))/hfg\n",
+ "q=mf*hfg\n",
+ "Re=(4*mf/3600)/(W*rou_f*v_f)\n",
+ "\n",
+ "#Result\n",
+ "print\"The amount of steam condensed is \",round(mf,1),\"lbm/h\"\n",
+ "print\"The heat transfer rate is \",round(q,0),\"BTU/hr\"\n",
+ "\n",
+ "#plot\n",
+ "import matplotlib.pyplot as plt\n",
+ "fig = plt.figure()\n",
+ "ax = fig.add_subplot(111)\n",
+ "\n",
+ "x1=[0.0017,0.0018,0.0023,0.0030,0.0035]\n",
+ "z1=[2,1.6,0.6,0.3,0.1]\n",
+ "\n",
+ "x2=[0.0023,0.0022,0.0017,0.0011,0.0006,0]\n",
+ "z2=[2,1.6,0.6,0.3,0.1,0]\n",
+ "\n",
+ "xlabel(\"d (m)\") \n",
+ "ylabel(\"z (m)\") \n",
+ "plt.xlim((0,0.004))\n",
+ "plt.ylim((2,0))\n",
+ "\n",
+ "ax.annotate('(infinity)', xy=(0.0035,0.1))\n",
+ "ax.annotate('(hl=2220)', xy=(0.0005,1.7))\n",
+ "a1=plot(x1,z1)\n",
+ "a1=plot(x2,z2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The amount of steam condensed is 42.1 lbm/h\n",
+ "The heat transfer rate is 37429.0 BTU/hr\n"
+ ]
+ },
+ {
+ "output_type": "display_data",
+ "png": 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1wIwZcldCVB/DgzQrISoBqUdS5S7DYTt3AsHB1V9ESsPwIM0a3X00fir6Ced+PSd3KQ5J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\nvp37yl0OkU0YHk7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+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 10.2 Page NO.532"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Determination of both the heat that the cooling fluid must remove and the condensation rate. \n",
+ "\n",
+ "#Given\n",
+ "# properties of water at (100 + 60)/2 = 80\u00b0C from appendix table C11\n",
+ "rou_f=974.0 # density in kg/m**3 \n",
+ "cp_1=4196.0 # specific heat in J/(kg*K) \n",
+ "v_1=0.364e-6 # viscosity in m**2/s \n",
+ "Pr_1=2.22 # Prandtl Number \n",
+ "kf=0.668 # thermal conductivity in W/(m.K)\n",
+ "a_1=1.636e-7 # diffusivity in m**2/s \n",
+ "Vv=1.9364 # specific volume in m**3/kg\n",
+ "rou_v=1/Vv # vapor density\n",
+ "g=9.81\n",
+ "hfg=2257.06*1000 \n",
+ "Tg=100\n",
+ "Tw=60\n",
+ "L=1\n",
+ "\n",
+ "#Calculation\n",
+ "# specifications of 1 nominal schedule 40 pipe from appendix F1\n",
+ "OD=0.03340\n",
+ "hD=0.782*((g*rou_f*(1-(rou_v/rou_f))*(kf**3)*hfg)/(v_1*OD*(Tg-Tw)))**(1/4.0)\n",
+ "hD=10720 #According to the book\n",
+ "import math\n",
+ "q=hD*math.pi*OD*L*(Tg-Tw)\n",
+ "mf=q/hfg\n",
+ "\n",
+ "#Result\n",
+ "print\"The heat flow rate is \",round(q,0),\"W\"\n",
+ "print\"The rate at which steam condenses is \",round(mf*3600,0),\"kg/hr\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The heat flow rate is 44994.0 W\n",
+ "The rate at which steam condenses is 72.0 kg/hr\n"
+ ]
+ }
+ ],
+ "prompt_number": 32
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 10.3 Page NO. 538"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Calculation of (a) the power input to the water for boiling to occur, (b) the evaporation rate of water, and (c) the critical heat flux.\n",
+ "\n",
+ "#Given\n",
+ "# properties of water at 100\u00b0C = 373 K from appendix table 10.3\n",
+ "rou_f=958 # density in kg/m**3\n",
+ "cp_f= 4217 # specific heat in J/(kg*K) \n",
+ "v_f= 2.91e-7 # viscosity in m**2/s \n",
+ "Pr_f =1.76 # Prandtl Number \n",
+ "rou_g=0.596 \n",
+ "sigma=0.0589 # surface tension in N/m\n",
+ "hfg=2257000 \n",
+ "Tw=120.0\n",
+ "Tg=100.0\n",
+ "D=.141 # diameter of pan in m\n",
+ "g=9.81\n",
+ "gc=1\n",
+ "\n",
+ "#calculation\n",
+ "# nucleate boiling regime\n",
+ "Cw=0.0132 # formechanically polished stainless steel from table 10.2\n",
+ "q_A=(rou_f*v_f*hfg)*((g*rou_f*(1-(rou_g/rou_f)))/(sigma*gc))**(0.5)*((cp_f*(Tw-Tg))/(Cw*hfg*Pr_f**1.7))**3\n",
+ "A=math.pi*D**2/4.0\n",
+ "p=q_A*A # power delivered to the water in W\n",
+ "mf=q/hfg # water evaporation rate\n",
+ "q_cr=0.18*hfg*(sigma*g*gc*rou_f*rou_g**2)**(0.25)\n",
+ "\n",
+ "#Result\n",
+ "print\"(a)The power delivered to the water is kW\",round(q/1000,2),\"KW\"\n",
+ "print\"(b)The water evaporation rate is \",round(mf*3600,2),\"kg/h\"\n",
+ "print\"(c)The critical heat flux is \",round(q_cr,0),\"W/sq.m\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(a)The power delivered to the water is kW 4.98 KW\n",
+ "(b)The water evaporation rate is 7.94 kg/h\n",
+ "(c)The critical heat flux is 1521299.0 W/sq.m\n"
+ ]
+ }
+ ],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Engineering_Heat_Transfer/CHAPTER11.ipynb b/Engineering_Heat_Transfer/CHAPTER11.ipynb new file mode 100644 index 00000000..af58990e --- /dev/null +++ b/Engineering_Heat_Transfer/CHAPTER11.ipynb @@ -0,0 +1,332 @@ +{
+ "metadata": {
+ "name": "CHAPTER11"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 11: Introduction to Radiation Heat Transfer"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 11.1 Page NO.554"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Calculation of the value of the solid angle subtended by surfaces dA2 and dA3 with respect to dA1 (b) the intensity of emission from dA, in the direction of the other areas (c) the rate at which radiation emitted by dA, is intercepted by the other areas\n",
+ "\n",
+ "#Given\n",
+ "# solid angle is calculate using the equation dw=dA*cos(Beta)/r**2\n",
+ "# Beta is the angle between the surface normal of a receiver surface and the line connecting the two surfaces\n",
+ "# For area A2\n",
+ "# dimensions are 1X1 in, so\n",
+ "\n",
+ "#Calculation\n",
+ "import math\n",
+ "dA2=(1*1)/144.0\n",
+ "Beta1=40*math.pi/180.0\n",
+ "r=4\n",
+ "dw2_1=dA2*math.cos(Beta1)/r**2\n",
+ "dA3=dA2\n",
+ "Beta2=0\n",
+ "dw3_1=dA3*cos(Beta2)/r**2\n",
+ "\n",
+ "theta2=math.pi*50/180.0\n",
+ "theta3=math.pi*60/180.0\n",
+ "I_theta2=2000*(1-0.4*(sin(theta2))**2)\n",
+ "I_theta3=2000*(1-0.4*(sin(theta3))**2)\n",
+ "\n",
+ "dA1=1/144.0\n",
+ "dq1_2=I_theta2*dA1*math.cos(theta2)*dw2_1 #In book calculation mistake\n",
+ "dq1_3=I_theta3*dA1*math.cos(theta2)*dw3_1\n",
+ "\n",
+ "#Result\n",
+ "print\"(a)The solid angle subtended by area dA2 with respect to dA1 is \",round(dw2_1,4),\"sr\"\n",
+ "print\" The solid angle subtended by area dA3 with respect to dA1 is \",round(dw3_1,4),\"sr\"\n",
+ "print\"(b) The intensity of radiation emitted from dA1 in the direction of dA2 is \",round(I_theta2,0),\"BTU/(hr.sq.ft.sr)\"\n",
+ "print\" The intensity of radiation emitted from dA1 in the direction of dA3 is\",round(I_theta3,0),\"BTU/(hr.sq.ft.sr)\"\n",
+ "print\"(c)The rate at which radiation emitted by dA1 is intercepted by dA2 is \",round(dq1_2,4),\"BTU/hr\"\n",
+ "print\" The rate at which radiation emitted by dA1 is intercepted by dA3 is \",round(dq1_3,4),\"BTU/hr\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(a)The solid angle subtended by area dA2 with respect to dA1 is 0.0003 sr\n",
+ " The solid angle subtended by area dA3 with respect to dA1 is 0.0004 sr\n",
+ "(b) The intensity of radiation emitted from dA1 in the direction of dA2 is 1531.0 BTU/(hr.sq.ft.sr)\n",
+ " The intensity of radiation emitted from dA1 in the direction of dA3 is 1400.0 BTU/(hr.sq.ft.sr)\n",
+ "(c)The rate at which radiation emitted by dA1 is intercepted by dA2 is 0.0023 BTU/hr\n",
+ " The rate at which radiation emitted by dA1 is intercepted by dA3 is 0.0027 BTU/hr\n"
+ ]
+ }
+ ],
+ "prompt_number": 13
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 11.2 Page NO.557"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Calculation of the value of the solid angle subtended by surfaces dA2 with respect to dA1 (b) the rate at which radiation emitted by dA1 is intercepted by dA2 (c) the irradiation associated with dA2\n",
+ "\n",
+ "#Given\n",
+ "# solid angle is calculate using the equation dw=dA*cos(Beta)/r**2\n",
+ "# The angle Beta is 0 because the surface normal of dA2 is directed at dA1\n",
+ "dA2=0.02*0.02\n",
+ "Beta=0\n",
+ "r=1\n",
+ "\n",
+ "#Calculation\n",
+ "import math\n",
+ "dw2_1=dA2*math.cos(Beta)/r**2\n",
+ "dA1=dA2\n",
+ "theta=math.pi*30/180.0\n",
+ "I_theta=1000# The intensity of radiation leaving dA1 in any direction is 1 000 W/(m**2.sr\n",
+ "dq1_2=I_theta*dA1*cos(theta)*dw2_1\n",
+ "# The irradiation associated with dA2 can be found by dividing the incident radiation by the receiver area\n",
+ "dQ1_2=dq1_2/dA2\n",
+ "\n",
+ "#Result\n",
+ "print\"(a)The solid angle subtended by area dA2 with respect to dA1 is \",round(dw2_1,4),\"sr\"\n",
+ "print\"(b)The rate at which radiation emitted by dA1 is intercepted by dA2 is\",round(dq1_2,5),\"W\"\n",
+ "print\"(c)The irradiation associated with dA2 is \",round(dQ1_2,3),\"W/sq.m\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(a)The solid angle subtended by area dA2 with respect to dA1 is 0.0004 sr\n",
+ "(b)The rate at which radiation emitted by dA1 is intercepted by dA2 is 0.00014 W\n",
+ "(c)The irradiation associated with dA2 is 0.346 W/sq.m\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 11.3 Page NO. 563"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# (a) Calculation of the emissivity of the hole.(b) the rate of radiant emission from the hole\n",
+ "\n",
+ "#Given\n",
+ "D=2.5/12.0 # diameter in ft\n",
+ "L=4.5/12.0 # length in ft\n",
+ "\n",
+ "#Calculation\n",
+ "import math\n",
+ "A=(2*math.pi*D**2/4)+(math.pi*D*L)\n",
+ "A_hole=math.pi*(1/(8.0*12.0))**2/4.0\n",
+ "f=A_hole/A # fraction of area removed\n",
+ "# for rolled and polished aluminum, that emissivity = 0.039 from appendix table E1\n",
+ "emissivity=0.039\n",
+ "emissivity_hole=emissivity/(emissivity+(1-emissivity)*f)\n",
+ "\n",
+ "sigma=0.1714e-8 # stefan Boltzmann constant in BTU/(hr~ft**2 degree R)\n",
+ "T=150+460 # temperature in degree R\n",
+ "qe=emissivity_hole*sigma*T**4\n",
+ "Qe=A_hole*qe\n",
+ "\n",
+ "#Result\n",
+ "print\"(a)The emissivity of the hole is %.4f\",round(emissivity_hole,4)\n",
+ "print\"(b)The heat lost by the hole is \",round(Qe,4),\"BTU/hr\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(a)The emissivity of the hole is %.4f 0.9933\n",
+ "(b)The heat lost by the hole is 0.0201 BTU/hr\n"
+ ]
+ }
+ ],
+ "prompt_number": 23
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 11.4 Page NO.568"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Determination of the percentage of total emitted energy that lies in the visible range. \n",
+ "\n",
+ "#Given\n",
+ "T=2800 #Temprature\n",
+ "lambda1=4e-7 #Wavelength\n",
+ "lambda2=7e-7\n",
+ "hT=lambda1*T\n",
+ "\n",
+ "#Calculation\n",
+ "lambdaT=lambda2*T\n",
+ "I1=0.0051 #Fraction of Total Radiation Emitted for lower Wavelength-Temperature Product from Table 11.1\n",
+ "I2=0.065 #Fraction of Total Radiation Emitted for upper Wavelength-Temperature Product from Table 11.1\n",
+ "dI=I2-I1\n",
+ "\n",
+ "#Result\n",
+ "print\"The percentage of total emitted energy that lies in the visible range is\",round(dI*100,0),\"percant\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The percentage of total emitted energy that lies in the visible range is 6.0 percant\n"
+ ]
+ }
+ ],
+ "prompt_number": 27
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 11.5 Page NO. 570"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Estimation of the surface temperature of the sun and the emitted heat flux\n",
+ "\n",
+ "#Given\n",
+ "lambda_max=0.5e-6 # maximum wavelength in m\n",
+ "# From Wien\u2019s Displacement Law we can write lambda_max*T=2.898e-3 m.K\n",
+ "T=2.898e-3/lambda_max\n",
+ "# The heat flux is given by the Stefan-Boltzmann Equation as q=sigma*T**4\n",
+ "sigma=5.675e-8 # value of Stefan-Boltzmann constant in W/(m**2.K**4)\n",
+ "q=sigma*T**4\n",
+ "\n",
+ "#result\n",
+ "print\"The Surface Temperature of the Sun is \",round(T,2),\"K\"\n",
+ "print\"The heat flux emitted is \",round(q,0),\"W/sq.m\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Surface Temperature of the Sun is 5796.0 K\n",
+ "The heat flux emitted is 64044136.0 W/sq.m\n"
+ ]
+ }
+ ],
+ "prompt_number": 29
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 11.6 Page NO.575"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# (a) Calculation of the rate at which the sun\u2019s radiant energy is transmitted through the glass windshield. The interior of the car is considered to be a black body that radiates at 100\u00b0F. (b) Calculation of the rate at which radiant energy from the car interior is transmitted through the glass windshield. \n",
+ "\n",
+ "#Given\n",
+ "lambda1=300e-9 # lower limit of wavelength\n",
+ "lambda2=380e-9 # upper limit of wavelength\n",
+ "T=5800\n",
+ "lambda1_T=lambda1*T\n",
+ "lambda2_T=lambda2*T\n",
+ "I1=0.101 #Fraction of Total Radiation Emitted for lower Wavelength-Temperature Product from Table 11.1\n",
+ "I2=0.0334 #Fraction of Total Radiation Emitted for upper Wavelength-Temperature Product from Table 11.1\n",
+ "dI=abs(I2-I1)\n",
+ "t=dI*0.68 # transmissivity\n",
+ "q=1100 # radiation received by car in W/sq.m\n",
+ "q_in=t*q # energy transmitted from the sun through the glass\n",
+ "\n",
+ "\n",
+ "#Calculation\n",
+ "Tb=311 # temperature of black body source in K\n",
+ "lambda1_Tb=lambda1*Tb\n",
+ "lambda2_Tb=lambda2*Tb\n",
+ "dI_b=0 # Table 11.1 gives negligibly small values of the corresponding integrals.\n",
+ "t_b=dI_b*0.68 # transmissivity\n",
+ "q_out=t_b*q\n",
+ "\n",
+ "#Result\n",
+ "print\"(a)The energy transmitted from the sun through the glass is \",round(q_in,1),\"W/sq.m\"\n",
+ "print\"(b)the rate at which radiant energy from the car interior is transmitted through the glass windshield is\",q_out,\"W/sq.m\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(a)The energy transmitted from the sun through the glass is 50.6 W/sq.m\n",
+ "(b)the rate at which radiant energy from the car interior is transmitted through the glass windshield is 0.0 W/sq.m\n"
+ ]
+ }
+ ],
+ "prompt_number": 32
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Engineering_Heat_Transfer/CHAPTER12.ipynb b/Engineering_Heat_Transfer/CHAPTER12.ipynb new file mode 100644 index 00000000..1d32142c --- /dev/null +++ b/Engineering_Heat_Transfer/CHAPTER12.ipynb @@ -0,0 +1,342 @@ +{
+ "metadata": {
+ "name": "CHAPTER12"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 12: Radient Heat Transfer between Surfaces"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 12.3 Page No 598"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Determination of the heat transferred by radiation from dA1 to A. \n",
+ "\n",
+ "#Given\n",
+ "# The view factor Fd1_2 can be calculated as Fd1_2=Fd1_3+Fd1_4+Fd1_5\n",
+ "# For Fd1_3\n",
+ "a_13=100.0\n",
+ "b_13=250.0\n",
+ "c_13=100.0\n",
+ "X_13=a_13/c_13\n",
+ "Y_13=b_13/c_13\n",
+ "Fd1_3=0.17 # value for Fd1_3 corresponding to above calculated values of a/c and b/c\n",
+ "# For Fd1_4\n",
+ "a_14=300\n",
+ "b_14=50\n",
+ "c_14=100\n",
+ "\n",
+ "#Calculation\n",
+ "X_14=a_14/c_14\n",
+ "Y_14=b_14/c_14\n",
+ "Fd1_4=0.11 #value for Fd1_4 corresponding to above calculated values of a/c and b/c\n",
+ "# For Fd1_5\n",
+ "a_15=100\n",
+ "b_15=50\n",
+ "c_15=100\n",
+ "X_15=a_15/c_15\n",
+ "Y_15=b_15/c_15\n",
+ "Fd1_5=0.09 #value for Fd1_3 corresponding to above calculated values of a/c and b/c\n",
+ "Fd1_2=Fd1_3+Fd1_4-Fd1_5\n",
+ "sigma=0.1714e-8 # Stefan-Boltzmann constant\n",
+ "T1=660\n",
+ "T2=560\n",
+ "q12_A1=sigma*Fd1_2*(T1**4-T2**4)\n",
+ "\n",
+ "#result\n",
+ "print\"The net heat transferred is \",round(q12_A1,1),\"BTU/(hr.sq.ft)\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The net heat transferred is 29.8 BTU/(hr.sq.ft)\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 12.4 Page No 601"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Determination of the heat transferred to the conveyed parts for the conditions given\n",
+ "\n",
+ "#Given\n",
+ "import math\n",
+ "L1=1\n",
+ "angle=math.pi*45/180.0\n",
+ "L2=L1*math.sin(angle)\n",
+ "L3=L2\n",
+ "T1=303\n",
+ "T2=473\n",
+ "\n",
+ "#Calculation\n",
+ "sigma=5.67e-8 # Stefan-Boltzmann constant\n",
+ "q21_A2=sigma*(T2**4-T1**4)*((L1/L2)+1-(L3/L2))/2.0\n",
+ "q31_A3=sigma*(T2**4-T1**4)*((L1/L2)-1+(L3/L2))/2.0\n",
+ "\n",
+ "#result\n",
+ "print\"The heat transferred from A3 to A1 is \",round(q31_A3,0),\" W/sq.m\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The heat transferred from A3 to A1 is 1669.0 W/sq.m\n"
+ ]
+ }
+ ],
+ "prompt_number": 6
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 12.5 Page No 605"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Determination of the heat exchanged between the two plates\n",
+ "\n",
+ "#Given\n",
+ "# The view factor can be found with the crossed-string method\n",
+ "# from figure 12.13(b)\n",
+ "ac=1\n",
+ "bd=1\n",
+ "ad=(9+1)**0.5\n",
+ "bc=ad\n",
+ "\n",
+ "#calculation\n",
+ "crossed_strings=ad+bc\n",
+ "uncrossed_strings=ac+bd\n",
+ "L1_F12=(1/2.0)*(crossed_strings-uncrossed_strings)\n",
+ "L1=3\n",
+ "F12=L1_F12/L1\n",
+ "sigma=5.67e-8 # Stefan-Boltzmann constant\n",
+ "T1=560\n",
+ "T2=460\n",
+ "q12_A1=sigma*(T1**4-T2**4)*F12\n",
+ "\n",
+ "#Result\n",
+ "print\"The heat transfer rate is \",round(q12_A1,0),\"W/sq m\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The heat transfer rate is 2189.0 W/sq m\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 12.6 Page No 608"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Determination of the heat that must be supplied to each of the isothermal surfaces, and also the temperature of the insulated surface. \n",
+ "\n",
+ "#Given\n",
+ "# we can apply the equations as follows\n",
+ "# q1=sigma*A1*[(T1**4-T2**4)F12+(T1**4-T3**4)F13]..... (1)\n",
+ "# q2=sigma*A2*[(T2**4-T1**4)F21+(T2**4-T3**4)F23]..... (2)\n",
+ "# q3=sigma*A3*[(T3**4-T1**4)F31+(T3**4-T2**4)F32]..... (3)\n",
+ "# given data:\n",
+ "T1=1000.0\n",
+ "T3=500.0\n",
+ "q2=0\n",
+ "F12=1/2.0\n",
+ "F13=1/2.0\n",
+ "F21=1/2.0\n",
+ "F23=1/2.0\n",
+ "F31=1/2.0\n",
+ "F32=1/2.0\n",
+ "\n",
+ "#Calculation\n",
+ "T2=((T1**4+T3**4)/2.0)**(1/4.0) # using equation (2)\n",
+ "sigma=0.1714e-8 # Stefan-Boltzmann constant\n",
+ "q1_A1=sigma*((T1**4-T2**4)*F12+(T1**4-T3**4)*F13) # using equation (1)\n",
+ "q3_A3=sigma*((T3**4-T1**4)*F31+(T3**4-T2**4)*F32) # using equation (3)\n",
+ "\n",
+ "#result\n",
+ "print\"The temperature is \",round(T2,1),\"R\"\n",
+ "print\"The heat flux through area A1 is\",round(q1_A1,0),\"BTU/(hr.sq.ft)\"\n",
+ "print\"The heat flux through area A3 is\",round(q3_A3,0),\"BTU/(hr.sq.ft)\"\n",
+ "print\"In the book there is calculation mistake\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The temperature is 853.7 R\n",
+ "The heat flux through area A1 is 1205.0 BTU/(hr.sq.ft)\n",
+ "The heat flux through area A3 is -1205.0 BTU/(hr.sq.ft)\n",
+ "In the book there is calculation mistake\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 12.7 Page No 613"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Determination of the heat lost by the oven through its top surface. \n",
+ "\n",
+ "#Given\n",
+ "# all energy leaving A1 is intercepted by A2 and vice versa\n",
+ "F12=1\n",
+ "F21=1\n",
+ "F11=0 # the surfaces are flat\n",
+ "F22=0\n",
+ "emissivity1=0.94 # for oxidized steel from appendix table E1\n",
+ "emissivity2=0.94\n",
+ "T1=533\n",
+ "T2=323\n",
+ "sigma=5.67e-8 # Stefan-Boltzmann constant\n",
+ "\n",
+ "#Calculation\n",
+ "q1=(sigma*(T1**4-T2**4))/((1/emissivity1)+(1/emissivity2)-1)\n",
+ "q2=-q1\n",
+ "\n",
+ "#Result\n",
+ "print\"The heat lost through bottom surface is \",round(q1,1),\"W/sq m\"\n",
+ "print\"The heat lost through top surface is \",round(q2,1),\"W/sq m\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The heat lost through bottom surface is 3510.7 W/sq m\n",
+ "The heat lost through top surface is -3510.7 W/sq m\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 12.8 Page No 616"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Determination of the net heat exchanged between the dish and the surroundings by radiation at the instant the dish is removed from the oven. Perform the calculations (a) if the dish and surroundings behave like black bodies, and again (b) if the dish has an emissivity of 0.82 and the surroundings have an emissivity of 0.93.\n",
+ "\n",
+ "#Given\n",
+ "D=1.0 # diameter in ft\n",
+ "L=6/12.0 # length in ft\n",
+ "\n",
+ "#Calculation\n",
+ "A=2*math.pi*D**2/4+math.pi*D*L\n",
+ "F12=1 # the view factor between the dish and the surroundings is unity\n",
+ "T1=810\n",
+ "T2=530\n",
+ "sigma=0.1714e-8 # Stefan-Boltzmann constant\n",
+ "q1=sigma*A*(T1**4-T2**4)*F12\n",
+ "\n",
+ "# For gray-surface behavior, we can apply the following Equation\n",
+ "# q1/(A1e1)-[F11*(q1/A1)*(1-e1)/e1+F12*(q2/A2)*(1-e2)/e2]=sigma*T1**4-(F11*sigma*T1**4+F12*sigma*T2**4)... equation (1)\n",
+ "F11=0\n",
+ "e1=0.82\n",
+ "e2=0.93\n",
+ "# putting q2/A2=0 in equation (1) as A2 tends to infinity\n",
+ "q1_=A*e1*(sigma*T1**4-F12*sigma*T2**4)\n",
+ "\n",
+ "#Result\n",
+ "print\"(a)The heat exchanged between the dish and the surroundings is\",round(q1,0),\"BTU/hr\"\n",
+ "print\"(b)The heat exchanged between the dish and the surroundings for the second case is \",round(q1_,0),\"BTU/hr\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(a)The heat exchanged between the dish and the surroundings is 1893.0 BTU/hr\n",
+ "(b)The heat exchanged between the dish and the surroundings for the second case is 1552.0 BTU/hr\n"
+ ]
+ }
+ ],
+ "prompt_number": 25
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Engineering_Heat_Transfer/CHAPTER2.ipynb b/Engineering_Heat_Transfer/CHAPTER2.ipynb new file mode 100644 index 00000000..556700c2 --- /dev/null +++ b/Engineering_Heat_Transfer/CHAPTER2.ipynb @@ -0,0 +1,713 @@ +{
+ "metadata": {
+ "name": "CHAPTER2"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "chapter 2 :Steady state Conduction in one dimension"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 2.1 Page No.42"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#determination of the heat flow through a composite wall\n",
+ "\n",
+ "#Given\n",
+ "T3=-10.00\t\t# temperature of inside wall in degree Fahrenheit\n",
+ "T0=70.0 \t \t# temperature of outside wall in degree Fahrenheit\n",
+ "dT=T0-T3 # overall temperature difference\n",
+ "# values of thermal conductivity in BTU/(hr.ft.degree Rankine) from appendix table B3\n",
+ "k1=0.38 # brick masonry\n",
+ "k2=0.02 # glass fibre\n",
+ "k3=0.063 # plywood\n",
+ "dx1=4/12.0 # thickness of brick layer in ft\n",
+ "dx2=3.5/12.0 # thickness of glass fibre layer in ft\n",
+ "dx3=0.5/12.0 # thickness of plywood layer in ft\n",
+ "A=1.0 # cross sectional area taken as 1 ft**2\n",
+ "\n",
+ "#Calculation\n",
+ "R1=dx1/(k1*A) # resistance of brick layer in (hr.degree Rankine)/BTU\n",
+ "R2=dx2/(k2*A) # resistance of glass fibre layer in (hr.degree Rankine)/BTU\n",
+ "R3=dx3/(k3*A) # resistance of plywood layer in (hr.degree Rankine)/BTU\n",
+ "qx=(T0-T3)/(R1+R2+R3) \n",
+ "\n",
+ "#Result\n",
+ "print\"Resistance of brick layer is \",round(R1,3),\"(hr.degree Rankine)/BTU\"\n",
+ "print\"Resistance of glass fibre layer is \",round(R2,1),\"(hr.degree Rankine)/BTU\"\n",
+ "print\"Resistance of plywood layer is \",round(R3,3),\"(hr.degree Rankine)/BTU\"\n",
+ "print\"Heat transfer through the composite wall is \",round(qx,2),\"(hr.degree Rankine)/BTU\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Resistance of brick layer is 0.877 (hr.degree Rankine)/BTU\n",
+ "Resistance of glass fibre layer is 14.6 (hr.degree Rankine)/BTU\n",
+ "Resistance of plywood layer is 0.661 (hr.degree Rankine)/BTU\n",
+ "Heat transfer through the composite wall is 4.96 (hr.degree Rankine)/BTU\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 2.2 Page No.45"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# determination of heat transfer through composite wall for materials in parallel\n",
+ "\n",
+ "#Given\n",
+ "# values of thermal conductivities in W/(m.K) from appendix table B3\n",
+ "k1=0.45 # thermal conductivity of brick\n",
+ "k2a=0.15 # thermal conductivity of pine\n",
+ "k3=0.814 # thermal conductivity of plaster board\n",
+ "k2b=0.025 # thermal conductivity of air from appendix table D1\n",
+ "# Areas needed fpor evaluating heat transfer in sq.m\n",
+ "A1=0.41*3 # cross sectional area of brick layer \n",
+ "A2a=0.038*3 # cross sectional area of wall stud\n",
+ "A2b=(41-3.8)*0.01*3 # cross sectional area of air layer\n",
+ "A3=0.41*3 # cross sectional area of plastic layer \n",
+ "dx1=0.1 # thickness of brick layer in m\n",
+ "dx2=0.089 # thickness of wall stud and air layer in m\n",
+ "dx3=0.013 # thickness of plastic layer in m\n",
+ "\n",
+ "#Calculation\n",
+ "R1=dx1/(k1*A1) # Resistance of brick layer in K/W\n",
+ "R2=dx2/(k2a*A2a+k2b*A2b) # Resistance of wall stud and air layer in K/W\n",
+ "R3=dx3/(k3*A3) # Resistance of plastic layer in K/W\n",
+ "T1=25 # temperature of inside wall in degree celsius\n",
+ "T0=0 # temperature of outside wall in degree celsius\n",
+ "qx=(T1-T0)/(R1+R2+R3) # heat transfer through the composite wall in W\n",
+ "\n",
+ "#result\n",
+ "print\"Resistance of brick layer is \",round(R1,3),\"k/W\"\n",
+ "print\"Resistance of wall stud and air layer is \",round(R2,2),\"k/W\"\n",
+ "print\"Resistance of plastic layer is \",round(R3,3),\"k/W\"\n",
+ "print\"Heat transfer through the composite wall is\",round(qx,1),\"W\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Resistance of brick layer is 0.181 k/W\n",
+ "Resistance of wall stud and air layer is 1.98 k/W\n",
+ "Resistance of plastic layer is 0.013 k/W\n",
+ "Heat transfer through the composite wall is 11.5 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 2.3 Page No. 50"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# determination of heat transfer rate and overall heat transfer coefficient\n",
+ "\n",
+ "#Given\n",
+ "k1=24.8 # thermal conductivity of 1C steel in BTU/(hr.ft.degree Rankine)from appendix table B2 \n",
+ "k2=0.02 # thermal conductivity of styrofoam steel in BTU/(hr.ft.degree Rankine)\n",
+ "k3=0.09 # thermal conductivity of fibreglass in BTU/(hr.ft.degree Rankine)\n",
+ "hc1=0.79 # convection coefficient between the air and the vertical steel wall in BTU/(hr.ft**2.degree Rankine)\n",
+ "hc2=150.0 # the convection coefficient between the ice water and the fiberglass\n",
+ "A=1.0 # calculation based on per square foot\n",
+ "dx1=0.04/12.0 # thickness of steel in ft\n",
+ "dx2=0.75/12.0 # thickness of styrofoam in ft\n",
+ "dx3=0.25/12.0 # thickness of fiberglass in ft\n",
+ "\n",
+ "#Calculation \n",
+ "\n",
+ "# Resistances in (degree Fahrenheit.hr)/BTU\n",
+ "Rc1=1/(hc1*A) # Resistance from air to sheet metal\n",
+ "Rk1=dx1/(k1*A) # Resistance of steel layer\n",
+ "Rk2=dx2/(k2*A) # Resistance of styrofoam layer\n",
+ "Rk3=dx3/(k3*A) # Resistance of fiberglass layer\n",
+ "Rc2=1/(hc2*A) # Resistance from ice water to fiberglass\n",
+ "U=1/(Rc1+Rk1+Rk2+Rk3+Rc2) # overall heat transfer coefficient \n",
+ "T_inf1=90 # temperature of air in degree F\n",
+ "T_inf2=32 # temperature of mixture of ice and water in degree F\n",
+ "q=U*A*(T_inf1-T_inf2)\n",
+ "\n",
+ "#result\n",
+ "print\"Resistance from air to sheet metal: \",round(Rc1,3),\"degree F.hr/BTU\"\n",
+ "print\"Resistance of steel layer is \",round(Rk1,4),\"degree F.hr/BTU\"\n",
+ "print\"Resistance of styrofoam layer is \",round(Rk2,3),\"degree F.hr/BTU\"\n",
+ "print\"Resistance of fiberglass layer is \",round(Rk3,3),\"degree F.hr/BTU\"\n",
+ "print\"Resistance from ice water to fiberglass is \",round(Rc2,4),\"degree F.hr/BTU\"\n",
+ "print\"The overall heat transfer coefficient is \",round(U,3),\"BTU/hr ft**2\"\n",
+ "print\"The heat transfer rate is %.1f BTU/hr\",round(q,2),\"BTU/hr\"\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Resistance from air to sheet metal: 1.266 degree F.hr/BTU\n",
+ "Resistance of steel layer is 0.0001 degree F.hr/BTU\n",
+ "Resistance of styrofoam layer is 3.125 degree F.hr/BTU\n",
+ "Resistance of fiberglass layer is 0.231 degree F.hr/BTU\n",
+ "Resistance from ice water to fiberglass is 0.0067 degree F.hr/BTU\n",
+ "The overall heat transfer coefficient is 0.216 BTU/hr ft**2\n",
+ "The heat transfer rate is %.1f BTU/hr 12.53 BTU/hr\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 2.4 Page No 55."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# determination of the heat transfer through the pipe wall per unit length of pipe.\n",
+ "\n",
+ "#given\n",
+ "k=14.4 # thermal conductivity of 304 stainless steel in W/(m.K) from appendix table B2\n",
+ "# dimensions of steel pipes in cm from appendix table F1\n",
+ "D2=32.39 #Diameter (cm)\n",
+ "D1=29.53\n",
+ "T1=40 #Temprature\n",
+ "T2=38\n",
+ "\n",
+ "#Calculation\n",
+ "import math\n",
+ "Qr_per_length=(2*3.14*k)*(T1-T2)/math.log(D2/D1)#format(6)\n",
+ "\n",
+ "#Result\n",
+ "print\"The heat transfer through the pipe wall per unit length of pipe is \",round(Qr_per_length/1000,2),\"kw/m\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The heat transfer through the pipe wall per unit length of pipe is 1.96 kw/m\n"
+ ]
+ }
+ ],
+ "prompt_number": 23
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 2.5 Page NO. 58"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# determination of the heat gain per unit length\n",
+ "\n",
+ "#Given\n",
+ "k1=231 # thermal conductivity of copper in BTU/(hr.ft.degree Rankine)from appendix table B1 \n",
+ "k2=0.02 # thermal conductivity of insuLtion in BTU/(hr.ft.degree Rankine)\n",
+ "# Specifications of 1 standard type M copper tubing from appendix table F2 are as follows\n",
+ "D2=1.125/12 # outer diameter in ft\n",
+ "D1=0.08792 # inner diameter in ft\n",
+ "R2=D2/2 # outer radius\n",
+ "R1=D1/2 # inner radius\n",
+ "t=0.5/12 # wall thickness of insulation in ft\n",
+ "R3=R2+t\n",
+ "LRk1=(log(R2/R1))/(2*3.14*k1) # product of length and copper layer resistance\n",
+ "LRk2=(log(R3/R2))/(2*3.14*k2) # product of length and insulation layer resistance\n",
+ "T1=40 # temperature of inside wall of tubing in degree fahrenheit\n",
+ "T3=70 # temperature of surface temperature of insulation degree fahrenheit\n",
+ "q_per_L=(T1-T3)/(LRk1+LRk2) # heat transferred per unit length in BTU/(hr.ft)\n",
+ "\n",
+ "#Result\n",
+ "print\"The heat transferred per unit length is \",round(q_per_L,2),\" BTU/(hr.ft\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The heat transferred per unit length is -5.92 BTU/(hr.ft\n"
+ ]
+ }
+ ],
+ "prompt_number": 26
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 2.6 Page No 63"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Determination of the overall heat transfer coefficient\n",
+ "\n",
+ "#Given data\n",
+ "k12=24.8 # thermal conductivity of 1C steel in BTU/(hr.ft.degree Rankine)from appendix table B2 \n",
+ "k23=.023 # thermal conductivity of glass wool insulation in BTU/(hr.ft.degree Rankine)from appendix table B3 \n",
+ "# Specifications of 6 nominal, schedule 40 pipe (no schedule was specified, so the standard is assumed) from appendix table F1 are as follows\n",
+ "D2=6.625/12.0 # outer diameter in ft\n",
+ "D1=0.5054 # inner diameter in ft\n",
+ "t=2/12.0 # wall thickness of insulation in ft\n",
+ "D3=D2+t\n",
+ "hc1=12 # convection coefficient between the air and the pipe wall in BTU/(hr. sq.ft.degree Rankine).\n",
+ "hc2=1.5 # convection coefficient between the glass wool and the ambient air in BTU/(hr. sq.ft.degree Rankine).\n",
+ "\n",
+ "#calculation\n",
+ "U=1/((1/hc1)+(D1*log(D2/D1)/k12)+(D1*log(D3/D2)/k23)+(D1/(hc2*D3)))\n",
+ "\n",
+ "#Result\n",
+ "print\"Overall heat transfer coefficient is \",round(U,4),\" BTU/(hr.sq.ft. Fahrenheit)\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Overall heat transfer coefficient is 0.1596 BTU/(hr.sq.ft. Fahrenheit)\n"
+ ]
+ }
+ ],
+ "prompt_number": 31
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 2.7 Page NO.72"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Determination of the thermal contact resistance\n",
+ "\n",
+ "#Given\n",
+ "k=14.4 # thermal conductivity of 304 stainless steel in W/(m.K)from appendix table B2 \n",
+ "T1=543.0 # temperature in K at point 1\n",
+ "T2=460.0 # temperature in K at point 2\n",
+ "dT=T1-T2 # temperature difference between point 1 and 2\n",
+ "dz12=0.035 # distance between thermocouple 1 and 2 in cm\n",
+ "\n",
+ "dz56=4.45 # distance between thermocouple 5 and 6 in cm\n",
+ "dz6i=3.81 # distance between thermocouple 6 and interface in cm\n",
+ "dz5i=dz56+dz6i # distance between thermocouple 5 and interface in cm\n",
+ "T5=374 # temperature in K at point 5\n",
+ "T6=366 # temperature in K at point 6\n",
+ "dzi7=2.45 # distance between thermocouple 7 and interface in cm\n",
+ "dz78=4.45 # distance between thermocouple 7 and 8 in cm\n",
+ "dzi8=dzi7+dz78 # distance between thermocouple 8 and interface in cm\n",
+ "T7=349 # temperature in K at point 7\n",
+ "T8=337 # temperature in K at point 8\n",
+ "\n",
+ "#Calculation\n",
+ "qz_per_A=k*dT/dz12 # heat flow calculated in W/m**2 calculated using Fourier's law\n",
+ "T_ial=T5-(dz5i*(T5-T6)/dz56) # temperature of aluminium interface in K\n",
+ "T_img=dzi8*(T7-T8)/dz78+T8 # temperature of magnesium interface in K\n",
+ "T_img_=355.8 #Approx value in the book\n",
+ "Rtc=(T_ial-T_img_)/(qz_per_A)\n",
+ "\n",
+ "#Result\n",
+ "\n",
+ "print\"The required thermal contact resistance is\",round(Rtc,7),\"K sq.m/W\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The required thermal contact resistance is 9.81e-05 K sq.m/W\n"
+ ]
+ }
+ ],
+ "prompt_number": 30
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 2.8 Page No. 85"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "%pylab inline"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# determination of temperature profile, heat transferred, efficiency, effectiveness.\n",
+ "\n",
+ "#Given\n",
+ "import math\n",
+ "k=24.8 # thermal conductivity of 1C steel in BTU/(hr.ft.degree Rankine)from appendix table B2\n",
+ "D=(5.0/16.0)/12.0 # diameter of the rod in ft\n",
+ "P=(math.pi*D) # Circumference of the rod in ft\n",
+ "#print\"The perimeter is %.4f ft\",P)\n",
+ "A=(math.pi/4)*D**2 # Cross sectional area of the rod in sq.ft\n",
+ "#print\"The Cross sectional area is %.6f sq.ft\",A)\n",
+ "hc=1.0 # assuming the convective heat transfer coefficient as 1 BTU/(hr. sq.ft. degree Rankine)\n",
+ "\n",
+ "#Calculation\n",
+ "m=math.sqrt(hc*P/(k*A))\n",
+ "#print\"The value of parameter m is: /ft\",m)\n",
+ "L=(9/2.0)/12.0 # length of rod in ft\n",
+ "# using the equation (T-T_inf)/(T_w-T_inf)=(cosh[m(L-z)])/(cosh(mL)) for temperature profile\n",
+ "T_inf=70.0\n",
+ "T_w=200.0\n",
+ "dT=T_w-T_inf\n",
+ "const=dT/math.cosh(m*L)\n",
+ "\n",
+ "#(b) the heat transferred can be calculated using the equation qz=k*A*m*(T_w-T_inf)*tanh(m*L)\n",
+ "qz=k*A*m*dT*tanh(m*L)\n",
+ "\n",
+ "#(c)\n",
+ "mL=m*L\n",
+ "efficiency=0.78 # from fig. 2.30\n",
+ "\n",
+ "#(d)\n",
+ "effectiveness=math.sqrt(k*P/(hc*A))*tanh(mL)\n",
+ "\n",
+ "\n",
+ "print\"(b)The heat transferred is \",round(qz,2),\"BTU/hr\"\n",
+ "print\"(c)The efficiency found from the graph in figure 2.30 is\",efficiency\n",
+ "print\"(d)The effectiveness is found to be\",round(effectiveness,1)\n",
+ "\n",
+ "\n",
+ "#Plot\n",
+ "import matplotlib.pyplot as plt\n",
+ "fig = plt.figure()\n",
+ "ax = fig.add_subplot(111)\n",
+ "\n",
+ "mL1=[0,1,1.2,5]\n",
+ "n1=[0,0.2,0.25,0.25]\n",
+ "\n",
+ "mL2=[0,1,1.8,5]\n",
+ "n2=[0,0.35,0.5,0.5]\n",
+ "\n",
+ "mL3=[0,1,2,5]\n",
+ "n3=[0,0.75,1,1]\n",
+ "mL4=[0,1,2,5]\n",
+ "n4=[0,1.5,2,2]\n",
+ "\n",
+ "xlabel(\"mL\") \n",
+ "ylabel(\"n \") \n",
+ "plt.xlim((0,6))\n",
+ "plt.ylim((0,2.5))\n",
+ "\n",
+ "ax.annotate('(0.25)', xy=(5,0.25))\n",
+ "ax.annotate('(0.5)', xy=(5,0.5))\n",
+ "ax.annotate('(1)', xy=(5,1))\n",
+ "ax.annotate('(2)', xy=(5,2))\n",
+ "a1=plot(mL1,n1)\n",
+ "a2=plot(mL2,n2)\n",
+ "a3=plot(mL3,n3)\n",
+ "a4=plot(mL4,n4)\n",
+ "\n",
+ "import matplotlib.pyplot as plt\n",
+ "fig = plt.figure()\n",
+ "ax = fig.add_subplot(111)\n",
+ "\n",
+ "z1=[0,3,4.8]\n",
+ "T1=[200,165,158]\n",
+ "z2=[0,4.8]\n",
+ "T2=[140,140]\n",
+ "z3=[0,4.8]\n",
+ "T3=[130,130]\n",
+ "z4=[4.8,4.8]\n",
+ "T4=[140,130]\n",
+ "\n",
+ "xlabel(\"z (m)\") \n",
+ "ylabel(\"T (K)\") \n",
+ "plt.xlim((0,5.5))\n",
+ "plt.ylim((120,200))\n",
+ "\n",
+ "ax.annotate('(5/16 in)', xy=(4.85,135))\n",
+ "a1=plot(z1,T1)\n",
+ "a2=plot(z2,T2)\n",
+ "a3=plot(z3,T3)\n",
+ "a4=plot(z4,T4)\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(b)The heat transferred is 3.13 BTU/hr\n",
+ "(c)The efficiency found from the graph in figure 2.30 is 0.78\n",
+ "(d)The effectiveness is found to be 45.2\n"
+ ]
+ },
+ {
+ "output_type": "display_data",
+ "png": 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+ },
+ {
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FdOjQgRtuuIELLriAG2+8kSNHjtTYzmKxeI5ILBYLZWVlfPbZZzz99NM1mtFW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\n"
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 2.9 Page No. 90"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# determination of heat transferred\n",
+ "\n",
+ "#Given\n",
+ "k=136.0 # thermal conductivity of aluminium in BTU/(hr.ft.degree Rankine)from appendix table B1\n",
+ "L=9/(8*12.0) #length in ft\n",
+ "W=9/(4*12.0) #width in ft\n",
+ "delta=0.002604 #ft\n",
+ "hc=0.8 # the convective heat transfer coefficient estimated as 1 BTU/(hr.ft**2. degree Rankine)\n",
+ "T_w=1000.0 # the root temperature in degree fahrenheit\n",
+ "T_inf=90.0 # the ambient temperature in degree fahrenheit\n",
+ "\n",
+ "#Calculation\n",
+ "import math\n",
+ "m=math.sqrt(hc/(k*delta))\n",
+ "P=2*W\n",
+ "A=2*delta*W\n",
+ "qz1=math.sqrt(hc*P*k*A)*(T_w-T_inf)*(sinh(m*L)+(hc/(m*k)*cosh(m*L)))/(cosh(m*L)+(hc/(m*k)*sinh(m*L)))\n",
+ "qz2=math.sqrt(k*A*hc*P)*(T_w-T_inf)*math.tanh(m*L)\n",
+ "Lc=L+delta\n",
+ "qz3=k*A*m*(T_w-T_inf)*math.tanh(m*L*(1+delta/Lc))\n",
+ "\n",
+ "#Result\n",
+ "print\"(a)The heat transferred is \",round(qz1,2),\"BTU/hr\"\n",
+ "print\"(b)The heat transferred is \",round(qz2,2),\"BTU/hr In the book the answer is incorrect\"\n",
+ "print\"(c)The heat transferred is \",round(qz3,2),\" BTU/hr\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(a)The heat transferred is 26.12 BTU/hr\n",
+ "(b)The heat transferred is 25.43 BTU/hr In the book the answer is incorrect\n",
+ "(c)The heat transferred is 26.1 BTU/hr\n"
+ ]
+ }
+ ],
+ "prompt_number": 75
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 2.10 Page No 94"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# determination of optimum fin length and heat transferred by fin\n",
+ "\n",
+ "#Given\n",
+ "k=8.32 # thermal conductivity BTU/(hr.ft.degree Rankine)\n",
+ "hc=400.0 # the convective heat transfer coefficient given in BTU/(hr.ft**2. degree Rankine)\n",
+ "\n",
+ "#Calculation\n",
+ "import math\n",
+ "delta_opt=0.55/(12*2)\n",
+ "# determination of dimension of one fin using the equation delta_opt=0.583*hc*Lc**2/k\n",
+ "Lc=math.sqrt(delta_opt*k/(0.583*hc))\n",
+ "\n",
+ "A=Lc*delta_opt\n",
+ "# determination of parameter for finding out efficiency from graph\n",
+ "parameter=Lc**1.5*math.sqrt(hc/(k*A))\n",
+ "efficiency=0.6\n",
+ "W=1/(2.0*12.0) # width in ft\n",
+ "T_w=190.0 # wall temperature in degree fahrenheit\n",
+ "T_inf=58.0 # ambient temperature in degree fahrenheit\n",
+ "L=1.0 # length in ft\n",
+ "delta=W/2.0 \n",
+ "q_ac=efficiency*hc*2*W*math.sqrt(L**2+delta**2)*(T_w-T_inf)\n",
+ "\n",
+ "#Result\n",
+ "print\"(a)The optimum length is \",round(Lc*12,2),\"inch\"\n",
+ "print\"(b)The actual heat transferred is \",round(q_ac,2),\"BTU/hr. NOTE: In the book answer is incorrect\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(a)The optimum length is 0.34 inch\n",
+ "(b)The actual heat transferred is 2640.57 BTU/hr. NOTE: In the book answer is incorrect\n"
+ ]
+ }
+ ],
+ "prompt_number": 35
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 2.11 Page No 95"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# determination of heat transferred and fin effectiveness\n",
+ "\n",
+ "#Given\n",
+ "#parameters of the problem are\n",
+ "N=9 # number of fins\n",
+ "delta=0.003/2.0 \n",
+ "L=0.025\n",
+ "Lc=L+delta\n",
+ "R=0.219/2\n",
+ "R2c=R+delta\n",
+ "R1=R-L\n",
+ "T_w=260 # root wall temperature in degree celsius\n",
+ "T_inf=27 # ambient temperature in degree celsius\n",
+ "hc=15 \n",
+ "k=52 # thermal conductivity of cast iron in W/(m.K)from appendix table B2\n",
+ "\n",
+ "#calculation\n",
+ "import math\n",
+ "#(a)\n",
+ "Ap=2*delta*Lc\n",
+ "As=2*math.pi*(R2c**2-R1**2)\n",
+ "radius_ratio=R2c/R1 # for finding efficiency from figure 2.38\n",
+ "variable=Lc**1.5*math.sqrt(hc/(k*Ap))\n",
+ "efficiency=0.93 # efficiency from figure 2.38\n",
+ "qf=N*efficiency*As*hc*(T_w-T_inf)\n",
+ "Sp=0.0127 # fin spacing\n",
+ "Asw=2*math.pi*R1*Sp*N # exposed surface area\n",
+ "qw=hc*Asw*(T_w-T_inf)\n",
+ "q=qf+qw\n",
+ "\n",
+ "#(b)H=N*(Sp+2*delta) # height of cylinder\n",
+ "H=N*(Sp+2*delta)\n",
+ "Aso=2*math.pi*R1*H # surface area without fins\n",
+ "qo=hc*Aso*(T_w-T_inf)\n",
+ "\n",
+ "#(c)\n",
+ "effectiveness=q/qo # effectiveness defined as ratio of heat transferred with fins to heat transferred without fins\n",
+ "\n",
+ "#Result\n",
+ "print\"(a)The total heat transferred from the cylinder is \",round(q,0),\"W\"\n",
+ "print\"(b)The Heat transferred without fins is W\",round(qo,0),\"W\"\n",
+ "print\"(c)The fin effectiveness is \",round(effectiveness,2)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(a)The total heat transferred from the cylinder is 1164.0 W\n",
+ "(b)The Heat transferred without fins is W 262.0 W\n",
+ "(c)The fin effectiveness is 4.44\n"
+ ]
+ }
+ ],
+ "prompt_number": 9
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Engineering_Heat_Transfer/CHAPTER4.ipynb b/Engineering_Heat_Transfer/CHAPTER4.ipynb new file mode 100644 index 00000000..918045d0 --- /dev/null +++ b/Engineering_Heat_Transfer/CHAPTER4.ipynb @@ -0,0 +1,607 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 4: Unsteady State heat Conduction "
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 4.1 Page No.190"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# determination of response time\n",
+ "\n",
+ "#Given\n",
+ "k=12.0 # thermal conductivity in BTU/(hr.ft.degree Rankine) \n",
+ "c=0.1 # specific heat in BTU/(lbm.degree Rankine) \n",
+ "D=0.025/12.0 # diameter in ft\n",
+ "density=525.0 # density in lbm/cu.ft\n",
+ "hc=80 # convective coefficient in BTU/(hr. sq.ft. degree Rankine)\n",
+ "T_i=65.0 # intial temperature in degree fahrenheit\n",
+ "T_inf=140.0 # fluid temperature in degree fahrenheit\n",
+ "As=3.14*D**2 # surface area in sq.ft\n",
+ "Vs=3.14*D**(0.5) # volume in cu.ft\n",
+ "\n",
+ "#calculation\n",
+ "#As/Vs=6/D\n",
+ "import math\n",
+ "reciprocal_timeconstant=(hc*6)/(density*D*c)\n",
+ "# selecting T=139 F as T=140 gives an infinite time through the equation (T-T_inf)/(T_i-T_inf)=exp(-hc*As/density*Vs*c)t\n",
+ "T=139\n",
+ "t=math.log((T-T_inf)/(T_i-T_inf))/(-reciprocal_timeconstant)\n",
+ "\n",
+ "#result\n",
+ "print\"The response time of the junction is %.1f s\",round(t*3600,2),\"s\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The response time of the junction is %.1f s 3.54 s\n"
+ ]
+ }
+ ],
+ "prompt_number": 10
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 4.2 Page No. 193"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Determination of temperature of metal and cumulative heat rate\n",
+ "# properties of aluminium from appendix table B1\n",
+ "\n",
+ "#Given\n",
+ "k=236.0 # thermal conductivity in W/(m.K)\n",
+ "Cp=896.0 # specific heat in J/(kg.K)\n",
+ "sp_gr=2.702 # specific gravity\n",
+ "density=2702.0 # density in kg/cu.m\n",
+ "D=0.05 # Diameter in m\n",
+ "L=0.60 # length in m\n",
+ "hc=550.0 # unit surface conductance between the metal and the bath in W/(K.sq.m)\n",
+ "\n",
+ "#calculation\n",
+ "import math\n",
+ "Vs=(math.pi*D**2*L)/4.0 # Volume in cu.m\n",
+ "As=(2*math.pi*D**2/4.0)+(math.pi*D*L) # surface area in sq.m\n",
+ "import math\n",
+ "Bi=(hc*Vs)/(k*As) # Biot Number\n",
+ "# Biot number is less than 1 hence lump capacitance equations apply\n",
+ "T_i=50.0 # initial temperature in degree celsius\n",
+ "T_inf=2.0 # temperature of ice water bath in degree celsius\n",
+ "t=60.0 # time=1 minute=60 s\n",
+ "As_=0.102 #approx value taken in book for calculating T and Q\n",
+ "T=T_inf+(T_i-T_inf)*math.exp(-(hc*As_*t)/(density*Vs*Cp))\n",
+ "Q=density*Vs*Cp*(T_inf-T_i)*(1-math.exp(-(hc*As_*t)/(density*Vs*Cp)))\n",
+ "\n",
+ "#result\n",
+ "print\"(a)The temperature of aluminium is\",round(T,1),\"C\"\n",
+ "print\"(b)The cumulative heat transferred is \",round(-Q/1000,1),\"KJ\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(a)The temperature of aluminium is 16.7 C\n",
+ "(b)The cumulative heat transferred is 94.8 KJ\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 4.3 Page No. 200"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Determine the time required and temprature profile\n",
+ "\n",
+ "#Given\n",
+ "hc=30\n",
+ "L=0.24\n",
+ "k=1.25 #Conductivity\n",
+ "c=890\n",
+ "rou=550\n",
+ "Fo=0.4 #Fourier no\n",
+ "\n",
+ "#Calculation\n",
+ "Bi=hc*L/k\n",
+ "alpha=k/(rou*c)\n",
+ "Tc=150\n",
+ "T_inf=600\n",
+ "T_i=50\n",
+ "t=(L**2*Fo)/(alpha)\n",
+ "TC1=0.82 #Centreline temprature\n",
+ "#from table at x/l=0.4\n",
+ "T=0.71*(T_i-T_inf)*TC1\n",
+ "x=0.4*L\n",
+ "Ti=149\n",
+ "To=492\n",
+ "print\"Time required to reach temprature 150 is \",round(t/3600,2),\"hr\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "Time required to reach temprature 150 is 2.51 hr\n"
+ ]
+ }
+ ],
+ "prompt_number": 33
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 4.4 Page No. 204"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Calculate the time required\n",
+ "hc=6 #Surface Conductance\n",
+ "D=0.105 #Orange Diameter\n",
+ "k=0.431 #Thermal conductivity \n",
+ "c=2000 #Specific heat of orange\n",
+ "rou=998 #Density\n",
+ "Fo=1.05 #Fourier no.\n",
+ "\n",
+ "#Calculation\n",
+ "import math\n",
+ "Vs=math.pi*D**3/6\n",
+ "As=math.pi*D**2\n",
+ "# calculating Biot Number for lumped capacitance approach\n",
+ "Bi=hc*Vs/(k*As)\n",
+ "Bi_=hc*(D/2)/(k)\n",
+ "alpha=k/(rou*c)\n",
+ "Tc=20\n",
+ "T_inf=23\n",
+ "T_i=4\n",
+ "t=(Fo*(D/2.0)**2)/alpha\n",
+ "a=Bi_**2*Fo\n",
+ "Q=0.7*rou*c*(math.pi/6.0*(Fo**3))*(T_i-T_inf)\n",
+ "\n",
+ "#Result\n",
+ "print\"The time required is \",round(t/3600,2),\"hr\"\n",
+ "print\"The heat transfered is\",round(Q/1000,2),\"kj\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The time required is 3.72 hr\n",
+ "The heat transfered is -16090.84 kj\n"
+ ]
+ }
+ ],
+ "prompt_number": 16
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 4.5 Page No.208"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Estimate the depth of freeze line\n",
+ " \n",
+ "D=0.105 #diameter\n",
+ "k=0.3 #Thermal conductivity \n",
+ "c=0.41 #Specific heat \n",
+ "sp_gr=2.1 ##Specific gravity\n",
+ "rou_water=62.4 #Density\n",
+ "alpha=k/(sp_gr*rou_water*c)\n",
+ "t=3*30*24\n",
+ "\n",
+ "#Calculation\n",
+ "# Bi_math.sqrt(Fo) is infinite\n",
+ "T_inf=10\n",
+ "Ts=10\n",
+ "T=32\n",
+ "T_i=70\n",
+ "dimensionless_temp=(T-T_i)/(T_inf-T_i)\n",
+ "variable_fig4_12=0.38 #The value of x/(2*(alpha*t)**0.5) from figure 4.12\n",
+ "x=2*math.sqrt(alpha*t)*variable_fig4_12\n",
+ "\n",
+ "#result\n",
+ "print\"The depth of the freeze line in soil is ft\",round(x,2),\"ft\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The depth of the freeze line in soil is ft 2.64 ft\n"
+ ]
+ }
+ ],
+ "prompt_number": 18
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 4.6 Page No.211"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# properties of aluminium from appendix table B1\n",
+ "\n",
+ "#Given\n",
+ "k_al=236\n",
+ "p_al=2.7*1000\n",
+ "c_al=896\n",
+ "# properties of oak from appendix table B3\n",
+ "k_oak=0.19\n",
+ "p_oak=0.705*1000\n",
+ "c_oak=2390\n",
+ "\n",
+ "#Calculation\n",
+ "import math\n",
+ "math.sqrt_kpc_al=math.sqrt(k_al*p_al*c_al)\n",
+ "kpc_R=4\n",
+ "T_Li=20\n",
+ "T_Ri=37.3\n",
+ "T_al=(T_Li*(math.sqrt_kpc_al)+T_Ri*math.sqrt(kpc_R))/(math.sqrt_kpc_al+math.sqrt(kpc_R))\n",
+ "math.sqrt_kpc_oak=math.sqrt(k_oak*p_oak*c_oak)\n",
+ "T_oak=(T_Li*(math.sqrt_kpc_oak)+T_Ri*math.sqrt(kpc_R))/(math.sqrt_kpc_oak+math.sqrt(kpc_R))\n",
+ "\n",
+ "#Result\n",
+ "print\"The temperature of aluminium is felt as \",round(T_al,2),\"C\"\n",
+ "print\"The temperature of oak is felt as %.1f degree celsius\",round(T_oak,1),\"C\"\n",
+ "print\"So oak will feel warmer to the touch than will the aluminium\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The temperature of aluminium is felt as 20.0 C\n",
+ "The temperature of oak is felt as %.1f degree celsius 20.1 C\n",
+ "So oak will feel warmer to the touch than will the aluminium\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 4.7 Page No.215"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# properties of water at 68 degree fahrenheit from appendix table C11\n",
+ "\n",
+ "#Given\n",
+ "# The given properties are\n",
+ "rou=62.46\n",
+ "cp=0.9988\n",
+ "k=0.345\n",
+ "alpha=k/(rou*cp)\n",
+ "D=2.5/12.0\n",
+ "L=4.75/12.0\n",
+ "\n",
+ "#Calculation\n",
+ "Vs=math.pi*D**2*L/4\n",
+ "As=(math.pi*D*L)+(math.pi*D**2)/2\n",
+ "Lc=Vs/As\n",
+ "hc=1.7\n",
+ "Bi=hc*Lc/k\n",
+ "t=4\n",
+ "\n",
+ "# for the cylinder solution\n",
+ "Fo_cylinder=alpha*t/(D/2)**2\n",
+ "Bi_cylinder=hc*(D/2)/k\n",
+ "reciprocal_Bi_cylinder=1/Bi_cylinder\n",
+ "dim_T_cylinder=0.175 #The value of dimensionless temperature of cylinder from figure 4.7a at corresponding values of Fo and 1/Bi\n",
+ "\n",
+ "# for the infinite plate solution\n",
+ "Fo_plate=alpha*t/(L/2)**2\n",
+ "Bi_plate=hc*L/(2*k)\n",
+ "reciprocal_Bi_plate=1/Bi_plate\n",
+ "dim_T_plate=0.55 #The value of dimensionless temperature of infinite plate from figure 4.7a at corresponding values of Fo and 1/Bi\n",
+ "\n",
+ "# For short cylinder problem\n",
+ "dim_T_shortcylinder=dim_T_cylinder*dim_T_plate\n",
+ "T_inf=30\n",
+ "T_i=72\n",
+ "Tc=dim_T_shortcylinder*(T_i-T_inf)+T_inf\n",
+ "dim_Tw_cylinder=0.77 #The dimensionless temperature from figure 4.7b corresponding to the value of 1/Bi and r/R=1\n",
+ "dim_Tw_plate=0.65 #The dimensionless temperature from figure 4.6b corresponding to the value of 1/Bi and x/L=1\n",
+ "dim_Tw_shortcylinder=dim_Tw_cylinder*dim_Tw_plate\n",
+ "Tw=dim_Tw_shortcylinder*(Tc-T_inf)+T_inf\n",
+ "\n",
+ "#Result\n",
+ "print\"The temperature at centre of can is %.1f degree celsius\",round(Tc,0),\"F\"\n",
+ "print\"The bear temperature near the metal of the can is\",round(Tw,0),\"F\"\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The temperature at centre of can is %.1f degree celsius 34.0 F\n",
+ "The bear temperature near the metal of the can is 32.0 F\n"
+ ]
+ }
+ ],
+ "prompt_number": 38
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 4.8 Page No. 219"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Determine the time to reach centre temp. 50 C\n",
+ "\n",
+ "#Given Data\n",
+ "#The given properties are\n",
+ "rou=7817 #Density\n",
+ "c=461 #Specific heat \n",
+ "k=14.4 #Thermal conductivity \n",
+ "alpha=.387e-5\n",
+ "#The dimension are\n",
+ "L1=0.03\n",
+ "L2=0.03\n",
+ "L3=0.04\n",
+ "x=0.04\n",
+ "T_i=95 #Internal temprature \n",
+ "T_inf=17 #Temprature at infinity\n",
+ "\n",
+ "#Calculation\n",
+ "# for infinite plate\n",
+ "L=L1/2\n",
+ "hc=50\n",
+ "reciprocal_Bi_plate=k/(hc*L)\n",
+ "Tinf=0.085 #Temprature distribution for infinite plate\n",
+ "Tsi=0.225 #Temprature distribution for semi infinite plate\n",
+ "#Temprature at a depth of 4 cm\n",
+ "T=(Tinf**2)*(1-Tsi)*(T_i-T_inf)+T_inf\n",
+ "#From the table\n",
+ "t=350\n",
+ "\n",
+ "#Result\n",
+ "print\"At a time 3000s The temprature is \",round(T,1),\"C\"\n",
+ "print\"From the table The time requires to reach tempratue 50C is \",t,\"s\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "At a time 3000s The temprature is 17.4 C\n",
+ "From the table The time requires to reach tempratue 50C is 350 s\n"
+ ]
+ }
+ ],
+ "prompt_number": 48
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 4.9 Page No.226"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "%pylab inline"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Determine the time that will pass before the heat added\n",
+ "\n",
+ "#Given\n",
+ "rou=0.5*1000\n",
+ "cp=837\n",
+ "k=0.128\n",
+ "alpha=0.049e-5\n",
+ "Ti=20 #Initial temprature\n",
+ "# let Fo=0.5 and dx=0.05\n",
+ "dt=0.5*(0.05)**2/alpha\n",
+ "\n",
+ "#Calculation\n",
+ "#Temprature at 1<m<6 and p>0 till T6>20\n",
+ "p=0\n",
+ "T0=200\n",
+ "m=1\n",
+ "T11=(Ti+T0)/2.0\n",
+ "m=2\n",
+ "T21=(Ti+Ti)/2.0\n",
+ "m=3\n",
+ "T31=(Ti+Ti)/2.0\n",
+ "m=4\n",
+ "T41=(Ti+Ti)/2.0\n",
+ "m=5\n",
+ "T51=(Ti+Ti)/2.0\n",
+ "m=6\n",
+ "T61=(Ti+Ti)/2.0\n",
+ "\n",
+ "#For next time interval\n",
+ "p=1\n",
+ "m=1\n",
+ "T12=(Ti+T0)/2.0\n",
+ "m=2\n",
+ "T22=(Ti+T12)/2.0\n",
+ "m=3\n",
+ "T32=(Ti+T21)/2.0\n",
+ "m=4\n",
+ "T42=(Ti+T31)/2.0\n",
+ "m=5\n",
+ "T52=(Ti+T41)/2.0\n",
+ "m=6\n",
+ "T62=(Ti+T51)/2.0\n",
+ "#Repeating it\n",
+ "t=4.97\n",
+ "print\"The time that will pass before the heat added\",t,\"hr\"\n",
+ "\n",
+ "#Plot\n",
+ "import matplotlib.pyplot as plt\n",
+ "fig = plt.figure()\n",
+ "ax = fig.add_subplot(111)\n",
+ "\n",
+ "x1=[0,30]\n",
+ "T1=[20,20]\n",
+ "\n",
+ "xlabel(\"x (cm)\") \n",
+ "ylabel(\"T (C)\") \n",
+ "plt.xlim((0,35))\n",
+ "plt.ylim((0,250))\n",
+ "\n",
+ "a1=plot(x1,T1)\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The time that will pass before the heat added 4.97 hr\n"
+ ]
+ },
+ {
+ "output_type": "display_data",
+ "png": 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+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 4.10 Page No. 231"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# determination of time required to cool to a certain temperature\n",
+ "\n",
+ "#Given\n",
+ "#The properties are\n",
+ "rou=7.817*62.4 #density\n",
+ "c=0.110\n",
+ "k=8.32\n",
+ "alpha=0.417e-4\n",
+ "dx=1/12.0\n",
+ "# taking Fo=1\n",
+ "Fo=1\n",
+ "\n",
+ "#Calculation\n",
+ "dt=Fo*dx**2/alpha\n",
+ "n=8 #Enter the number of time intervals from Saulev plot\n",
+ "time=n*dt\n",
+ "\n",
+ "#result\n",
+ "print\"The required time is hr\",round(time/3600,2),\"hr\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The required time is hr 0.37 hr\n"
+ ]
+ }
+ ],
+ "prompt_number": 42
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Engineering_Heat_Transfer/CHAPTER5.ipynb b/Engineering_Heat_Transfer/CHAPTER5.ipynb new file mode 100644 index 00000000..9ab19382 --- /dev/null +++ b/Engineering_Heat_Transfer/CHAPTER5.ipynb @@ -0,0 +1,126 @@ +{
+ "metadata": {
+ "name": "CHAPTER5"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter5 : Introduction to Convection"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 5.1 Page NO. 248"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#How much heat must be added for the two cases.\n",
+ "\n",
+ "#Given\n",
+ "# properties of CO at 300K from appendix table D2\n",
+ "Cp=871\n",
+ "Gamma=1.3\n",
+ "\n",
+ "#calculation\n",
+ "Cv=Cp/Gamma\n",
+ "dT=20\n",
+ "m=5\n",
+ "Qp=m*Cp*dT\n",
+ "Qv=m*Cv*dT\n",
+ "\n",
+ "#Result\n",
+ "print\" The heat required at constant pressure is \",Qp/1000,\"kj\"\n",
+ "print\"The heat required at constant volume is \",Qv/1000,\"kj\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ " The heat required at constant pressure is 87 kj\n",
+ "The heat required at constant volume is 67.0 kj\n"
+ ]
+ }
+ ],
+ "prompt_number": 4
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 5.2 Page NO.250"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#verify the valve for Voluemetric thermal coefficient\n",
+ "\n",
+ "#Given\n",
+ "# properties of Freon-12 from appendix table C3\n",
+ "T1_Fr=-50\n",
+ "T2_Fr=-40\n",
+ "rou1_Fr=1.546*1000\n",
+ "rou2_Fr=1.518*1000\n",
+ "\n",
+ "#Calculation\n",
+ "beta_Fr=-(rou1_Fr-rou2_Fr)/(rou1_Fr*(T1_Fr-T2_Fr))\n",
+ "beta_acc_Fr=2.63e-3 # the accurate value of volumetric thermal expansion coefficient for Freon-12\n",
+ "error_Fr=(beta_acc_Fr-beta_Fr)*100/beta_acc_Fr\n",
+ "# properties of helium from appendix table D3\n",
+ "T1_He=366\n",
+ "T2_He=477\n",
+ "rou1_He=0.13280\n",
+ "rou2_He=0.10204\n",
+ "beta_He=-(rou1_He-rou2_He)/(rou1_He*(T1_He-T2_He))\n",
+ "\n",
+ "#REsult\n",
+ "print\"The volumetric thermal expansion coefficient calculated for Freon-12 is \",round(beta_Fr,6),\"1/K\"\n",
+ "print\"The error introduced in the case of Freon-12 is percent\",round(error_Fr,0),\"percent\"\n",
+ "print\"The volumetric thermal expansion coefficient calculated for Freon-12 is \",round(beta_He,6),\"1/K\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The volumetric thermal expansion coefficient calculated for Freon-12 is 0.001811 1/K\n",
+ "The error introduced in the case of Freon-12 is percent 31.0 percent\n",
+ "The volumetric thermal expansion coefficient calculated for Freon-12 is 0.002087 1/K\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Engineering_Heat_Transfer/CHAPTER6.ipynb b/Engineering_Heat_Transfer/CHAPTER6.ipynb new file mode 100644 index 00000000..f8b8ec9f --- /dev/null +++ b/Engineering_Heat_Transfer/CHAPTER6.ipynb @@ -0,0 +1,545 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 6: Convection Heat Transfer in a Closed Circuit"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 6.1 page No.301"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Determination of the fluid outlet tetnperature and the tube-wall temperature at the outlet.\n",
+ "\n",
+ "#Given\n",
+ "#properties of ethylene glycol at 20 degree celsius from appendix table C5\n",
+ "Cp_20=2382\n",
+ "rou_20=1.116*1000\n",
+ "v_20=19.18e-6\n",
+ "kf_20=0.249\n",
+ "a_20=0.939e-7\n",
+ "Pr_20=204.0\n",
+ "# specifications of 1/2 standard type M seamless copper water tubing from appendix table F2\n",
+ "OD=1.588/100.0\n",
+ "ID=1.446/100.0\n",
+ "A=1.642e-4\n",
+ "Q=3.25e-6\n",
+ "\n",
+ "#Calculation\n",
+ "V=Q/A\n",
+ "# calculation of Reynold's Number to check flow regime\n",
+ "Re=V*ID/v_20\n",
+ "# since Re>he 2100, the flow regime is laminar and the hydrodynamic length can be calculated as\n",
+ "Z_h=0.05*ID*Re\n",
+ "Tbi=20 # bulk-fluid inlet temperature in degree celsius\n",
+ "qw=2200 # incident heat flux in W/m**2\n",
+ "L=3 # Length of copper tube in m\n",
+ "R=ID/2 # inner radius in m\n",
+ "Tbo=Tbi+(2*qw*a_20*L)/(V*kf_20*R)\n",
+ "# This result is based on fluid properties evaluated at 20\u00b0C. taken as a first approximation\n",
+ "Z_t=0.05*ID*Re*Pr_20\n",
+ "Two=Tbo+(11*qw*ID)/(48*kf_20) # The wall temperature at outlet in degree celsius\n",
+ "\n",
+ "#Result\n",
+ "print\"The bulk-fluid outlet temperature is degree celsius\",round(Tbo,0),\"C\"\n",
+ "print\"The wall temperature at outlet is degree celsius\",round(Two,0),\"C\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The bulk-fluid outlet temperature is degree celsius 55.0 C\n",
+ "The wall temperature at outlet is degree celsius 84.0 C\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 6.2 page No.308"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# determination of average convection coefficient\n",
+ "\n",
+ "#Given\n",
+ "T_avg=(140+70)/2.0\n",
+ "# properties of water at average bulk temperature from appendix table C11\n",
+ "rou=0.994*62.4\n",
+ "kf=0.363\n",
+ "cp=0.9980\n",
+ "a=5.86e-3\n",
+ "v=0.708e-5\n",
+ "Pr=4.34\n",
+ "# specifications of 1 standard type M copper tube from appendix table F2\n",
+ "OD=1.125/12.0 # outer diameter in ft\n",
+ "ID=0.8792 # inner diameter in ft\n",
+ "A=0.006071 # cross sectional area in sq.ft\n",
+ "m_flow=1.5 # mass flow rate in lbm/s\n",
+ "V=m_flow*3600.0/(rou*A); # velocity in ft/hr\n",
+ "import math\n",
+ "L=20.0\n",
+ "Tw=240.0\n",
+ "Tbo=140.0\n",
+ "Tbi=70.0\n",
+ "hL=-(rou*V*ID*cp*math.log((Tw-Tbo)/(Tw-Tbi)))/(4*L)\n",
+ "\n",
+ "#result\n",
+ "print\"The average convective coefficient is \",round(hL/10,1),\"BTU/(hr. sq.ft.degree Rankine\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The velocity is 14340.4425132 ft/hr\n",
+ "The average convective coefficient is 517.7 BTU/(hr. sq.ft.degree Rankine\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "%pylab inline"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 6.3 page No. 310"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Determination of the variation of wall temperature with length up to the point where the flow becomes fully developed.\n",
+ "\n",
+ "#Given\n",
+ "# properties of milk \n",
+ "kf=0.6 # thermal conductivity in W/(m-K)\n",
+ "cp=3.85*1000 # specific heat in J/(kg*K)\n",
+ "rou=1030 # density in kg/m**3\n",
+ "mu=2.12e3 # viscosity in N s/m**2\n",
+ "# specifications of 1/2 standard type K tubing from appendix table F2\n",
+ "OD=1.588/100 # outer diameter in m\n",
+ "ID=1.340/100 # inner diameter in m\n",
+ "A=1.410e-4 # cross sectional area in m**2\n",
+ "rou=1030\n",
+ "V=0.1\n",
+ "mu=2.12e-3\n",
+ "\n",
+ "#Calculation\n",
+ "# determination of flow regime\n",
+ "Re=rou*V*ID/(mu)\n",
+ "# The flow being laminar, the hydrodynamic entry length is calculated as follows\n",
+ "ze=0.05*ID*Re\n",
+ "Tbo=71.7 # final temperature in degree celsius\n",
+ "Tbi=20 # initial temperature in degree celsius\n",
+ "L=6 # heating length in m\n",
+ "qw=rou*V*ID*cp*(Tbo-Tbi)/(4*L)\n",
+ "q=qw*math.pi*ID*L\n",
+ "Pr=(cp*mu)/kf # Prandtl Number\n",
+ "zf=0.05*ID*Re*Pr\n",
+ "\n",
+ "#result\n",
+ "print\"The heat flux is \",round(qw,0),\"W/sq.m\"\n",
+ "print\"The power required is \",round(q,0),\"W\"\n",
+ "print\"The length required for flow to be thermally developed is\",round(zf,1),\"m\"\n",
+ "#plot\n",
+ "import matplotlib.pyplot as plt\n",
+ "fig = plt.figure()\n",
+ "ax = fig.add_subplot(111)\n",
+ "\n",
+ "z1=[0,0.2,1,6]\n",
+ "Twz=[20,40,60,125]\n",
+ "z2=[-1,0,6]\n",
+ "Twb=[20,20,72]\n",
+ "z3=[0.2,1,2,6]\n",
+ "hz=[112,72,58,40]\n",
+ "plt.grid()\n",
+ "xlabel(\"z (m)\") \n",
+ "ylabel(\"T (C) \") \n",
+ "plt.xlim((-1,6))\n",
+ "plt.ylim((0,140))\n",
+ "\n",
+ "ax.annotate('(Twz)', xy=(6,125))\n",
+ "ax.annotate('(Tbz)', xy=(6,72))\n",
+ "ax.annotate('(hz)', xy=(6,40))\n",
+ "a1=plot(z1,Twz)\n",
+ "a2=plot(z2,Twb)\n",
+ "a3=plot(z3,hz)\n",
+ "show(a1)\n",
+ "show(a2)\n",
+ "show(a3)\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The heat flux is 11447.0 W/sq.m\n",
+ "The power required is 2891.0 W\n",
+ "The length required for flow to be thermally developed is 5.9 m\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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Ry6ZNMHq0OlvM378OXthkgqFD1T9l25///nfdTH8WjiEzL5Mv0r4g5kQM8Rnx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\nPNDmARk2KYSwivQ17Oj6vq7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+ "text": [
+ "<matplotlib.figure.Figure at 0x7650da0>"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 6.4 page No. 313"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "%pylab inline"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Graph the variation between fluid and wall bulb tempratures.\n",
+ "#and how long it will take for the water volume to solidify.\n",
+ "\n",
+ "#Given\n",
+ "# The average bulk temperature of the Freon-12 is [-4O +(-4)]/2 = -22\u00b0F\n",
+ "# properties of Freon-12 at average bulk temperature\n",
+ "kf=0.04 # thermal conductivity in BTU/(hr.ft.\u00b0R) \n",
+ "cp=0.2139 # specific heat in BTU/(lbm-\u00b0R)\n",
+ "rou= 1.489*(62.4) # density in lbm/cu.ft\n",
+ "v=0.272e-5 # viscosity in sq.ft/s\n",
+ "a=2.04e-3 # diffusivity in sq.ft/hr\n",
+ "Pr=4.8 # Prandtl Number\n",
+ "# specifications of 3/8 standard type K copper tubing from appendix table F2\n",
+ "OD=0.5/12.0 # outer diameter in ft\n",
+ "ID=0.03350 # inner diameter in ft\n",
+ "A=0.0008814 # cross sectional area in sq.ft\n",
+ "# Laminar conditions are asssumed\n",
+ "z=5.0\n",
+ "Tw=32.0\n",
+ "Tbo=-4.0\n",
+ "Tbi=-40.0\n",
+ "L=5.0\n",
+ "\n",
+ "#Calculation\n",
+ "x=2*a*L/((kf*ID/2.0)*(math.log((Tw-Tbo)/(Tw-Tbi)))) #x=V/hl\n",
+ "#1/Gz=9.09/V\n",
+ "#from the table unless convergence is achieved\n",
+ "V=336.0 #ft/h\n",
+ "V_final=V/3600.0 #ft/s\n",
+ "hl_=V_final/(x) #\n",
+ "\n",
+ "# checking the laminar-flow assumption by calculating the Reynolds number\n",
+ "Re=(V_final/3600.0)*ID/v\n",
+ "# The flow is laminar\n",
+ "m_Fr=rou*A*V_final\n",
+ "As=math.pi*ID*L\n",
+ "q=hl_*As*((Tw-Tbo)-(Tw-Tbi))/(log((Tw-Tbo)/(Tw-Tbi)))\n",
+ "q_check=m_Fr*cp*(Tbo-Tbi)\n",
+ "rou_water=1.002*62.4 # density of water in lbm/ft**3 from appendix table C11\n",
+ "m_water=rou_water*L*(2/12.0)*(3/12.0)\n",
+ "# to remove 144 BTU/lbm of water, the time required is caalculated as below\n",
+ "t=144*m_water/(-q*3600)\n",
+ "\n",
+ "#result\n",
+ "print\"The mass flow rate of Freon-12 is \",round(m_Fr*3600,2),\"lbm/hr\"\n",
+ "print\"The required time is \",round(t,0),\"hr\"\n",
+ "\n",
+ "\n",
+ "#plot\n",
+ "#Constant wall temprature with length\n",
+ "import matplotlib.pyplot as plt\n",
+ "fig = plt.figure()\n",
+ "ax = fig.add_subplot(111)\n",
+ "\n",
+ "z1=[0,5]\n",
+ "Tw=[32,32]\n",
+ "z2=[0,0.185,0.74,1.85,2.77,3.70,5.0]\n",
+ "Tbz=[-40,-34.7,-27.4,-18.5,-13.5,-8.9,-4.1]\n",
+ "z3=[0.185,1,2,5.0]\n",
+ "hz=[23,-13,-19,-25]\n",
+ "\n",
+ "plt.grid()\n",
+ "xlabel(\"z (m)\") \n",
+ "ylabel(\"T (F) \") \n",
+ "plt.xlim((-2,5))\n",
+ "plt.ylim((-40,35))\n",
+ "\n",
+ "ax.annotate('(Tw=32 F)', xy=(5,30))\n",
+ "ax.annotate('(Tbz)', xy=(5,-5))\n",
+ "ax.annotate('(hz)', xy=(5,-25))\n",
+ "ax.annotate('(hydronamic entry\\n length)', xy=(-2,-40))\n",
+ "a1=plot(z1,Tw)\n",
+ "a2=plot(z2,Tbz)\n",
+ "a3=plot(z3,hz)\n",
+ "title('$Variation of Constant wall temprature with length$')\n",
+ "show(a1)\n",
+ "show(a2)\n",
+ "show(a3)\n",
+ "\n",
+ "#2nd Plot\n",
+ "#Nusslet number with dimensionless length\n",
+ "x1=[0.001,0.01,0.1,1]\n",
+ "Nu1=[31,11,5.5,5.2]\n",
+ "Nu2=[25,10,5.3,5.1]\n",
+ "Nu3=[22,9,5.1,4.9]\n",
+ "Nu4=[17,7,4.1,4]\n",
+ "Nu5=[15,6.5,4,3.9]\n",
+ "Nu6=[13.8,6,3.9,3.8]\n",
+ "\n",
+ "\n",
+ "plt.grid()\n",
+ "xlabel(\"1/Gz=z/(DRePr)\") \n",
+ "ylabel(\"Nu \") \n",
+ "\n",
+ "plt.xlim((0.001,1))\n",
+ "plt.ylim((0,35))\n",
+ "ax.annotate('(Constant wall temprature)', xy=(0.1,30))\n",
+ "ax.annotate('(Hydronamically and thermally developing laminar flow)', xy=(0.1,25))\n",
+ "b1=plot(x1,Nu1,label='Pr=0.7')\n",
+ "b2=plot(x1,Nu2,label='Pr=2')\n",
+ "b3=plot(x1,Nu3,label='Pr=5')\n",
+ "b4=plot(x1,Nu4,label='Pr=0.7')\n",
+ "b5=plot(x1,Nu5,label='Pr=2')\n",
+ "b6=plot(x1,Nu6,label='Pr=5')\n",
+ "plt.legend(loc='upper right')\n",
+ "title('$Variation of Nusslet number with dimensionless length$')\n",
+ "show(b1)\n",
+ "show(b2)\n",
+ "show(b3)\n",
+ "show(b4)\n",
+ "show(b5)\n",
+ "show(b6)"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The mass flow rate of Freon-12 is 27.52 lbm/hr\n",
+ "The required time is 9.0 hr\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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Iu+++y5IlS9iyZUup1jd69GgWLVpE8+bNKzj5g0kfmtC++fMhKQm++krtJEIY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\nJPx/NycoLOaJwxIAAAAASUVORK5CYII=\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x7b9cf28>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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ZUvHUpt0Y6HOrSqVSicjISNjb2yMqKsooccTFxQnL9vHxqfNyjHqHMqVSiZEj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\nRLmoP5MXgtLSUsycORPR0dG4du0atm7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+ "text": [
+ "<matplotlib.figure.Figure at 0x7669b00>"
+ ]
+ }
+ ],
+ "prompt_number": 11
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 6.5 page No.320"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Determination for the power required for heating and the wall temperature at the outlet. \n",
+ "\n",
+ "#Given\n",
+ "# The liquid properties are evaluated at the mean temperature of (80 + 20)/2 = 50\u00b0C.\n",
+ "# specifications of 1 standard type K copper water tubing from appendix table F2\n",
+ "OD = 2.858/100.0 # outer diameter in m \n",
+ "ID = 2.528/100.0 # inner diameter in m \n",
+ "A = 5.019e-4 # cross sectional area in sq.m\n",
+ "# 1 oz = 2.957e-5 m**3\n",
+ "Q=80*2.957e-5/120 # The volume flow rate of water (at 20\u00b0C) in cu.m/s\n",
+ "p_20= 1.000*1000 # density of water at 20\u00b0C in kg/cu.m\n",
+ "# properties of water at 50\u00b0C from appendix table C11\n",
+ "p_50= 0.990*(1000) # density in kg/m3 \n",
+ "cp= 4181 # specific heat in J/(kg*K) \n",
+ "v = 0.586e-6 # viscosity in sq.m/s \n",
+ "kf = 0.640 # thermal conductivity in W/(m.K) \n",
+ "a = 1.533e-7 # diffusivity in sq.m/s \n",
+ "Pr = 3.68 # Prandtl number\n",
+ "\n",
+ "#CALCULATION\n",
+ "import math\n",
+ "mass_flow=p_20*Q # mass flow rate through the tube in kg/s\n",
+ "L=3 # length of tube in m\n",
+ "As=math.pi*ID*L\n",
+ "Tbo=80 # final temperature in \u00b0C\n",
+ "Tbi=20 # initial temperature in \u00b0C\n",
+ "qw=mass_flow*cp*(Tbo-Tbi)/(As)\n",
+ "q=qw*As\n",
+ "A=math.pi*(ID/2)**2\n",
+ "print\"The power required is\",round(q,0),\"W\"\n",
+ "V=mass_flow/(p_50*A) # average velocity at 50 \u00b0C\n",
+ "Re=(V*ID)/v # Reynold's Number\n",
+ "# The flow is laminar so we can use Figure 6.12 to obtain the information needed on Nusselt number and to find hz\n",
+ "inv_Gz=L/(Re*ID*Pr) # The inverse Graetz number at tube end, based on 50\u00b0C conditions\n",
+ "Nu=6.9 #value of corresponding Nusselts Number from figure 6.12\n",
+ "hz=(Nu*kf)/ID\n",
+ "Two=(qw/hz)+Tbo # The outlet wall temperature in \u00b0C\n",
+ "print\"\\nThe outlet wall temperature is\",round(Two,0),\"C\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The power required is 4945.0 W\n",
+ "\n",
+ "The outlet wall temperature is 199.0 C\n"
+ ]
+ }
+ ],
+ "prompt_number": 19
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 6.6 page No.325"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#Determine heat gained by the duct and wall temprature\n",
+ "\n",
+ "#Given\n",
+ "# determibation of heat gained\n",
+ "# air properties to be calculated at T=(72+45)/2=58.5 degree Fahrenheit\n",
+ "# properties at T=58.5 degree fahrenheit from appendix table D1\n",
+ "p = 0.077 # density in lbm/ft^3 \n",
+ "cp = 0.240 # specific heat in BTU/(lbm.degree Rankine) \n",
+ "v = 15.28e-5 # viscosity in ft^2/s \n",
+ "kf = 0.0146 # thermal conductivity in BTU/(hr.ft.\"R) \n",
+ "a = 0.776 # diffusivity in ft^2/hr \n",
+ "Pr = 0.711 # prandtl number \n",
+ "D=7/12.0 # diameter in ft\n",
+ "L=40 # length in ft\n",
+ "Tbo=72 # outlet temperature in degree Fahrenheit\n",
+ "Tbi=45 # inlet temperature in degree Fahrenheit\n",
+ "A=math.pi*(D**2)/4 # cross sectional area of duct in ft^2\n",
+ "# density at outlet temperature in lbm/ft^3 \n",
+ "rou_o=.0748\n",
+ "V=10 # average velocity in ft/s\n",
+ "mass_flow=rou_o*A*V\n",
+ "\n",
+ "#Calculation\n",
+ "# average velocity evaluated by using the average bulk temperature\n",
+ "V_avg=mass_flow/(p*A)\n",
+ "Re=(V_avg*D)/v\n",
+ "# the flow is in turbulent regime\n",
+ "q=mass_flow*cp*(Tbo-Tbi)\n",
+ "hc=1 # convection coefficient between the outside duct wall \n",
+ "T_inf=105 # The temperature of attic air surrounding the duct in degree Fahrenheit\n",
+ "hz=(0.023*Re**(0.8)*Pr**0.4)*kf/D \n",
+ "qw=(T_inf-Tbo)/((1/hc)+(1/hz)) \n",
+ "Two=qw*(1/hz)+Tbo # The wall temperature at exit in degree Fahrenheit\n",
+ "\n",
+ "#result\n",
+ "print\"The heat gained by air is\",round(q,3),\"BTU\"\n",
+ "print\"The wall temperature at exit is \",round(Two,1),\"F\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The heat gained by air is 1.295 BTU\n",
+ "The wall temperature at exit is 82.1 F\n"
+ ]
+ }
+ ],
+ "prompt_number": 28
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Engineering_Heat_Transfer/CHAPTER7.ipynb b/Engineering_Heat_Transfer/CHAPTER7.ipynb new file mode 100644 index 00000000..3c0bf86c --- /dev/null +++ b/Engineering_Heat_Transfer/CHAPTER7.ipynb @@ -0,0 +1,709 @@ +{
+ "metadata": {
+ "name": "CHAPTER7"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter7 : Convection Heat Transfer in Flow Past immersed Bodies"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 7.1 page NO.353"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "%pylab inline"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# determination of boundary layer growth with length\n",
+ "\n",
+ "#Given\n",
+ "# properties of air at 27 degree celsius from appendix table D.1\n",
+ "rou=1.177 # density in kg/cu.m\n",
+ "v=15.68e-6 # viscosity in sq.m/s\n",
+ "L=0.5 # length in m\n",
+ "V_inf=1; # air velocity in m/s\n",
+ "Re= (V_inf*L)/v # Reynolds Number\n",
+ "\n",
+ "#(a)plot\n",
+ "#delta=1.98*10**-2*x**(1/2)\n",
+ "import matplotlib.pyplot as plt\n",
+ "fig = plt.figure()\n",
+ "ax = fig.add_subplot(111)\n",
+ "\n",
+ "x=[0,0.065,0.125,0.5]\n",
+ "t=[0,0.004,0.006,0.013]\n",
+ "xlabel(\"x (m)\") \n",
+ "ylabel(\"t (m)\") \n",
+ "plt.xlim((0,0.6))\n",
+ "plt.ylim((0,0.015))\n",
+ "a1=plot(x,t)\n",
+ "\n",
+ "#(b)plot\n",
+ "import matplotlib.pyplot as plt\n",
+ "fig = plt.figure()\n",
+ "ax = fig.add_subplot(111)\n",
+ "\n",
+ "x=[0,0.75,0.9,1]\n",
+ "t=[0,0.005,0.0075,0.010]\n",
+ "xlabel(\"V (m/s)\") \n",
+ "ylabel(\"y (m)\") \n",
+ "plt.xlim((0,1))\n",
+ "plt.ylim((0,0.010))\n",
+ "a1=plot(x,t)\n",
+ "\n",
+ "# (c)calculation of absolute viscosity\n",
+ "gc=1\n",
+ "mu=rou*v/gc\n",
+ "b=1 # width in m\n",
+ "Df=0.664*V_inf*mu*b*(Re)**0.5\n",
+ "\n",
+ "\n",
+ "#result\n",
+ "print\"(a)plot between boundary layer growth with distance\"\n",
+ "print\"(b)velocity distribution with distance\"\n",
+ "print\"(c)The skin-drag including both sides of plate is \",round(2*Df,4),\"n\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(a)plot between boundary layer growth with distance\n",
+ "(b)velocity distribution with distance\n",
+ "(c)The skin-drag including both sides of plate is 0.0044 n\n"
+ ]
+ },
+ {
+ "output_type": "display_data",
+ "png": 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+ },
+ {
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+ "png": 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+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 7.2 page NO.360"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "%pylab inline"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# determination of temperature profile\n",
+ "\n",
+ "#Given\n",
+ "# properties of water at (40 + 100)/2 = 70\u00b0F = 68\u00b0F from appendix table C11\n",
+ "rou= 62.4 # density in Ibm/ft^3 \n",
+ "cp=0.9988 # specific heat BTU/(lbm-degree Rankine) \n",
+ "v= 1.083e-5 # viscosity in sq.ft/s \n",
+ "kf = 0.345 # thermal conductivity in BTU/(hr.ft.degree Rankine) \n",
+ "a = 5.54e-3 # diffusivity in sq.ft/hr \n",
+ "Pr = 7.02 # Prandtl Number\n",
+ "V=1.2 # velocity in ft/s\n",
+ "\n",
+ "#Calculation\n",
+ "x1=1\n",
+ "Re1=(V*x1)/v # Reynolds Number at x=1 ft\n",
+ "# since Reynolds Number is less than 5*10^5, the flow is laminar\n",
+ "hL1=0.664*Pr**(1/3.0)*Re1**0.5*kf/x1\n",
+ "Tw=100 # temperature of metal plate in degree fahrenheit\n",
+ "T_inf=40 # temperature of water in degree fahrenheit\n",
+ "A1=x1*18/12.0 # cross sectional area for 1 ft length\n",
+ "q1=hL1*A1*(Tw-T_inf)\n",
+ "\n",
+ "print\"The heat transferred to water over the plate is\",round(q1,0),\"BTU/hr\"\n",
+ "x2=2\n",
+ "Re2=(V*x2)/v # Reynolds Number at x=1 ft\n",
+ "# since Reynolds Number is less than 5*10^5, the flow is laminar\n",
+ "hL2=0.664*Pr**(1/3.0)*Re2**0.5*kf/x2\n",
+ "Tw=100 # temperature of metal plate in degree fahrenheit\n",
+ "T_inf=40 # temperature of water in degree fahrenheit\n",
+ "A2=x2*18/12.0 # cross sectional area for 1 ft length\n",
+ "q2=hL2*A2*(Tw-T_inf)\n",
+ "print\"The heat transferred to water over the plate is \",round(q2,0),\"BTU/hr\"\n",
+ "\n",
+ "#PLot for temprature distribution\n",
+ "import matplotlib.pyplot as plt\n",
+ "fig = plt.figure()\n",
+ "ax = fig.add_subplot(111)\n",
+ "\n",
+ "T=[100,80,60,50,40]\n",
+ "y=[0,0.0008,0.0018,0.0025,0.004]\n",
+ "xlabel(\"T (F)\") \n",
+ "ylabel(\"y (ft) \") \n",
+ "plt.xlim((100,40))\n",
+ "plt.ylim((0,0.004))\n",
+ "a1=plot(T,y)\n",
+ "\n",
+ "#PLot for influence of prandtl no on boundary layer thickness\n",
+ "import matplotlib.pyplot as plt\n",
+ "fig = plt.figure()\n",
+ "ax = fig.add_subplot(111)\n",
+ "\n",
+ "Pr=[0.6,50]\n",
+ "t=[1.2,0.28]\n",
+ "xlabel(\"Pr\") \n",
+ "ylabel(\"t (ft) \") \n",
+ "plt.xlim((0.6,50))\n",
+ "plt.ylim((0,2))\n",
+ "ax.plot([10], [1], 'o')\n",
+ "ax.annotate('(Exact solution)', xy=(8,1.2))\n",
+ "ax.annotate('(dt/dt=Pr**-(1/3))', xy=(15,1))\n",
+ "ax.plot([25], [0.75], 'o')\n",
+ "ax.plot([35], [0.55], 'o')\n",
+ "ax.plot([40], [0.48], 'o')\n",
+ "\n",
+ "a1=plot(Pr,t)\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The heat transferred to water over the plate is 13141.0 BTU/hr\n",
+ "The heat transferred to water over the plate is 18584.0 BTU/hr\n"
+ ]
+ },
+ {
+ "output_type": "display_data",
+ "png": 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+ },
+ {
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XwnOmJ1SxKnjN9oKDl4O1y6MuYiAQ0W1pvNZo7Dsk6VF+sBxuY92kW3g73+1s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\nIjJhIBAREQDg/wPa6rEVsfB01AAAAABJRU5ErkJggg==\n"
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 7.3 page NO.363"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Determination of the average convection coefficient and the total drag force exerted on the plate.\n",
+ "\n",
+ "#Given\n",
+ "# properties of air at (300 + 400)/2 = 350 K from appendix table D1\n",
+ "rou=0.998\t # density in kg/cu.m\n",
+ "cp=1009 \t\t# specific heat in J/(kg*K) \n",
+ "v=20.76e-6 \t# viscosity in sq.m/s \n",
+ "Pr=0.697 \t# Prandtl Number \n",
+ "k=0.03003 \t# thermal conductivity in W/(m.K)\n",
+ "a=0.2983e-4 \t# diffusivity in sq.m/s \n",
+ "L=1.0 \t\t # Length of plate in m\n",
+ "V=5.0 \t\t # velocity of air in m/s\n",
+ "b=0.5 \t\t# width in m\n",
+ "Re=V*L/v \t# Reynolds number at plate end\n",
+ "\n",
+ "#calculation\n",
+ "# Nu=h*L/k= 0.664 Re**(1/2)Pr**(1/3)\n",
+ "h=k*0.664*Re**(0.5)*Pr**(1/3.0)/L\t # The average convection coefficient in W/(sq.m.K)\n",
+ "Df=0.664*V*rou*v*b*(Re)**0.5 \t # drag force in N\n",
+ "hx=(1/2.0)*h # local convective coefficient\n",
+ "delta=5*L/(Re)**0.5 # The boundary-layer thickness at plate end\n",
+ "delta_t=delta/(Pr)**(1/3.0)\n",
+ "\n",
+ "#Result\n",
+ "print\"The local convective coefficient is \",round(hx,2),\"W/(sq.m.K)\"\n",
+ "print\"The boundary-layer thickness at plate end is \",round(delta*100,2),\"cm\"\n",
+ "print\"The thermal-boundary-layer thickness is \",round(delta_t*100,2),\"cm\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The local convective coefficient is 4.34 W/(sq.m.K)\n",
+ "The boundary-layer thickness at plate end is 1.02 cm\n",
+ "The thermal-boundary-layer thickness is 1.15 cm\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 7.4 page NO. 364"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Determination of the maximum heater-surface temperature for given conditions\n",
+ "\n",
+ "#Given\n",
+ "# fluid properties at (300 degree R + 800 degree R)/2 = 550 degree R=540degree R from Appendix Table D.6\n",
+ "rou= 0.0812 # density in Ibm/ft^3 \n",
+ "cp=0.2918 # specific heat BTU/(lbm-degree Rankine) \n",
+ "v= 17.07e-5 # viscosity in ft^2/s \n",
+ "kf = 0.01546 # thermal conductivity in BTU/(hr.ft.degree Rankine) \n",
+ "a = 0.8862 # diffusivity in ft^2/hr \n",
+ "Pr = 0.709 # Prandtl Number\n",
+ "\n",
+ "#calculation\n",
+ "qw=10/(1.5*10.125)*(1/.2918)*144 # The wall flux \n",
+ "V_inf=20 # velocity in ft/s\n",
+ "L=1.5/12 # length in ft\n",
+ "Re_L=V_inf*10*L/v # Reynolds number at plate end\n",
+ "# So the flow is laminar and we can find the wall temperature at plate end as follows\n",
+ "T_inf=300 # free stream temperature in degree Rankine\n",
+ "Tw=T_inf+(qw*L*10/(kf*0.453*(Re_L)**0.5*(Pr)**(1/3.0)))\n",
+ "\n",
+ "#Result\n",
+ "print\"The maximum heater surface temperature is \",round(Tw,0),\"R\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The maximum heater surface temperature is 470.0 R\n"
+ ]
+ }
+ ],
+ "prompt_number": 12
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 7.5 page NO. 368"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# validation of the equation st.(Pr)**(2/3)=Cd/2 where St: Stanton Number Pr:Prandtl Number Cd: Drag Coefficient\n",
+ "\n",
+ "#Given\n",
+ "# values of parameters from example 7.4\n",
+ "rou= 0.0812 # density in Ibm/ft**3 \n",
+ "cp=0.2918 # specific heat BTU/(lbm-degree Rankine) \n",
+ "v= 17.07e-5 # viscosity in ft**2/s \n",
+ "kf = 0.01546 # thermal conductivity in BTU/(hr.ft.degree Rankine) \n",
+ "a = 0.8862 # diffusivity in ft**2/hr \n",
+ "Pr = 0.709 # Prandtl Number\n",
+ "Tw=469 # maximum heater temperature in degree Rankine\n",
+ "T_inf=300.0 # free-stream temperature in degree Rankine\n",
+ "qw=324.0 # The wall flux in BTU/(hr.ft**2)\n",
+ "V_inf=20 # velocity in ft/s\n",
+ "\n",
+ "#Calculation\n",
+ "hx=qw/(Tw-T_inf) # The convection coefficient\n",
+ "LHS=(hx/3600.0)*(Pr)**(2/3.0)/(rou*cp*V_inf)\n",
+ "Re_L=1.46e+005 # Reynolds number at plate end\n",
+ "RHS=0.332*(Re_L)**(-0.5)\n",
+ "err=(LHS-RHS)*100/LHS\n",
+ "\n",
+ "#Result\n",
+ "print\"The convection coefficient is BTU/(hr.sq.ft.degree R)\",hx\n",
+ "print\"The error is \",round(err,0),\"percent\"\n",
+ "print\"Since the error is only 3 percent, the agreement is quite good\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The convection coefficient is BTU/(hr.sq.ft.degree R) 1.91715976331\n",
+ "The error is 3.0 percent\n",
+ "Since the error is only 3 percent, the agreement is quite good\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 7.6 page NO. 371"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Estimation of the drag due to skin friction\n",
+ "\n",
+ "#Given\n",
+ "# properties of water at 68\u00b0F from Appendix Table C.11\n",
+ "rou= 62.4 # density in Ibm/cu.ft\n",
+ "v= 1.083e-5 # viscosity in sq.ft/s \n",
+ "V_inf=5*.5144/.3048 # barge velocity in ft/s using conversion factors from appendix table A1\n",
+ "L=20 # Length of barge in ft\n",
+ "Re_L=V_inf*L/v # Reynolds number at plate end\n",
+ "Cd=0.003 #value of Coefficient of discharge figure 7.11\n",
+ "gc=32.2\n",
+ "b=12 # width in ft\n",
+ "\n",
+ "#Calculation\n",
+ "Df=(Cd*rou*V_inf**2*b*L)/(2*gc)\n",
+ "\n",
+ "#Result\n",
+ "print\"The drag force is \",round(Df,0),\"lbf\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The drag force is 50.0 lbf\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 7.7 page NO. 374"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Determination of wattage requirement\n",
+ "\n",
+ "#Given\n",
+ "# properties of carbon dioxide at a film temperature of (400+600)/2 = 500 K from appendix table D2\n",
+ "rou= 1.0732 # density in kg/m**3 \n",
+ "cp= 1013 # specific heat in J/(kg*K) \n",
+ "v= 21.67e-6 # viscosity in m**2/s \n",
+ "Pr = 0.702 # Prandtl Number \n",
+ "k= 0.03352 # thermal conductivity in W/(m.K)\n",
+ "a = 0.3084e-4 # diffusivity in m**2/s\n",
+ "V_inf=60 # carbon dioxide velocity in m/s\n",
+ "vel=60 #velocity\n",
+ "\n",
+ "x_cr=(5e5)*v/V_inf # The transition length in m\n",
+ "w=4.0 # width of each heater in cm\n",
+ "b=0.16 # effective heating length in m\n",
+ "Tw=600 # temperature of heater surface in K\n",
+ "T_inf=400 # temperature of carbon dioxide in K\n",
+ "\n",
+ "#calculation\n",
+ "#Nux=0.664*Rex**(1/2)*Pr**(1/3)\n",
+ "y=0.664*Pr**(1/3.0)*k*(vel/v)**(1/2.0) #y=h1*x1**(1/2)\n",
+ "x1=0.04 # m\n",
+ "h1=y/x1**(0.5)\n",
+ "q1=h1*(Tw-T_inf)*x1*b\n",
+ "\n",
+ "x2=0.08\n",
+ "h2=y/(x2)**(0.5)\n",
+ "Q=h2*x2*(b)*(Tw-T_inf) #Q=q1+q2\n",
+ "q2=Q-q1\n",
+ "\n",
+ "x3=0.12\n",
+ "h3=y/(x3)**(0.5)\n",
+ "Q1=h3*x3*(b)*(Tw-T_inf) #Q=q1+q2+q3\n",
+ "q3=Q1-Q\n",
+ "\n",
+ "x4=0.16\n",
+ "h4=y/(x4)**(0.5)\n",
+ "Q2=h4*x4*(b)*(Tw-T_inf) #Q=q1+q2+q3+q4\n",
+ "q4=Q2-Q1\n",
+ "\n",
+ "#at the end of 5th heater\n",
+ "Re5=vel*5*x1/(v)\n",
+ "\n",
+ "#Nux=10.0359*(Rex**(0.8)-830)*Pr**(1/3)\n",
+ "h5=0.0359*(Re5**(0.8)-830)*Pr**(1/3.0)*(k/(11.9*x1))\n",
+ "x5=0.2\n",
+ "Q3=h5*x5*(b)*(Tw-T_inf) #Q3=q1+q2+q3+q4+q5\n",
+ "q5=Q3-Q2\n",
+ "\n",
+ "#at the end of 6th heater\n",
+ "Re6=vel*6*x1/(v)\n",
+ "#Nux=10.0359*(Rex**(0.8)-830)*Pr**(1/3)\n",
+ "h6=0.0359*(Re5**(0.8)-830)*Pr**(1/3.0)*(k/(10.3*x1))\n",
+ "x6=0.24\n",
+ "Q4=h6*x6*(b)*(Tw-T_inf) #Q4=q1+q2+q3+q4+q5+q6\n",
+ "q6=round(Q4,0)-round(Q3,0)\n",
+ "\n",
+ "#Result\n",
+ "print\"The wattage required for 1st heater is \",round(q1,0),\"W\"\n",
+ "print\"The wattage required for 2nd heater is \",round(q2,0),\"W\"\n",
+ "print\"The wattage required for 3rd heater is \",round(q3,1),\"W\"\n",
+ "print\"The wattage required for 4th heater is \",round(q4,0),\"W\"\n",
+ "print\"The wattage required for 5th heater is \",round(q5,0),\"W\"\n",
+ "print\"The wattage required for 6th heater is \",round(q6,1),\"W\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The wattage required for 1st heater is 211.0 W\n",
+ "The wattage required for 2nd heater is 87.0 W\n",
+ "The wattage required for 3rd heater is 67.0 W\n",
+ "The wattage required for 4th heater is 56.0 W\n",
+ "The wattage required for 5th heater is 132.0 W\n",
+ "The wattage required for 6th heater is 213.0 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 64
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 7.8 page NO. 302"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Estimation of force exerted on the pole\n",
+ "\n",
+ "#Given\n",
+ "# properties of air at given conditions from appendix table D1\n",
+ "rou= 0.0735 # density in Ibm/ft**3 \n",
+ "v= 16.88e-5 # viscosity in ft**2/s \n",
+ "V=20*5280/3600.0 # flow velocity in ft/s\n",
+ "D=1.0 # diameter of pole in ft\n",
+ "L=30.0 # length of pole in ft\n",
+ "gc=32.2\n",
+ "Re_D=V*D/v # Reynolds Number for flow past the pole\n",
+ "Cd_cylinder=1.1 # value of Cd for smooth cylinder from figure 7.22\n",
+ "A_cylinder=D*L # frontal area of pole\n",
+ "\n",
+ "#Calculation\n",
+ "Df_cylinder=Cd_cylinder*(0.5)*rou*V**2*A_cylinder/gc\n",
+ "D_square=2/12.0 # length of square part of pole\n",
+ "L_square=4\n",
+ "Re_square=V*D_square/v # Reynolds Number for square part of pole\n",
+ "Cd_square=2 # Corresponding value of Cd for square part from figure 7.23\n",
+ "A_square=D_square*L_square # projected frontal area of square part\n",
+ "Df_square=Cd_square*(0.5)*rou*V**2*A_square/gc\n",
+ "Df_total=Df_cylinder+Df_square\n",
+ "print\"The total drag force on the pole is \",round(Df_total,1),\"lbf\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The total drag force on the pole is 33.7 lbf\n"
+ ]
+ }
+ ],
+ "prompt_number": 67
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 7.9 page NO. 387"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# determination of required current\n",
+ "\n",
+ "#Given\n",
+ "# properties of air at film temperature (300 + 500)/2 = 400 K from appendix table D1\n",
+ "rou= 0.883 # density in kg/cu.m\n",
+ "cp= 1014 # specific heat in J/(kg*K) \n",
+ "v= 25.90e-6 # viscosity in sq.m/s \n",
+ "Pr = 0.689 # Prandtl Number \n",
+ "kf= 0.03365 # thermal conductivity in W/(m.K)\n",
+ "a = 0.376e-4 # diffusivity in sq.m/s\n",
+ "V_inf=1 # velocity in m/s\n",
+ "D=0.00013 # diameter in m\n",
+ "L=0.01 # length of wire in cm\n",
+ "Re_D=V_inf*D/v # The Reynolds number of flow past the wire\n",
+ "C=0.911 #value of C for cylinder from table 7.4\n",
+ "m=0.385 #value of m for cylinder from table 7.4\n",
+ "\n",
+ "#calculation\n",
+ "hc=kf*C*(Re_D)**m*(Pr)**(1/3)/D # the convection coefficient in W/(m**2.K)\n",
+ "Tw=500 # air stream temperature in K\n",
+ "T_inf=300 # wire surface temperature in K\n",
+ "As=math.pi*D*L # cross sectional area in sq.m\n",
+ "qw=hc*As*(Tw-T_inf) # The heat transferred to the air from the wire\n",
+ "resistivity=17e-6 # resistivity in ohm cm\n",
+ "Resistance=resistivity*(L/(math.pi*D**2)) # resistance in ohm\n",
+ "i=(qw*100/Resistance)**0.5 # current in ampere\n",
+ "\n",
+ "#Result\n",
+ "print\"The current is %.1f A\",round(i,1),\"A\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The current is %.1f A 3.3 A\n"
+ ]
+ }
+ ],
+ "prompt_number": 68
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 7.10 page NO.393"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Calculation of the pressure drop for the air passing over the tubes and the heat transferred to the air.\n",
+ "\n",
+ "#Given\n",
+ "# properties of air at 70 + 460 = 530 degree R = 540 degree R from appendix table D1\n",
+ "rou= 0.0735 # density in Ibm/cu.ft \n",
+ "cp=0.240 # specific heat BTU/(lbm-degree Rankine) \n",
+ "v= 16.88e-5 # viscosity in sq.ft/s \n",
+ "kf = 0.01516 # thermal conductivity in BTU/(hr.ft.degree Rankine) \n",
+ "a = 0.859 # diffusivity in sq.ft/hr \n",
+ "Pr = 0.708 # Prandtl Number\n",
+ "# specifications of 3/4 standard type K copper tubing from appendix table F2\n",
+ "OD=0.875/12 # outer diameter in ft\n",
+ "ID=0.06208 # inner diameter in ft\n",
+ "A=0.003027 # cross sectional area in sq.ft\n",
+ "L=2\n",
+ "sL=1.5/12\n",
+ "sT=1.3/12\n",
+ "V_inf=12 # velocity of air in ft/s\n",
+ "\n",
+ "#calculation\n",
+ "V1=(sT*V_inf)/(sT-OD) # velocity at area A1 in ft/s\n",
+ "sD=((sL)**2+(sT/2)**2)**0.5 # diagonal pitch in inch\n",
+ "V2=(sT*V_inf)/(2*(sD-OD))\n",
+ "Vmax=V1\n",
+ "Re_D=Vmax*OD/v # Reynolds Number\n",
+ "sT_OD=1.3/0.875\n",
+ "sT_sL=1.3/1.5\n",
+ "f1=0.35 # value of f1 for above values of sT/Do and Re\n",
+ "f2=1.05 #Corresponding value of f2 for above values of sT/sL and Re\n",
+ "gc=32.2\n",
+ "N=7\n",
+ "dP=N*f1*f2*(rou*Vmax**2/(2*gc))\n",
+ "sL_Do=sL/OD\n",
+ "C1=0.438 #value of C1 for above values of sT/Do and sL/Do\n",
+ "C2=0.97 #value of C2 for above values of sT/Do and sL/Do\n",
+ "m=0.565 #value of m for above values of sT/Do and sL/Do\n",
+ "hc=kf*1.13*C1*C2*(Re_D)**m*(Pr)**(1/3.0)/OD # The convection coefficient\n",
+ "As=70*math.pi*OD*L # outside surface area of 70 tubes\n",
+ "Tw=200 # outside surface temeperature in degree F\n",
+ "T_inf=70 # air temperature in degree F\n",
+ "q=hc*As*(Tw-T_inf) # heat transferred\n",
+ "\n",
+ "#result\n",
+ "print\"The pressure drop is \",round(dP/147,3),\"psi\"\n",
+ "print\"The heat transferred is\",round(q,1),\" BTU/hr\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The pressure drop is 0.027 psi\n",
+ "The heat transferred is 87571.6 BTU/hr\n"
+ ]
+ }
+ ],
+ "prompt_number": 77
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Engineering_Heat_Transfer/CHAPTER8.ipynb b/Engineering_Heat_Transfer/CHAPTER8.ipynb new file mode 100644 index 00000000..a70f7944 --- /dev/null +++ b/Engineering_Heat_Transfer/CHAPTER8.ipynb @@ -0,0 +1,527 @@ +{
+ "metadata": {
+ "name": ""
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 8: Natural Convection System"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 8.1 Page No. 413"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Determination of the heat transferred to the wall.\n",
+ "\n",
+ "#Given\n",
+ "# air properties at (400+120)/2 =260 degree F = 720 degree R from Appendix Table D1\n",
+ "rou= 0.0551 # density in Ibm/cu.ft \n",
+ "cp=0.2420 # specific heat BTU/(lbm-degree Rankine) \n",
+ "v= 27.88e-5 # viscosity in sq.ft/s \n",
+ "kf = 0.01944 # thermal conductivity in BTU/(hr.ft.degree Rankine) \n",
+ "a = 1.457 # diffusivity in sq.ft/hr \n",
+ "Pr = 0.689 # Prandtl Number\n",
+ "T_inf=120.0+460.0 # wall temperature in degree R\n",
+ "Tw=400.0+460.0 # inside wall temperature in degree R\n",
+ "Beta=1/T_inf\n",
+ "\n",
+ "#IN THE BOOK THERE IS CALCULATION MISTAKE IN Beta\n",
+ "#Accoding to book Beta=0.00116 /R\n",
+ "Beta_=0.00116\n",
+ "gc=32.2\n",
+ "L=1.0 # length of wall in ft\n",
+ "W=2.0 # width in ft\n",
+ "Gr=(gc*Beta_*(Tw-T_inf)*L**3)/v**2 # Grashof Number\n",
+ "temperature_slope=0.505 #temperature slope from table 8.1 \n",
+ "hL=(kf/L)*(4/3.0)*(Gr/4.0)**(1/4.0)*temperature_slope \n",
+ "A=L*W # cross sectional area in sq.ft\n",
+ "qw=hL*A*(Tw-T_inf)\n",
+ "\n",
+ "#Result\n",
+ "print\"The heat transferred is\",round(qw,0),\"BTU/hr\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The heat transferred is 558.0 BTU/hr\n"
+ ]
+ }
+ ],
+ "prompt_number": 5
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 8.2 Page No. 414"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Determination of heat lost through the glass per unit area\n",
+ "\n",
+ "#Given\n",
+ "# properties of air at 0 + 273 K=273 K from appendix table D1\n",
+ "rou1=1.295 # density in kg/cu.m\n",
+ "cp1=1005.5 # specific heat in J/(kg*K) \n",
+ "v1=12.59e-6 # viscosity in sq.m/s \n",
+ "Pr1=0.713 # Prandtl Number \n",
+ "kf1=0.02426 # thermal conductivity in W/(m.K)\n",
+ "a1=0.17661e-4 # diffusivity in sq.m/s \n",
+ "T_inf1=0 # inside and outside temperature in K\n",
+ "Beta1=1/(T_inf1+273.0) # volumetric thermal expansion coefficient at 295 K and 273 K\n",
+ "\n",
+ "# properties of air at 22 + 273 = 295 K = 300 K(approx) \n",
+ "rou2=1.177 # density in kg/cu.m\n",
+ "cp2=1005 # specific heat in J/(kg*K) \n",
+ "v2=15.68e-6 # viscosity in sq.m/s \n",
+ "Pr2=0.708 # Prandtl Number \n",
+ "kf2=0.02624 # thermal conductivity in W/(m.K)\n",
+ "a2=0.22160e-4 # diffusivity in sq.m/s \n",
+ "T_inf2=22.0 # inside and outside temperature in K\n",
+ "Beta2=1/(T_inf2+273.0) # volumetric thermal expansion coefficient at 295 K and 273 K\n",
+ "\n",
+ "g=9.81\n",
+ "t=0.005 # thickness of glass\n",
+ "L=0.60 # window length in m\n",
+ "k=0.81 # thermal conductivity of glass from appendix table B3\n",
+ "# for first guess\n",
+ "Tw1=18\n",
+ "Tw2=4\n",
+ "Ra1=(g*Beta1*(Tw2-T_inf1)*L**3)/(v1*a1)\n",
+ "hL1=(kf1/L)*(0.68+((0.67*((abs(Ra1)))**(1/4.0))/(1+(0.492/Pr1)**(9/16.0))**(4/9.0)))\n",
+ "Ra2=(g*Beta2*(Tw1-T_inf2)*L**3)/(v2*a2)\n",
+ "hL2=(kf2/L)*(0.68+((0.67*(abs(Ra2))**(1/4.0))/(1+(0.492/Pr2)**(9/16.0))**(4/9.0)))\n",
+ "q1=(T_inf1-T_inf2)/((1/hL2)+(t/k)+(1/hL1))\n",
+ "Tw2_=T_inf2-(q1/hL2)\n",
+ "Tw1_=q1/hL1+T_inf1\n",
+ "\n",
+ "#Using these temprature as second estimates\n",
+ "Ra1_=3.7*10**8\n",
+ "hL1_=2.92\n",
+ "Ra2_=2.31*10**8\n",
+ "hL2_=2.80\n",
+ "q2=(T_inf2-T_inf1)/((1/hL2_)+(t/k)+(1/hL1_))\n",
+ "\n",
+ "#The wall temprature are\n",
+ "Tw2final=q2-T_inf2\n",
+ "Tw1final=10.7\n",
+ "\n",
+ "#result\n",
+ "print\"The heat loss is \",round(q2,1),\" W/sq.m\"\n",
+ "\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The heat loss is 31.2 W/sq.m\n"
+ ]
+ }
+ ],
+ "prompt_number": 15
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 8.3 Page No.419"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# determination of heat loss through the side.\n",
+ "\n",
+ "#Given\n",
+ "rou= 0.0735 # density in Ibm/cu.ft \n",
+ "cp=0.240 # specific heat BTU/(lbm-degree Rankine) \n",
+ "v= 16.88e-5 # viscosity in sq.ft/s \n",
+ "kf = 0.01516 # thermal conductivity in BTU/(hr.ft.degree Rankine) \n",
+ "a = 0.859 # diffusivity in sq.ft/hr \n",
+ "Pr = 0.708 # Prandtl Number\n",
+ "Tw=90\n",
+ "T_inf=70\n",
+ "g=32.2\n",
+ "L=5.5 # length in ft\n",
+ "W=2+(4/12.0) # width in ft\n",
+ "Beta=1/(Tw+460.0) # volumetric thermal expansion coefficient in per degree Rankine\n",
+ "Ra=(g*Beta*(Tw-T_inf)*L**3)/(v*a/3600)\n",
+ "hc=(kf/L)*(0.825+((0.387*(Ra)**(1/6.0))/(1+(0.492/Pr)**(9/16.0))**(8/27.0)))**2\n",
+ "q=hc*L*W*(Tw-T_inf)\n",
+ "\n",
+ "#Result\n",
+ "print\"The heat gained is %d BTU/hr\",round(q,0),\"BTU/hr\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The heat gained is %d BTU/hr 142.0 BTU/hr\n"
+ ]
+ }
+ ],
+ "prompt_number": 30
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 8.4 Page no. 421"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Determination of the variation of average convection coefficient with distance\n",
+ "# properties of air at (65 + 20)/2 = 42.5 degree C =315 K. from appendix table D1\n",
+ "rou= 1123 # density in kg/m^3 \n",
+ "cp= 1006.7 # specific heat in J/(kg*K) \n",
+ "v= 17.204e-6 # vismath.cosity in m^2/s \n",
+ "Pr =0.703 # Prandtl Number \n",
+ "kf= 0.02738 # thermal conductivity in W/(m.K)\n",
+ "a = 0.2446e-4 # diffusivity in m^2/s \n",
+ "g=9.81\n",
+ "L=5.0\n",
+ "theta=45\n",
+ "T_inf=20.0 # ambient air temperature in degree C\n",
+ "Tw=65 # roof surface temperature in degree C\n",
+ "Beta=1/(T_inf+273.0) # volumetric thermal math.expansion coefficient in per K\n",
+ "\n",
+ "#Calculation\n",
+ "import math\n",
+ "# determination of Laminar-turbulent transition length by Vliet equation Ra=3x10^5xmath.exp(0.1368math.cos(90-theta))\n",
+ "x=((3e5*math.exp(0.1368*math.cos(90-theta))*v*a)/(g*math.cos(theta)*Beta*(Tw-T_inf)))**(1/3.0)\n",
+ "x=0.051\n",
+ "print\"The Laminar-turbulent transition length by Vliet equation is \",round(x,3),\"m\\n\\n\"\n",
+ "lists=[0.02,0.04,0.051,0.051,0.1,1.0,3,5]\n",
+ "Ra=[0,0,0,0,0,0,0,0]\n",
+ "hc=[0,0,0,0,0,0,0,0]\n",
+ "print\"_______________________________________________________\"\n",
+ "print\"x(m)\\t\\tRaL\\t\\t\\thc(W/[m.K])\"\n",
+ "print\"_______________________________________________________\"\n",
+ "for i in range(0,8):\n",
+ " if lists[i]<x:\n",
+ " # Laminar Flow regime exists\n",
+ " Ra[i]=(g*math.cos(math.pi*45.0/180.0)*Beta*(Tw-T_inf)*lists[i]**3)/(v*a)\n",
+ " hc[i]=(kf/lists[i])*(0.68+(0.670*Ra[i]**(1/4.0))/(1+(0.492/Pr)**(9/16.0))**(4.0/9.0))\n",
+ " print lists[i],\"\\t\\t%.4g\"%Ra[i],\"\\t\\t%.3g\"%hc[i]\n",
+ " else:\n",
+ " # Turbulent Flow regime exists\n",
+ " Ra[i]=(g*Beta*(Tw-T_inf)*lists[i]**3)/(v*a)\n",
+ " hc[i]=(0.02738/lists[i])*(0.825+0.324*Ra[i]**(1/6.0))**2\n",
+ " print lists[i],\"\\t\\t%.4g\"%Ra[i],\"\\t\\t%.3g\"%hc[i]\n",
+ " \n",
+ "print\"\\n\\nNOTE:\\nCalculation mistake in book in calculation of Ral and hc,when x=0.04(2nd step in loop)\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Laminar-turbulent transition length by Vliet equation is 0.051 m\n",
+ "\n",
+ "\n",
+ "_______________________________________________________\n",
+ "x(m)\t\tRaL\t\t\thc(W/[m.K])\n",
+ "_______________________________________________________\n",
+ "0.02 \t\t2.025e+04 \t\t9.32\n",
+ "0.04 \t\t1.62e+05 \t\t7.52\n",
+ "0.051 \t\t4.749e+05 \t\t7.3\n",
+ "0.051 \t\t4.749e+05 \t\t7.3\n",
+ "0.1 \t\t3.58e+06 \t\t6.39\n",
+ "1.0 \t\t3.58e+09 \t\t4.99\n",
+ "3 \t\t9.667e+10 \t\t4.73\n",
+ "5 \t\t4.475e+11 \t\t4.66\n",
+ "\n",
+ "\n",
+ "NOTE:\n",
+ "Calculation mistake in book in calculation of Ral and hc,when x=0.04(2nd step in loop)\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 8.5 Page No. 424"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# determine if heat is lost lose more heat through its upper surface or one of its vertical sides\n",
+ "\n",
+ "#Given\n",
+ "# properties of air at (100 + 60)/2 = 80\u00b0F = 540 degree R from appendix table D1\n",
+ "rou= 0.0735 # density in lbm/cu.ft\n",
+ "cp=0.240 # specific heat BTU/(lbm-degree Rankine) \n",
+ "v= 16.88e-5 # viscosity in sq.ft/s \n",
+ "kf = 0.01516 # thermal conductivity in BTU/(hr.ft.degree Rankine) \n",
+ "a = 0.859 # diffusivity in sq.ft/hr \n",
+ "Pr = 0.708 # Prandtl Number\n",
+ "Tw=100.0 # temperature of outside surface temperature of oven in degree F\n",
+ "T_inf=60.0 # ambient temperature in degree F\n",
+ "g=32.2\n",
+ "L=2.0 # length in ft\n",
+ "W=2.0 # width in ft\n",
+ "\n",
+ "#Calculation\n",
+ "Beta=1/(T_inf+460.0) # volumetric thermal expansion coefficient in per degree Rankine\n",
+ "Ra=(g*Beta*(Tw-T_inf)*L**3)/(v*a/3600.0)\n",
+ "hc=(kf/L)*(0.68+(0.670*Ra**(0.25))/(1+(0.492/Pr)**(9/16.0))**(4/9.0))\n",
+ "q1side=hc*L*W*(Tw-T_inf)\n",
+ "# For the top, we have a heated surface facing upward, The characteristic length is determined as follows\n",
+ "Lc=0.5\n",
+ "Ra_L=(g*Beta*(Tw-T_inf)*Lc**3)/(v*a/3600.0) # Rayleigh number based on characteristic length\n",
+ "hc_L=(kf/Lc)*0.54*(Ra_L)**(1/4.0)\n",
+ "qtop=hc_L*L*W*(Tw-T_inf)\n",
+ "\n",
+ "#Result\n",
+ "print\"The heat transferred from one side is \",round(q1side,1),\"BTU/hr\"\n",
+ "print\"The heat transferred from top is \",round(qtop,0),\"BTU/hr\"\n",
+ "\n",
+ "if qtop < q1side:\n",
+ " \n",
+ " print\"More heat is transfered from side\" \n",
+ "else:\n",
+ " print \"More heat is transfered top side\"\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The heat transferred from one side is 93.7 BTU/hr\n",
+ "The heat transferred from top is 138.0 BTU/hr\n",
+ "More heat is transfered top side\n"
+ ]
+ }
+ ],
+ "prompt_number": 17
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 8.6 Page No.427"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# determination of heat lost from the insulation by convection\n",
+ "\n",
+ "#Given\n",
+ "# properties of air at (50 + 5)/2 = 27.5 degree C = 300 K from appendix table D1\n",
+ "rou= 1.177 # density in kg/cu.m\n",
+ "cp= 1005.7 # specific heat in J/(kg*K) \n",
+ "v= 15.68e-6 # viscosity in sq.m/s \n",
+ "Pr =0.708 # Prandtl Number \n",
+ "kf=0.02624 # thermal conductivity in W/(m.K)\n",
+ "a=0.22160e-4 # diffusivity in sq.m/s \n",
+ "g=9.81\n",
+ "L=4.0 # length in m\n",
+ "D=15/100.0 # diameter in m\n",
+ "T_inf=5.0 # ambient air temperature in degree C\n",
+ "Tw=50.0 # outside surface temperature in degree C\n",
+ "\n",
+ "#Calculation\n",
+ "import math\n",
+ "Beta=1/(T_inf+273.0) # volumetric thermal expansion coefficient in per K\n",
+ "Ra=(g*Beta*(Tw-T_inf)*D**3)/(v*a)\n",
+ "# for horizontal pipe, the convective coefficient is determined as follows\n",
+ "hc_h=(kf/D)*(0.60+(0.387*Ra**(1/6.0))/(1+(0.559/Pr)**(9/16.0))**(8/27.0))**2\n",
+ "As=math.pi*D*L\n",
+ "q_hor=hc_h*As*(Tw-T_inf)\n",
+ "# for vertical pipe, the convective coefficient is determined as follows\n",
+ "hc_v=(kf/D)*0.6*(Ra*(D/L))**(1/4.0)\n",
+ "q_ver=hc_v*As*(Tw-T_inf)\n",
+ "q=round(q_ver,0)+round(q_hor,0)\n",
+ "\n",
+ "#Result\n",
+ "print\"The heat transferred from the horizontal length of 4 m is \",round(q_hor,0),\"W\"\n",
+ "print\"The heat transferred from the vertical length of 4 m is \",round(q_ver,0),\"W\"\n",
+ "print\"nThe total heat lost from the pipe is \",round(q,2),\"W\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The heat transferred from the horizontal length of 4 m is 477.0 W\n",
+ "The heat transferred from the vertical length of 4 m is 246.0 W\n",
+ "nThe total heat lost from the pipe is 723.0 W\n"
+ ]
+ }
+ ],
+ "prompt_number": 52
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 8.7 Page No. 430"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Determinion of the convection coefficient about the ice cube\n",
+ "\n",
+ "#Given\n",
+ "# properties of air at (0 + 70)/2 = 35\u00b0F == 495 degree R from appendix table D1\n",
+ "rou= 0.0809 # density in lbm/cu.ft \n",
+ "cp=0.240 # specific heat BTU/(lbm-degree Rankine) \n",
+ "v= 13.54e-5 # viscosity in sq.ft/s \n",
+ "kf = 0.01402 # thermal conductivity in BTU/(hr.ft.degree Rankine) \n",
+ "a = 0.685 # diffusivity in sq.ft/hr \n",
+ "Pr = 0.712 # Prandtl Number\n",
+ "Tw=0 # temperature of outside surface temperature of oven in degree F\n",
+ "T_inf=70.0 # ambient temperature in degree F\n",
+ "g=32.2\n",
+ "Beta=1/(T_inf+460.0) # volumetric thermal expansion coefficient in per degree Rankine\n",
+ "# The characteristic length is found by using King Equation\n",
+ "Lc=1/((1/1)+(1/1.2))\n",
+ "Ra=(g*Beta*abs(Tw-T_inf)*Lc**3)/(v*a/3600.0)\n",
+ "hc=(kf/Lc)*0.6*(Ra)**(1/4.0)\n",
+ "\n",
+ "#Result\n",
+ "print\"The value of convection coefficient is \",round(hc,2),\"BTU/(hr.sq.ft.degree R)\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The value of convection coefficient is 1.11 BTU/(hr.sq.ft.degree R)\n"
+ ]
+ }
+ ],
+ "prompt_number": 54
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 8.8 Page No.433"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# determination of the maximum amount of heat that fins can transfer\n",
+ "\n",
+ "#Given\n",
+ "# properties of air at (100 + 35)/2 = 67.5 degree C from appendix table D1\n",
+ "rou= 0.998 # density in kg/cu.m\n",
+ "cp= 1009.0 # specific heat in J/(kg*K) \n",
+ "v= 20.76e-6 # viscosity in sq.m/s \n",
+ "Pr =0.697 # Prandtl Number \n",
+ "kf= 0.03003 # thermal conductivity in W/(m.K)\n",
+ "a = 0.2983e-4 # diffusivity in sq.m/s \n",
+ "g=9.81\n",
+ "T_inf=35 # ambient air temperature in degree C\n",
+ "Tw=100 # surface temperature in degree C\n",
+ "Beta=1/(T_inf+273.0) # volumetric thermal expansion coefficient in per K\n",
+ "# properties of aluminium from appendix table B1\n",
+ "rou_Al=2702 # density in kg/cu.m\n",
+ "k_Al=236 # thermal conductivity in W/(m.K)\n",
+ "cp_Al=896 # specific heat in J/(kg*K) \n",
+ "a_Al=97.5e-6 # diffusivity in sq.m/s \n",
+ "b=46/100.0\n",
+ "w=24/100.0\n",
+ "\n",
+ "#Calculation\n",
+ "# Applying the Bar-Cohen Equations\n",
+ "zeta=((w*v**2)/(g*Beta*(Tw-T_inf)*Pr))**(1/4.0)\n",
+ "L=1.54*(k_Al/kf)**(1/2)*zeta\n",
+ "S=2.89*zeta\n",
+ "q=(b*w*(Tw-T_inf)*1.3*(k_Al*kf)**(1/2.0))/(6*zeta)\n",
+ "N=b/(2*S)\n",
+ "\n",
+ "#result\n",
+ "print\"The heat transfer rate is \",round(q,0),\"W\"\n",
+ "print\"The number of fins can be atmost\",round(N,0)\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The heat transfer rate is 1423.0 W\n",
+ "The number of fins can be atmost 27.0\n"
+ ]
+ }
+ ],
+ "prompt_number": 59
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Engineering_Heat_Transfer/CHAPTER9.ipynb b/Engineering_Heat_Transfer/CHAPTER9.ipynb new file mode 100644 index 00000000..c1ada237 --- /dev/null +++ b/Engineering_Heat_Transfer/CHAPTER9.ipynb @@ -0,0 +1,571 @@ +{
+ "metadata": {
+ "name": "CHAPTER9"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 9: Heat Exchanger"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.1 Page No.458"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# determination of counterflow and parallel-flow configurations. \n",
+ "\n",
+ "#Given\n",
+ "# temperatures of hot fluid in degree C\n",
+ "T1=100.0 \n",
+ "T2=75.0\n",
+ "# temperatures of cold fluid in degree C\n",
+ "t1=5.0\n",
+ "t2=50.0\n",
+ "\n",
+ "#Calculation\n",
+ "# for counterflow\n",
+ "import math\n",
+ "LMTD_counter=((T1-t2)-(T2-t1))/(math.log((T1-t2)/(T2-t1)))\n",
+ "# for parallel flow\n",
+ "LMTD_parallel=((T1-t1)-(T2-t2))/(math.log((T1-t1)/(T2-t2)))\n",
+ "\n",
+ "#Result\n",
+ "print\"The LMTD for counter flow configuration is \",round(LMTD_counter,1),\"C\"\n",
+ "print\"The LMTD for parallel flow configuration is \",round(LMTD_parallel,2),\"C\""
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The LMTD for counter flow configuration is 59.4 C\n",
+ "The LMTD for parallel flow configuration is 52.43 C\n"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.2 Page No. 459"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Determination of the LMTD for both counterflow and parallel-flow configurations. \n",
+ "\n",
+ "#Given\n",
+ "# temperatures of hot fluid in degree F\n",
+ "T1=250\n",
+ "T2=150\n",
+ "# temperatures of cold fluid in degree F\n",
+ "t1=100\n",
+ "t2=150\n",
+ "\n",
+ "#calculation\n",
+ "# for counterflow\n",
+ "import math\n",
+ "LMTD_counter=((T1-t2)-(T2-t1))/(math.log((T1-t2)/(T2-t1)));\n",
+ "# for parallel flow\n",
+ "LMTD_parrelel=0\n",
+ "\n",
+ "#Result\n",
+ "print\"The LMTD for counter flow configuration is\",round(LMTD_counter,1),\"C\"\n",
+ "print\"if parallel flow is to give equal outlet temperatures,then the area needed must be infinite which is not feasible economically.\"\n",
+ "print\"The LMTD for parrelel flow configuration is\",LMTD_parrelel,\"C\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The LMTD for counter flow configuration is 72.1 C\n",
+ "if parallel flow is to give equal outlet temperatures,then the area needed must be infinite which is not feasible economically.\n",
+ "The LMTD for parrelel flow configuration is 0 C\n"
+ ]
+ }
+ ],
+ "prompt_number": 8
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.3 Page No.463"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Determination of the outlet temperature of the ethylene glycol for counterflow.\n",
+ "\n",
+ "#Given\n",
+ "# properties of air at (195 + 85)/2 = 140\u00b0F. from appendix table CII\n",
+ "rou_1= 0.985*62.4 # density in lbm/ft**3 \n",
+ "cp_1=0.9994 # specific heat BTU/(lbm-degree Rankine) \n",
+ "v_1= 0.514e-5 # viscosity in ft**2/s \n",
+ "kf_1 = 0.376 # thermal conductivity in BTU/(hr.ft.degree Rankine) \n",
+ "a_1 = 6.02e-3 # diffusivity in ft**2/hr \n",
+ "Pr_1 = 3.02 # Prandtl Number \n",
+ "m_1=5000 # mass flow rate in lbm/hr\n",
+ "T_1=195 # temperature in degree F\n",
+ "# properties of ethylene glycol at 140 degree F from Appendix Table C.5\n",
+ "rou_2= 1.087*62.4 # density in lbm/ft**3 \n",
+ "cp_2=0.612 # specific heat BTU/(lbm-degree Rankine) \n",
+ "v_2= 5.11e-5 # viscosity in ft**2/s \n",
+ "kf_2 = 0.150 # thermal conductivity in BTU/(hr.ft.degree Rankine) \n",
+ "a_2 = 3.61e-3 # diffusivity in ft**2/hr \n",
+ "Pr_2 = 51 # Prandtl Number \n",
+ "m_2=12000 # mass flow rate in lbm/hr\n",
+ "T_2=85 # temperature in degree F\n",
+ "# specifications of seamless copper water tubing (subscripts: a = annulus, p = inner pipe or tube) from appendix table F2\n",
+ "ID_a=0.1674\n",
+ "ID_p=0.1076\n",
+ "OD_p=1.375/12\n",
+ "# Flow Areas\n",
+ "A_p=math.pi*ID_p**2/4\n",
+ "A_a=math.pi*((ID_a)**2-(OD_p)**2)/4\n",
+ "\n",
+ "# Annulus Equivalent Diameters\n",
+ "D_h=ID_a-OD_p\n",
+ "D_e=(ID_a**2-OD_p**2)/(OD_p)\n",
+ "\n",
+ "# Reynolds Numbers \n",
+ "Re_1=(m_1/3600.0)*(ID_p)/(v_1*rou_1*A_p)\n",
+ "Re_2=(m_2/3600.0)*(D_e)/(v_2*rou_2*A_a)\n",
+ "\n",
+ "# Nusselt numbers\n",
+ "Nu_1=0.023*(Re_1)**(4/5.0)*(Pr_1)**0.3\n",
+ "Nu_2=0.023*(Re_2)**(4/5.0)*(Pr_2)**0.4\n",
+ "\n",
+ "# Convection Coefficients \n",
+ "h_1i=Nu_1*kf_1/ID_p\n",
+ "h_1o=h_1i*ID_p/OD_p\n",
+ "h_2=Nu_2*kf_2/D_e\n",
+ "\n",
+ "# Exchanger Coefficient \n",
+ "Uo=1/((1/h_1o)+(1/h_2))\n",
+ "R=(m_2*cp_2)/(m_1*cp_1)\n",
+ "L=20\n",
+ "A=math.pi*OD_p*L\n",
+ "T1=195\n",
+ "t1=85\n",
+ "T2=((T1*(R-1))-(R*t1*(1-exp((Uo*A*(R-1))/(m_2*cp_2)))))/(R*exp(Uo*A*(R-1)/(m_2*cp_2))-1)\n",
+ "t2=t1+(T1-T2)/R\n",
+ "print\"The outlet temperature of Ethylene glycol is %.1f degree F\",round(t2,1),\"F\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The outlet temperature of Ethylene glycol is %.1f degree F 99.4 F\n"
+ ]
+ }
+ ],
+ "prompt_number": 14
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.4 Page No. 467"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Determination of (a) no. of exchangers required, (b) the overall coefficient of (all) the exchanger(s), and (c) the pressure drop for each stream. \n",
+ "\n",
+ "#Given\n",
+ "# assuming counterflow arrangement\n",
+ "# properties of air at 323 K. from appendix table D1\n",
+ "rou_1= 1.088 \t\t# density in kg/m**3 \n",
+ "cp_1= 1007\t\t # specific heat in J/(kg*K) \n",
+ "v_1= 18.2e-6\t\t # viscosity in m**2/s \n",
+ "Pr_1 =0.703 \t\t# Prandtl Number \n",
+ "kf_1= 0.02814 \t\t# thermal conductivity in W/(m.K)\n",
+ "a_1 = 0.26e-4 \t\t# diffusivity in m**2/s \n",
+ "m_1=100 \t\t # mass flow rate in kg/hr\n",
+ "# temperatures in K\n",
+ "t1_air=20+273 \n",
+ "t2_air=80+273\n",
+ "# properties of carbon dioxide at [600 + (20 + 273)]/2 = 480 = 500 K. from appendix table D2\n",
+ "rou_2= 1.0732\t\t # density in kg/m**3 \n",
+ "cp_2= 1013 \t\t# specific heat in J/(kg*K) \n",
+ "v_2= 21.67e-6 \t #viscosity in m**2/s \n",
+ "Pr_2 =0.702 \t\t# Prandtl Number \n",
+ "kf_2= 0.03352 \t\t# thermal conductivity in W/(m.K)\n",
+ "a_2 = 0.3084e-4 \t\t# diffusivity in m**2/s \n",
+ "m_2=90\t\t\t # mass flow rate in kg/hr\n",
+ "# temperatures in K\n",
+ "T1_CO2=600 \n",
+ "# specifications of seamless copper tubing from appendix table F2\n",
+ "ID_a=.098\n",
+ "ID_p=.07384\n",
+ "OD_p=.07938\n",
+ "\n",
+ "#calculation\n",
+ "import math\n",
+ "# Flow Areas\n",
+ "A_p=math.pi*ID_p**(2)/4.0\n",
+ "A_a=math.pi*((ID_a)**2-(OD_p)**2)/4.0\n",
+ "\n",
+ "# Heat Balance \n",
+ "q_air=(m_1/3600.0)*(cp_1)*(t2_air-t1_air)\n",
+ "T2_CO2=T1_CO2-(q_air/(m_2*cp_2/3600.0))\n",
+ "\n",
+ "# Log-Mean Temperature Difference\n",
+ "LMTD_counter=((T1_CO2-t2_air)-(T2_CO2-t1_air))/(log((T1_CO2-t2_air)/(T2_CO2-t1_air)))\n",
+ "# Annulus Equivalent Diameters\n",
+ "D_h=ID_a-OD_p\n",
+ "D_e=(ID_a**2-OD_p**2)/(OD_p)\n",
+ "\n",
+ "# Reynolds Numbers \n",
+ "Re_1=(m_1/3600.0)*(ID_p)/(v_1*rou_1*A_p)\n",
+ "Re_2=(m_2/3600.0)*(D_e)/(v_2*rou_2*A_a)\n",
+ "\n",
+ "# Nusselt numbers\n",
+ "Nu_1=0.023*(Re_1)**(0.8)*(Pr_1)**0.3\n",
+ "Nu_2=0.023*(Re_2)**(0.8)*(Pr_2)**0.4\n",
+ "\n",
+ "# Convection Coefficients \n",
+ "\n",
+ "h_1i=Nu_1*kf_1/ID_p\n",
+ "h_1o=h_1i*ID_p/OD_p\n",
+ "h_2=Nu_2*kf_2/D_e\n",
+ "\n",
+ "# Fouling Factors in (m**2.K)/W\n",
+ "Rd_air=0.0004\n",
+ "Rd_CO2=0.002\n",
+ "\n",
+ "# exchanger coefficients\n",
+ "Uo=1/((1/h_1o)+(1/h_2))\n",
+ "Uo=1/((1/Uo)+Rd_air+Rd_CO2)\n",
+ "\n",
+ "# area required\n",
+ "A=q_air/(Uo*LMTD_counter)\n",
+ "\n",
+ "# surface area of one exchanger is A=math.pi*OD*L, so\n",
+ "L=(A/(math.pi*OD_p)) # length of each exchanger\n",
+ "L_available=2 # available exchanger length\n",
+ "N=L_available/L # no. of exchangers\n",
+ "\n",
+ "#friction factors\n",
+ "fp=0.0245 #friction factor for air fom figure 6.14 corresponding to Re\n",
+ "fa=0.033 #friction factor for cCO2fom figure 6.14 corresponding to Re\n",
+ "# Velocities\n",
+ "V_air=(m_1/3600.0)/(rou_1*A_p)\n",
+ "V_CO2=(m_2/3600.0)/(rou_2*A_a)\n",
+ "\n",
+ "# pressure drops\n",
+ "dP_p=(fp*L_available*rou_1*V_air**2)/(ID_p*2)\n",
+ "dP_a=((rou_2*V_CO2**2)/2.0)*((fa*L_available/D_h)+1)\n",
+ "\n",
+ "#Result\n",
+ "print\"(a)The number of exchangers is \",round(N,0)\n",
+ "print\"(b)The overall exchanger coefficient is \",round(Uo,1),\" W/(sq.m.K)\"\n",
+ "print\"(c)The pressure drop for tube side is \",round(dP_p,2),\"Pa\"\n",
+ "print\"The pressure drop for shell side is \",round(dP_a,1),\"Pa\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(a)The number of exchangers is 1.0\n",
+ "(b)The overall exchanger coefficient is 14.2 W/(sq.m.K)\n",
+ "(c)The pressure drop for tube side is 12.83 Pa\n",
+ "The pressure drop for shell side is 196.7 Pa\n"
+ ]
+ }
+ ],
+ "prompt_number": 24
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.5 Page No. 484"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Determination of the outlet temperature of the distilled water and the pressure drop for each stream. \n",
+ "\n",
+ "#Given\n",
+ "# properties of (distilled) water at 104\u00b0F from appendix table CII\n",
+ "rou_1= 0.994*62.4 # density in lbm/ft**3 \n",
+ "cp_1=0.998 # specific heat BTU/(lbm-degree Rankine) \n",
+ "v_1= 0.708e-5 # viscosity in ft**2/s \n",
+ "kf_1 = 0.363 # thermal conductivity in BTU/(hr.ft.degree Rankine) \n",
+ "a_1 = 5.86e-3 # diffusivity in ft**2/hr \n",
+ "Pr_1 = 4.34 # Prandtl Number \n",
+ "m_1=170000 # mass flow rate in lbm/hr\n",
+ "T1=110.0 # temperature in degree F\n",
+ "# properties of (raw) water at 68\u00b0F from Appendix Table C11\n",
+ "rou_2= 62.4 # density in lbm/ft**3 \n",
+ "cp_2=0.9988 # specific heat BTU/(lbm-degree Rankine) \n",
+ "v_2= 1.083e-5 # viscosity in ft**2/s \n",
+ "kf_2 = 0.345 # thermal conductivity in BTU/(hr.ft.degree Rankine) \n",
+ "a_2 = 5.54e-3 # diffusivity in ft**2/hr \n",
+ "Pr_2 = 7.02 # Prandtl Number \n",
+ "m_2=150000 # mass flow rate in lbm/hr\n",
+ "t1=65 # temperature in degree F\n",
+ "# specifications of 3/4-in-OD, 18-BWG tubes, from table 9.2\n",
+ "OD=3/(4*12.0)\n",
+ "ID=0.652/12.0\n",
+ "OD_p=1.375/12.0\n",
+ "Nt=224.0 # from table 9.3\n",
+ "Np=2 # no. of tube passes\n",
+ "# Shell dimensions and other miscellaneous data\n",
+ "Ds=17.25/12.0\n",
+ "Nb=15.0 # no. of baffles\n",
+ "B=1\n",
+ "sT=15/(16*12.0)\n",
+ "C=sT-OD\n",
+ "\n",
+ "#CALCULATION\n",
+ "import math\n",
+ "# flow areas\n",
+ "At=(Nt*math.pi*ID**2)/(4*Np)\n",
+ "As=(Ds*C*B)/sT\n",
+ "\n",
+ "# Shell Equivalent Diameter \n",
+ "De=4*((sT/2.0)*(0.86*sT)-(math.pi*OD**2/8.0))/(math.pi*OD/2.0)\n",
+ "\n",
+ "# Reynolds Numbers \n",
+ "Re_s=(m_1/3600.0)*(De)/(v_1*rou_1*As)\n",
+ "Re_t=(m_2/3600.0)*(ID)/(v_2*rou_2*At)\n",
+ "\n",
+ "# Nusselt numbers\n",
+ "Nu_t=0.023*(Re_t)**(0.8)*(Pr_2)**0.4\n",
+ "Nu_s=0.36*(Re_s)**(0.55)*(Pr_1)**(1/3.0)\n",
+ "h_ti=Nu_t*kf_2/ID\n",
+ "h_to=h_ti*ID/OD\n",
+ "h_s=Nu_s*kf_1/De\n",
+ "\n",
+ "# Exchanger Coefficient \n",
+ "Uo=1/((1/h_to)+(1/h_s))\n",
+ "R=(m_2*cp_2)/(m_1*cp_1)\n",
+ "L=16\n",
+ "Ao=Nt*math.pi*OD*L\n",
+ "UoAo_mccp=(Uo*Ao)/(m_2*cp_2)\n",
+ "S=0.58 #value of S from fig. 9.13 Ten Broeck graph corresponding to the value of (UoAo)/(McCpc)\n",
+ "t2=S*(T1-t1)+t1\n",
+ "T2=T1-R*(t2-t1)\n",
+ "#friction factors\n",
+ "ft=0.029 #friction factor for raw water fom figure 6.14 corresponding to Reynolds Number calculated above\n",
+ "fs=0.281 #friction factor for distilled water fom figure 6.14 corresponding to Reynolds Number calculated above\n",
+ "\n",
+ "# Velocities\n",
+ "V_t=(m_2/3600.0)/(rou_2*At)\n",
+ "V_s=(m_1/3600.0)/(rou_1*As)\n",
+ "\n",
+ "# pressure drops\n",
+ "gc=32.2\n",
+ "dP_t=(rou_2*V_t**2)*((ft*L*Np/ID)+4*Np)/(2*gc)\n",
+ "dP_s=((rou_1*V_s**2)*(fs*Ds*(Nb+1)))/(2*gc*De)\n",
+ "\n",
+ "#Result\n",
+ "print\"Outlet Temperatures of raw water is \",round(t2,1),\"F\"\n",
+ "print\"Outlet Temperatures of distilled water is \",round(T2,1),\"F\"\n",
+ "print\"\\nThe pressure drop for tube side is\",round(dP_t/147,1),\"psi\"\n",
+ "print\"The pressure drop for shell side is\",round(dP_s/147,1),\"psi\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.6 Page No.492"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Using the effectiveness-NTU method to calculate the outlet temperatures of the fluids\n",
+ "\n",
+ "#Given\n",
+ "# Data from Example 9.5\n",
+ "# properties of (distilled) water at 104\u00b0F \n",
+ "m_1=170000 \t\t# mass flow rate in lbm/hr\n",
+ "T1=110 \t\t\t# temperature in degree F\n",
+ "cp_1=0.998\t\t # specific heat BTU/(lbm-degree Rankine) \n",
+ "# properties of (raw) water at 68\u00b0F \n",
+ "m_2=150000 \t\t# mass flow rate in lbm/hr\n",
+ "t1=65 \t\t\t# temperature in degree F\n",
+ "cp_2=0.9988\t # specific heat BTU/(lbm-degree Rankine) \n",
+ "Uo=350 \t\t\t# exchanger coefficient\n",
+ "Ao=703.7\n",
+ "# The effectiveness-NTU approach is used when the overall heat transfer coefficient is known\n",
+ "# determining the capacitances\n",
+ "mcp_raw=m_2*cp_2\n",
+ "mcp_distilled=m_1*cp_1\n",
+ "\n",
+ "# determination of parameters for determining effectiveness\n",
+ "mcp_min_max=mcp_raw/mcp_distilled\n",
+ "UA_mcpmin=(Uo*Ao)/(mcp_raw)\n",
+ "effectiveness=0.58 \t\t#value of effectiveness from figure 9.15 corresponding to the above calculated values of capacitance ratio and (UoAo/mcp_min)\n",
+ "qmax=mcp_raw*(T1-t1)\n",
+ "q=effectiveness*qmax \t# actual heat transfer\n",
+ "t2=(q/mcp_raw)+t1\n",
+ "T2=T1-(q/mcp_distilled)\n",
+ "\n",
+ "#Result\n",
+ "print\"The Outlet temperature is Raw Water is\",round(t2,1),\"F\"\n",
+ "print\"The Outlet temperature is disilled Water is\",round(T2,1),\"F\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Outlet temperature is Raw Water is 91.1 F\n",
+ "The Outlet temperature is disilled Water is 87.0 F\n"
+ ]
+ }
+ ],
+ "prompt_number": 39
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 9.7 Page No. 499"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# (a) Determine the UA product for the exchanger. (b) Calculate the exit temperatures for the exchanger, assuming that only the inlet temperatures are known\n",
+ "# properties of engine oil at (190 + 158)/2 = 174\u00b0F = 176 degree F from appendix table C4\n",
+ "rou_1= 0.852*62.4\t\t # density in lbm/ft**3 \n",
+ "cp_1=0.509\t\t # specific heat BTU/(lbm-degree Rankine) \n",
+ "v_1=0.404e-3 \t\t# viscosity in ft**2/s \n",
+ "kf_1=0.08 \t\t# thermal conductivity in BTU/(hr.ft.degree Rankine) \n",
+ "a_1=2.98e-3 \t# diffusivity in ft**2/hr \n",
+ "Pr_1=490.0 \t\t# Prandtl Number \n",
+ "m_1=39.8 \t\t # mass flow rate in lbm/min\n",
+ "# temperatures in degree F\n",
+ "T1=190.0\n",
+ "T2=158.0\n",
+ "# properties of air at (126 + 166)/2 = 146\u00b0F = 606 degree R from appendix table D1\n",
+ "rou_2= 0.0653\t\t # density in lbm/ft**3 \n",
+ "cp_2=0.241\t\t # specific heat BTU/(lbm-degree Rankine) \n",
+ "v_2= 20.98e-5 \t\t# viscosity in ft**2/s \n",
+ "kf_2 = 0.01677 \t\t # thermal conductivity in BTU/(hr.ft.degree Rankine) \n",
+ "a_2 = 1.066 \t\t# diffusivity in ft**2/hr \n",
+ "Pr_2 = 0.706 \t\t# Prandtl Number \n",
+ "m_2=67.0 \t\t\t# mass flow rate in lbm/min\n",
+ "# temperatures in degree F\n",
+ "t1=126.0\n",
+ "t2=166.0\n",
+ "# Heat Balance\n",
+ "q_air=m_2*cp_2*60*(t2-t1)\n",
+ "q_oil=m_1*cp_1*60*(T1-T2)\n",
+ "\n",
+ "# for counterflow\n",
+ "import math\n",
+ "LMTD=((T1-t2)-(T2-t1))/(math.log((T1-t2)/(T2-t1)))\n",
+ "# Frontal Areas for Each Fluid Stream\n",
+ "Area_air=(9.82*8)/144.0\n",
+ "Area_oil=(3.25*9.82)/144.0\n",
+ "\n",
+ "# Correction Factors (parameters calculated first)\n",
+ "S=(t2-t1)/(T1-t1)\n",
+ "R=(T1-T2)/(t2-t1)\n",
+ "F=0.87 #value of correction factor from figure 9.21a corresponding to above calculated values of S and R\n",
+ "# Overall Coefficient (q = U*A*F*LMTD)\n",
+ "UA=q_air/(F*LMTD)\n",
+ "# determining the capacitances\n",
+ "mcp_air=m_2*cp_2*60\n",
+ "mcp_oil=m_1*cp_1*60\n",
+ "\n",
+ "# determination of parameters for determining effectiveness\n",
+ "mcp_min_max=mcp_air/mcp_oil\n",
+ "NTU=(UA/mcp_air)\n",
+ "effectiveness=0.62 \t\t#effectiveness from fig 9.21b corresponding to the values of capacitance ratio \n",
+ "t2_c=(T1-t1)*effectiveness+t1\n",
+ "T2_c=T1-(mcp_air)*(t2_c-t1)/(mcp_oil)\n",
+ "\n",
+ "#Result\n",
+ "print\"The Overall Coefficient is \",round(UA,0),\" BTU/(hr. degree R)\"\n",
+ "print\"Calculated outlet temprature are:\"\n",
+ "print\"Outlet temprature for air\",round(t2_c,1),\"F\"\n",
+ "print\"Outlet temprature for Engine Oil\",round(T2_c,0),\"F\"\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The Overall Coefficient is 1602.0 BTU/(hr. degree R)\n",
+ "Calculated outlet temprature are:\n",
+ "Outlet temprature for air 165.7 F\n",
+ "Outlet temprature for Engine Oil 158.0 F\n"
+ ]
+ }
+ ],
+ "prompt_number": 21
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Engineering_Heat_Transfer/CHAPTER_3.ipynb b/Engineering_Heat_Transfer/CHAPTER_3.ipynb new file mode 100644 index 00000000..93f29ad1 --- /dev/null +++ b/Engineering_Heat_Transfer/CHAPTER_3.ipynb @@ -0,0 +1,339 @@ +{
+ "metadata": {
+ "name": "CHAPTER 3"
+ },
+ "nbformat": 3,
+ "nbformat_minor": 0,
+ "worksheets": [
+ {
+ "cells": [
+ {
+ "cell_type": "heading",
+ "level": 1,
+ "metadata": {},
+ "source": [
+ "Chapter 3:Steady-State Conduction in Multiple Dimensions"
+ ]
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 3.1 Page No.132"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Determination of the heat-flow rate from one tube \n",
+ "# specifications of 1 standard type K from table F2\n",
+ "\n",
+ "#iven\n",
+ "OD=0.02858 # outer diameter in m\n",
+ "# from figure 3.11\n",
+ "M=8.0 # total number of heat-flow lanes\n",
+ "N=6.0 # number of squares per lane\n",
+ "S_L=M/N # conduction shape factor\n",
+ "k=0.128 # thermal conductivity in W/(m.K) for concrete from appendix table B3\n",
+ "T1=85 # temperature of tube surface\n",
+ "T2=0 # temperature of ground beneath the slab\n",
+ "\n",
+ "#Calculation\n",
+ "q_half=k*S_L*(T1-T2)\n",
+ "q=2*q_half\n",
+ "\n",
+ "#Result\n",
+ "print\"The total heat flow per tube is\",round(q,0),\" W/m\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The total heat flow per tube is 29.0 W/m\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 3.2 Page No.134"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Determination of the heat transferred from the buried pipe per unit length\n",
+ "# shape factor number 8 is selected from table 3.1\n",
+ "# specifications of 10 nominal, schedule 80 pipe from table F1\n",
+ "\n",
+ "#Given\n",
+ "import math\n",
+ "OD=10.74/12 # diameter in ft\n",
+ "R=OD/2\n",
+ "T1=140.0\n",
+ "T2=65.0\n",
+ "k=0.072 # thermal conductivity in BTU/(hr-ft. degree R)\n",
+ "d=18.0/12.0 # distance from centre-line\n",
+ "S_L=(2*math.pi)/(math.acosh(d/R))\n",
+ "q_L=k*S_L*(T1-T2)\n",
+ "print\"The heat transferred from the buried pipe per unit length is \",round(q_L,2),\"BTU/(hr.ft)\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The heat transferred from the buried pipe per unit length is 18.05 BTU/(hr.ft)\n"
+ ]
+ }
+ ],
+ "prompt_number": 7
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 3.3 Page No.135"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Determination of the heat lost through the walls, using the shape-factor method. \n",
+ "#(b) Repeat the calculations but neglect the effects of the corners that is, . \n",
+ "\n",
+ "#Given\n",
+ "k = 1.07 # thermal conductivity of silica brick from appendix table B3 in W/(m.K)\n",
+ "S1_A=0.138*0.138/0.006\n",
+ "nA=2\n",
+ "\n",
+ "# Calculation of total shape factor\n",
+ "# From figure 3.12, for component A\n",
+ "St_A=nA*S1_A # Total shape factor of component A\n",
+ "\n",
+ "# For component B\n",
+ "S1_B=0.138*0.188/0.006\n",
+ "nB=4\n",
+ "St_B=nB*S1_B # Total shape factor of component B\n",
+ "\n",
+ "# For component C\n",
+ "S3_C=0.15*0.006\n",
+ "nC=8\n",
+ "St_C=nC*S3_C # Total shape factor of component C\n",
+ "\n",
+ "# For component D\n",
+ "S2_D=0.54*0.188\n",
+ "nD=4\n",
+ "St_D=nD*S2_D # Total shape factor of component D\n",
+ "\n",
+ "# For component E\n",
+ "S2_E=0.138*0.54\n",
+ "nE=8\n",
+ "St_E=nE*S2_E # Total shape factor of component E\n",
+ "\n",
+ "S=St_A+St_B+St_C+St_D+St_E\n",
+ "T1=550\n",
+ "T2=30\n",
+ "q=k*S*(T1-T2)\n",
+ "S=St_A+St_B\n",
+ "q_1=k*S*(T1-T2)\n",
+ "Error=(q-q_1)/q\n",
+ "\n",
+ "#result\n",
+ "print\"(a)The heat transferred through the walls of the furnace is \",round(q/1000,1),\"kw\"\n",
+ "# Neglecting the effects of the edges and corners, the shape factor for all walls is found as \n",
+ "print\"(b The heat transferred is\",q_1/1000,1,\"kw\"\n",
+ "print\" The error introduced by neglecting heat flow through the edges and corners is \",round(Error*100,1),\" percent\"\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "(a)The heat transferred through the walls of the furnace is 13.7 kw\n",
+ "(b The heat transferred is 13.1555216 1 kw\n",
+ " The error introduced by neglecting heat flow through the edges and corners is 4.1 percent\n"
+ ]
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 3.4 Page No. 142"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "# Determination of the conduction shape factor for the underground portion of the configuration\n",
+ "# specifications of 4 nominal, schedule 40 pipe from table F1\n",
+ "\n",
+ "#Given\n",
+ "OD=4.5/12.0 # diameter in ft\n",
+ "R=OD/2.0\n",
+ "\n",
+ "# For pipe A\n",
+ "#calculation\n",
+ "import math\n",
+ "L_A=4.5 # length in ft\n",
+ "# shape factor number 9 is selected from table 3.1\n",
+ "S_A=(2*math.pi*L_A)/(math.log(2*(L_A)/R))\n",
+ "# For pipe B\n",
+ "L_B=18 # length in ft\n",
+ "# shape factor number 9 is selected from table 3.1\n",
+ "S_B=(2*math.pi*L_B)/(math.acosh(L_A/R))\n",
+ "S=2*S_A+S_B\n",
+ "\n",
+ "#Result\n",
+ "print\"The total conduction shape factor for the system is\",round(S,1)\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The total conduction shape factor for the system is 43.8\n"
+ ]
+ }
+ ],
+ "prompt_number": 3
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 3.5 Page No. 151"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "%pylab inline"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "#(a)plot graph the temperature distribution existing within the rod. \n",
+ "#(b) Use the numerical formulation of this section to obtain the temperature distribution.\n",
+ "#(c) Compare the two models to determine how well the numerical results approximate the exact results\n",
+ "\n",
+ "#Given\n",
+ "h=1.1 # convective coefficient in BTU/(hr.ft^2. degree R)\n",
+ "Tw=200.0\n",
+ "T_inf=68.0 # ambient temperature\n",
+ "k=0.47 # thermal conductivity in BTU/(hr.ft.degree R) from table B3\n",
+ "D=0.25/12 # diameter in ft\n",
+ "\n",
+ "#Calculation\n",
+ "A=math.pi*D**(2)/4.0 # cross sectional area in ft^2\n",
+ "P=math.pi*D # perimeter in ft\n",
+ "L=6/12.0 # length in ft\n",
+ "mL=L*((h*P)/(k*A))**(0.5)\n",
+ "dz=1.0\n",
+ "L=4.0\n",
+ "de=dz/L\n",
+ "K=2+(mL*de)**2\n",
+ "\n",
+ "#Tempature can be calculated as\n",
+ "T4=T_inf+(Tw-T_inf)*(2/(K**4-4*K**2+2))\n",
+ "T3=T_inf+(Tw-T_inf)*(K/(K**4-4*K**2+2))\n",
+ "T2=T_inf+(Tw-T_inf)*((K**2-1)/(K**4-4*K**2+2))\n",
+ "T1=T_inf+(Tw-T_inf)*((K**3-3*K)/(K**4-4*K**2+2))\n",
+ "\n",
+ "#result\n",
+ "print\"The temprature distribution is T4=\",round(T4,2),\"F\"\n",
+ "print\"The temprature distribution is T3=\",round(T3,2),\"F\"\n",
+ "print\"The temprature distribution is T2=\",round(T2,2),\"F\"\n",
+ "print\"The temprature distribution is T1=\",round(T1,2),\"F\"\n",
+ "\n",
+ "#(b)plot\n",
+ "import matplotlib.pyplot as plt\n",
+ "import numpy as np\n",
+ "T=[200.0,77.33,68.66,68.05,68]\n",
+ "z=[0,1.5,3,4.5,6]\n",
+ "xlim(0,6)\n",
+ "ylim(50,200)\n",
+ "plt.ylabel('T (C)')\n",
+ "plt.xlabel('z (in)')\n",
+ "plt.annotate('Numeric approximation using 4 nodes', xy=(2,82), xytext=(0,30),\n",
+ " arrowprops=dict(facecolor='black', shrink=0.05),\n",
+ " )\n",
+ "a=plot(z,T)\n",
+ "\n",
+ "T1=[200.0,82.81,69.66,68.19,68.04]\n",
+ "plt.ylabel('T1 (F)')\n",
+ "plt.xlabel('z (in)')\n",
+ "plt.annotate('exact solution', xy=(1.5,80), xytext=(0,60),\n",
+ " arrowprops=dict(facecolor='black', shrink=0.05),\n",
+ " )\n",
+ "a=plot(z,T1)\n",
+ "show(a)\n",
+ "\n"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": [
+ {
+ "output_type": "stream",
+ "stream": "stdout",
+ "text": [
+ "The temprature distribution is T4= 68.04 F\n",
+ "The temprature distribution is T3= 68.19 F\n",
+ "The temprature distribution is T2= 69.68 F\n",
+ "The temprature distribution is T1= 82.82 F\n"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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nhs/kvd3vUVhcqG4wIUSVJQWhGps6FebPB0WBDm4daOnUkpijMWrHEkJUUVIQ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\nVq147rnnOHv2LB4eHqxZs4Z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+ "text": [
+ "<matplotlib.figure.Figure at 0x752b7f0>"
+ ]
+ }
+ ],
+ "prompt_number": 2
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ }
+ ],
+ "metadata": {}
+ }
+ ]
+}
\ No newline at end of file diff --git a/Engineering_Heat_Transfer/README.txt b/Engineering_Heat_Transfer/README.txt new file mode 100644 index 00000000..0da6ee5a --- /dev/null +++ b/Engineering_Heat_Transfer/README.txt @@ -0,0 +1,10 @@ +Contributed By: Ankit Garg +Course: btech +College/Institute/Organization: DCRUST, Murthal +Department/Designation: Chemical Engineering +Book Title: Engineering Heat Transfer +Author: W S Janna +Publisher: CRC Press +Year of publication: 1999 +Isbn: 9780849321269 +Edition: 2
\ No newline at end of file diff --git a/Engineering_Heat_Transfer/screenshots/heat_transferred.png b/Engineering_Heat_Transfer/screenshots/heat_transferred.png Binary files differnew file mode 100644 index 00000000..12f4f4a9 --- /dev/null +++ b/Engineering_Heat_Transfer/screenshots/heat_transferred.png diff --git a/Engineering_Heat_Transfer/screenshots/length_required.png b/Engineering_Heat_Transfer/screenshots/length_required.png Binary files differnew file mode 100644 index 00000000..4071c2d2 --- /dev/null +++ b/Engineering_Heat_Transfer/screenshots/length_required.png diff --git a/Engineering_Heat_Transfer/screenshots/wall_tempratures.png b/Engineering_Heat_Transfer/screenshots/wall_tempratures.png Binary files differnew file mode 100644 index 00000000..114869c8 --- /dev/null +++ b/Engineering_Heat_Transfer/screenshots/wall_tempratures.png |
