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Diffstat (limited to 'Engineering_Heat_Transfer_by_W_S_Janna')
16 files changed, 4981 insertions, 0 deletions
diff --git a/Engineering_Heat_Transfer_by_W_S_Janna/CHAPTER1.ipynb b/Engineering_Heat_Transfer_by_W_S_Janna/CHAPTER1.ipynb new file mode 100755 index 00000000..e3bdd6dc --- /dev/null +++ b/Engineering_Heat_Transfer_by_W_S_Janna/CHAPTER1.ipynb @@ -0,0 +1,441 @@ +{
+ "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": [
+ "\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",
+ "Q=6.3*3600 # [BTU/hr.sq.ft]\n",
+ "dx=0.5 # thickness in [inch]\n",
+ "Dx=0.5/12.0 # thickness in [ft]\n",
+ "T2=T1-(Q*Dx/k) # [\u02daF]\n",
+ "\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": [
+ "\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",
+ "k_al=k_ss*dt_ss*dz_al/(dt_al*dz_ss);# thermal conductivity of Al in [W/m.K]\n",
+ "\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": [
+ "\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",
+ "dT= (T_w-T_inf)\n",
+ "Q_c=h_c*A*dT # Convective heat transfer in BTU/hr\n",
+ "\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": [
+ "\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",
+ "m=Q*density/10**6 # mass flowa rate in kg/s\n",
+ "hc=m*cp*(T_b2-T_in)/(A*(T_w-T_in))\n",
+ "\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": [
+ "\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",
+ "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",
+ "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": [
+ "\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",
+ "hr=Qr/(A*(T1-T2)) # radiation thermal conductance in BTU/(hr.ft**2.(degree Rankine)\n",
+ "\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": [
+ "%matplotlib inline"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\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",
+ "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",
+ "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",
+ "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": [
+ "\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",
+ "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",
+ "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",
+ "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_by_W_S_Janna/CHAPTER10.ipynb b/Engineering_Heat_Transfer_by_W_S_Janna/CHAPTER10.ipynb new file mode 100755 index 00000000..d47a2ad1 --- /dev/null +++ b/Engineering_Heat_Transfer_by_W_S_Janna/CHAPTER10.ipynb @@ -0,0 +1,220 @@ +{
+ "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": [
+ "%matplotlib inline"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\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",
+ "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",
+ "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",
+ "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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\nRK5CYII=\n"
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 10.2 Page NO.532"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\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",
+ "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",
+ "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": [
+ "\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",
+ "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",
+ "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_by_W_S_Janna/CHAPTER11.ipynb b/Engineering_Heat_Transfer_by_W_S_Janna/CHAPTER11.ipynb new file mode 100755 index 00000000..30fa585c --- /dev/null +++ b/Engineering_Heat_Transfer_by_W_S_Janna/CHAPTER11.ipynb @@ -0,0 +1,299 @@ +{
+ "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": [
+ "\n",
+ "\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",
+ "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": [
+ "\n",
+ "dA2=0.02*0.02\n",
+ "Beta=0\n",
+ "r=1\n",
+ "\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",
+ "dQ1_2=dq1_2/dA2\n",
+ "\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": [
+ "\n",
+ "D=2.5/12.0 # diameter in ft\n",
+ "L=4.5/12.0 # length in ft\n",
+ "\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",
+ "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",
+ "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": [
+ "\n",
+ "T=2800 #Temprature\n",
+ "lambda1=4e-7 #Wavelength\n",
+ "lambda2=7e-7\n",
+ "hT=lambda1*T\n",
+ "\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",
+ "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": [
+ "\n",
+ "lambda_max=0.5e-6 # maximum wavelength in m\n",
+ "T=2.898e-3/lambda_max\n",
+ "sigma=5.675e-8 # value of Stefan-Boltzmann constant in W/(m**2.K**4)\n",
+ "q=sigma*T**4\n",
+ "\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": [
+ "\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",
+ "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",
+ "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_by_W_S_Janna/CHAPTER12.ipynb b/Engineering_Heat_Transfer_by_W_S_Janna/CHAPTER12.ipynb new file mode 100755 index 00000000..dacb5289 --- /dev/null +++ b/Engineering_Heat_Transfer_by_W_S_Janna/CHAPTER12.ipynb @@ -0,0 +1,303 @@ +{
+ "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": [
+ "\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",
+ "a_14=300\n",
+ "b_14=50\n",
+ "c_14=100\n",
+ "\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",
+ "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",
+ "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": [
+ "\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",
+ "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",
+ "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": [
+ "\n",
+ "ac=1\n",
+ "bd=1\n",
+ "ad=(9+1)**0.5\n",
+ "bc=ad\n",
+ "\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",
+ "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": [
+ "\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",
+ "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",
+ "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": [
+ "\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",
+ "q1=(sigma*(T1**4-T2**4))/((1/emissivity1)+(1/emissivity2)-1)\n",
+ "q2=-q1\n",
+ "\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": [
+ "\n",
+ "D=1.0 # diameter in ft\n",
+ "L=6/12.0 # length in ft\n",
+ "\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",
+ "F11=0\n",
+ "e1=0.82\n",
+ "e2=0.93\n",
+ "q1_=A*e1*(sigma*T1**4-F12*sigma*T2**4)\n",
+ "\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_by_W_S_Janna/CHAPTER2.ipynb b/Engineering_Heat_Transfer_by_W_S_Janna/CHAPTER2.ipynb new file mode 100755 index 00000000..43341b6f --- /dev/null +++ b/Engineering_Heat_Transfer_by_W_S_Janna/CHAPTER2.ipynb @@ -0,0 +1,650 @@ +{
+ "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": [
+ "\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",
+ "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",
+ "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",
+ "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": [
+ "\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",
+ "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",
+ "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",
+ "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": [
+ "\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",
+ "\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",
+ "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": [
+ "\n",
+ "k=14.4 # thermal conductivity of 304 stainless steel in W/(m.K) from appendix table B2\n",
+ "D2=32.39 #Diameter (cm)\n",
+ "D1=29.53\n",
+ "T1=40 #Temprature\n",
+ "T2=38\n",
+ "\n",
+ "import math\n",
+ "Qr_per_length=(2*3.14*k)*(T1-T2)/math.log(D2/D1)#format(6)\n",
+ "\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": [
+ "\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",
+ "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",
+ "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": [
+ "\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",
+ "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",
+ "U=1/((1/hc1)+(D1*log(D2/D1)/k12)+(D1*log(D3/D2)/k23)+(D1/(hc2*D3)))\n",
+ "\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": [
+ "\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",
+ "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",
+ "\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": [
+ "%matplotlib inline"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\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",
+ "A=(math.pi/4)*D**2 # Cross sectional area of the rod in sq.ft\n",
+ "hc=1.0 # assuming the convective heat transfer coefficient as 1 BTU/(hr. sq.ft. degree Rankine)\n",
+ "\n",
+ "m=math.sqrt(hc*P/(k*A))\n",
+ "L=(9/2.0)/12.0 # length of rod in ft\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",
+ "qz=k*A*m*dT*tanh(m*L)\n",
+ "\n",
+ "mL=m*L\n",
+ "efficiency=0.78 # from fig. 2.30\n",
+ "\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",
+ "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": [
+ "\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",
+ "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",
+ "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": [
+ "\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",
+ "import math\n",
+ "delta_opt=0.55/(12*2)\n",
+ "Lc=math.sqrt(delta_opt*k/(0.583*hc))\n",
+ "\n",
+ "A=Lc*delta_opt\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",
+ "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": [
+ "\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",
+ "import math\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",
+ "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",
+ "effectiveness=q/qo # effectiveness defined as ratio of heat transferred with fins to heat transferred without fins\n",
+ "\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_by_W_S_Janna/CHAPTER4.ipynb b/Engineering_Heat_Transfer_by_W_S_Janna/CHAPTER4.ipynb new file mode 100755 index 00000000..3a94d489 --- /dev/null +++ b/Engineering_Heat_Transfer_by_W_S_Janna/CHAPTER4.ipynb @@ -0,0 +1,547 @@ +{
+ "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": [
+ "\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",
+ "import math\n",
+ "reciprocal_timeconstant=(hc*6)/(density*D*c)\n",
+ "T=139\n",
+ "t=math.log((T-T_inf)/(T_i-T_inf))/(-reciprocal_timeconstant)\n",
+ "\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": [
+ "\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",
+ "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",
+ "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",
+ "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": [
+ "\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",
+ "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",
+ "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": [
+ "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",
+ "import math\n",
+ "Vs=math.pi*D**3/6\n",
+ "As=math.pi*D**2\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",
+ "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": [
+ " \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",
+ "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",
+ "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": [
+ "\n",
+ "k_al=236\n",
+ "p_al=2.7*1000\n",
+ "c_al=896\n",
+ "k_oak=0.19\n",
+ "p_oak=0.705*1000\n",
+ "c_oak=2390\n",
+ "\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",
+ "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": [
+ "\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",
+ "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",
+ "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",
+ "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",
+ "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",
+ "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": [
+ "\n",
+ "rou=7817 #Density\n",
+ "c=461 #Specific heat \n",
+ "k=14.4 #Thermal conductivity \n",
+ "alpha=.387e-5\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",
+ "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",
+ "T=(Tinf**2)*(1-Tsi)*(T_i-T_inf)+T_inf\n",
+ "t=350\n",
+ "\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": [
+ "%matplotlib inline"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\n",
+ "rou=0.5*1000\n",
+ "cp=837\n",
+ "k=0.128\n",
+ "alpha=0.049e-5\n",
+ "Ti=20 #Initial temprature\n",
+ "dt=0.5*(0.05)**2/alpha\n",
+ "\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",
+ "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",
+ "t=4.97\n",
+ "print\"The time that will pass before the heat added\",t,\"hr\"\n",
+ "\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": [
+ "\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",
+ "Fo=1\n",
+ "\n",
+ "dt=Fo*dx**2/alpha\n",
+ "n=8 #Enter the number of time intervals from Saulev plot\n",
+ "time=n*dt\n",
+ "\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_by_W_S_Janna/CHAPTER5.ipynb b/Engineering_Heat_Transfer_by_W_S_Janna/CHAPTER5.ipynb new file mode 100755 index 00000000..eed3e1b0 --- /dev/null +++ b/Engineering_Heat_Transfer_by_W_S_Janna/CHAPTER5.ipynb @@ -0,0 +1,115 @@ +{
+ "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": [
+ "\n",
+ "Cp=871\n",
+ "Gamma=1.3\n",
+ "\n",
+ "Cv=Cp/Gamma\n",
+ "dT=20\n",
+ "m=5\n",
+ "Qp=m*Cp*dT\n",
+ "Qv=m*Cv*dT\n",
+ "\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": [
+ "\n",
+ "T1_Fr=-50\n",
+ "T2_Fr=-40\n",
+ "rou1_Fr=1.546*1000\n",
+ "rou2_Fr=1.518*1000\n",
+ "\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",
+ "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",
+ "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_by_W_S_Janna/CHAPTER6.ipynb b/Engineering_Heat_Transfer_by_W_S_Janna/CHAPTER6.ipynb new file mode 100755 index 00000000..a9d21547 --- /dev/null +++ b/Engineering_Heat_Transfer_by_W_S_Janna/CHAPTER6.ipynb @@ -0,0 +1,486 @@ +{
+ "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": [
+ "\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",
+ "OD=1.588/100.0\n",
+ "ID=1.446/100.0\n",
+ "A=1.642e-4\n",
+ "Q=3.25e-6\n",
+ "\n",
+ "V=Q/A\n",
+ "Re=V*ID/v_20\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",
+ "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",
+ "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": [
+ "\n",
+ "T_avg=(140+70)/2.0\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",
+ "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",
+ "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": [
+ "%matplotlib inline"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 6.3 page No. 310"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\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",
+ "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",
+ "Re=rou*V*ID/(mu)\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",
+ "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",
+ "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\ndHHrgtnLzIZxG+jWuhsuJhfi4+Np1qiZ1lENSZM1mSlTptC/f3+mTZtGcXExBQUF/OMf/6BVq1ZE\nRESwePFiLly4QFRUVPmw0i7TjVsNqvzzn+0wqPLYMfXo5tNPYcoUmDsXPDxs/KbCkVQ0bNLsZWZw\nx8FWDZs0Gl2uyZw/f56WNvhN8eLFiwQEBNx00TNfX1/27NmDm5sbZ8+eJTg4mGPHjpUPK0VGc7oZ\nVHn6tDr9efVqu0x/FsZWl8MmjUiXazK2KDAA6enp3HXXXTz66KN0796dGTNmUFBQQE5ODm5u6nwe\nNzc3cnJybPL+WjJCT7oiWVkwenQ8HTpAcrI6sHL/fnXHmCaTkN3d4bXX1EUfb291+/PDD8PXX1f4\nJUb+/EHyV0dxaTGJPyWycOdCAt4JoPPKznx58ktG+Izg+OzjJM9I5qWQlwh0D7SqwBj9s9eS3WeX\nFRcXc/DgQd5880169uzJnDlzbtkWq2hRberUqXh6egLg6uqKv7+/5dKoZd8Ier2dkpKiqzzW3m7c\nOJjRo8HHJ4V33oHx4/WVL3jhQpg7l/jnnoMxYwj28YH584lv3BhMJsN//pLfutufffEZSWeSSG+e\nTtzJOJqfbU5gu0DeGP8Gvd1781XCV5CHZdik1p+HLW/Hx8ezZs0aAMvPS63YfazM2bNnefDBB0lP\nTwfgq6++YtGiRfz444/s3r2b1q1bk52dTUhIiLTLdGD9enUL8nvvqQcKuifbn51GZcMmh3oNdchh\nkzWlyzUZW+rXrx/vvfcePj4+vPjii1z5bVtqy5YtmT9/PlFRUeTl5cnCv4ZKS+HFF9WpyJs3Q7du\nWieqprLrBSxeDOnp6j7q8ePBzU1O7jQwPQybNCKnKzLffvstjz32GNeuXaNjx45ER0dTUlLChAkT\n+Omnnyrcwmz0IhMfH285tNWzggJ141Z2Nvz3v+rPZTBO/pvs3w9LlhC/fTvBAD4+cN996t9l/+3t\nDU30e8Y2GPjz/01N8utl2KTRP3stf3Zqcj2Zbt26kZycfNP9O3bs0CCNuN7p0+pmrc6dYedOaNRI\n60R1IDAQPvkE4uPVC6ilpqp/jh9XT+45fhzS0qBFi/KFp+xvT0/1BFFhF5euXmLnjzsthaVR/UYM\n8x7GwqCF9G/fn9sbyAWGjERG/QuLpCQYM0Zdg4mIcLKuUmmpWmGPH/+9AJUVo6wstdBcX3jKipG0\n32qtsmEBrS4QAAAWbElEQVSTZm+zDJusA07XLqspKTK2Y7gFfnsqLFS3Sl9feMr++9o1w7bftGTk\nYZNGJEXGSkYvMnrs61ZngV+P+avDJvlzc28uPDZqvxn98/9oy0ecdztvyGGTRv/snW5NRujD9Qv8\n+/f/vsAvqqFFC+jdW/1zvVu13778Uv07O9sp2m+FxYUkZCZYjlbOHTnH6KGjmdF9BhvGbZBZYE5C\njmSc1PUL/P/+t4Ms8BvFje2369twBm+/VTRs0uxttgybFPYn7TIrSZGpG069wK93dmy/1QVnHDZp\nRFJkrGT0IqOHvm5tFvj1kL82DJ2/tJT4jz8muEWLmwuQndtvNR02aeTP38jZQdZkhB1cv8C/Y4cB\nz+B3di4uasEIDobQ0PKP3dh+S0xUL2NdR+234tJi9p/ebzlvJTMvk9COoYzwGcEK8wrLLDAhbkWO\nZJxARWfwCydQ1n67cft1Fe23X65eUI9W0mKIOxmHx50elvNWerv3pr6L/H5qJNIus5IUmeo7fVpt\ni3XqJAv84jqlpXDqlKXwKMeOcenwAUqPH6PxuYtkNjeRd8/dNPLrinvPQbToFuhwu9+ciS6vJyPq\nXtkobntJSlJ31k6YAGvX1r7A2Dt/XZP813Fx4cLdd7KhTS5T2iXRuv1GHhx/kX+snc7/DsfQYcc3\n9IpcQVe/EFocPALPPQdduoCrK/TsCX/8I/ztb+oi36FDcPmyffPbmZGza02OeR2UnMEvblTZsMkX\n+79487DJrv43v8iN7bfrZ781b37rzQcdOsjsNycm7TIHY/gR/aJOVTRs0uxtrtthkze037Tc/SZu\nJmsyVpIiUzlZ4Be6HDbpwCefGoUUGSsZvcjYcq+9PRb4jX6ugKPmN8qwyVvmr2z3m47ab0b/3pHz\nZEStyBn8zictN81SVK4fNvn5pM91P2yynMpmv93Yfqto9tv1RUjab7ojRzIGJwv8zuHGYZP51/It\nZ9kPuneQcw2btKb9duO5P07efpN2mZWkyPxOFvgdnwybrAGDtN/sTYqMlYxeZOqqr6vVAr/R+9J6\nz1/VsMnDSYd1nb8qmn7+1dn9dov2m96/d6oiazLCatcv8O/cKWfwG11FwyZXjVxV6bBJUU0uLtC+\nvfqnqtlvX38Na9aUb781awYJCdJ+qwE5kjEQWeA3vlsNmxzccTBhXmEM9Roqwyb15sb2W9nfBmu/\nmUwmCgsLGTx4MC+88AL/+te/2Lp1q1VfO3fuXEaPHk1QUFCN3ltfn4SokCzwG9cvBb/cctjkG2Fv\nyLBJvbNm91tZ4dH57rePPvqI4cOHU69e9Y6OZ86cyTPPPFPjIiNHMnZUk76unhb4jd6Xtlf+UqWU\nb7K+sRytHDt3jIEdBmL2NjPUayjud7rX6HXl89dOtbLrcPebyWRi0KBBrFixguzsbF588UVatWrF\n999/zwMPPMCHH37IgQMHmDFjBgDFxcX88MMPlJaWAtC1a1cSEhJwdXWt9ntr9itUSUkJPXr0wN3d\nna1bt5Kbm8vEiRPJzMzE09OTjRs31ugf5EiuX+Dfv1/O4NezC79eIO5kHDFpMcSmxdLy9paYvc0s\nGriIvvf0pWG9hlpHFPbSqJG6aNqp082P3dh+++QTu7Xfvv/+e3x8fMjKyuLQoUMcOXKENm3a8NBD\nD5GYmMhDDz3EoUOHAIiIiMBsNlu+NiAggP/973+EhYVV+301KzLLli3Dz8+P/Px8AKKioggNDSUi\nIoLFixcTFRVFVFSUVvFsojq/xelxgd+ov4WWqcv81R42WQfk89dOnWXXsP3WtGlTy3/36tWLtm3b\nAuDv709GRgYPPfQQABs2bODgwYNs377d8vy2bduSkZFRo3+yJkXm9OnTxMTEsHDhQv75z38CsGXL\nFvbs2QPAlClTCA4OdrgiYy1Z4NenioZNLgxaWLfDJoXzqWr3W1ra7y23st1vx49DUZHV7bfrlxpu\nu+02y3/Xq1eP4uJiQD3aeemll9i7d2+5qRGKotR4ioQmReYvf/kLS5Ys4dKlS5b7cnJycPutH+Tm\n5kZOTo4W0WzKmr7uli0wfbo+F/iN3FOH6ue/1bDJPh59CPMKY95D8+w+bNLZPn890TR7o0bQubP6\n50bnz8OJE1W334DLVVzzJy8vj/DwcD744ANatmxZ7rHs7Owa//vtXmS2bdvG3XffTUBAQIUXAjKZ\nTBX+n3fq1Kl4enoC4Orqir+/v+UfX/Z6er2dkpJS5fPnzIGPPgpm8GDt89Ykv55vW5P/16JfKWlf\nQsyJGP77xX8pVUoZGzaWOYFzqP9TfW5vcDvBvfWbX8+3jZ5f17d791Zvh4YSHBxM/K5drFm5Ei5d\nwvOnnwDo3Lkzx48fv+XPV5PJxJYtW/jpp5947LHHLPcdPHgQgEOHDrF8+XJqwu67yyIjI/nggw+o\nX78+hYWFXLp0iTFjxpCcnEx8fDytW7cmOzubkJAQjh07Vj6swXeXVSUzU73oYHY2VHOXoaiFioZN\nmr3Nxho2KUQFTCYT0dHR5OTkMH/+/Gp9bWpqKs8++yxbtmyp2XtruYV5z549vPbaa2zdupWIiAha\ntmzJ/PnziYqKIi8v76Y1GUcvMm++CQcOqO1WYTsybFI4G5PJxNWrVxk0aBB79uyp1i9Oc+fOZcyY\nMfTt27dm7611kVm6dClbtmwhNzeXCRMm8NNPP1W4hdnoRSa+ir7u0KEwYwaMHWu/TNVRVX49y8zL\nZNmGZaTdmWbYYZNG/vzB2PmNnB2ceHZZ//796d+/PwAtWrRgx44dWsbRVH6+umlk40atkziGWw2b\n9C/0Z1qfaUQ/HE3Lxi2rfhEhRK3JGf868d//wttvQ1yc1kmM68Zhkz4tfQjzCsPsbZZhk8KpOe2R\njPjd1q0wYoTWKYylomGTI+8byQrzChk2KYQO6L8R7UDKthzeqKQEPv9c/0Wmovz29EvBL3zw7QeE\nbwrH7TU3noh5AgWFN8Le4Od5P7N+3Homd5t8ywKjh/y1Ifm1Y+TsWpMjGR1ISlKnQ/x2+o+4TmXD\nJpeELqnxsEkhhH3ImowOLFwIigKvvKJ1En2oaNik2dsswyaFqAG5/LKVHLXIdO2qLvr36aN1Em1U\nNmwyzCvMJsMmhXAmWv7slDUZO7pVXzczE86ehcBA++eprrrsS1+6eolPj37KjC0zcP+XO2M3jiX7\ncjYLgxaS82wO2yZtY1bPWXVaYIzeV5f82jFydq3JmozGtm4Fs9nxx8hUNGzS7GUm4qEIvFt6ax1R\nCGED0i7T2JAh8Pjj+j3LvzYKrhWwO2O35YTIUqWUYd7DMHubCekQQpOGtrsSoBDid7ImYyVHKzL5\n+dC2LWRlwXXXEzI0GTYphP7ImoyTuLGvu307PPigcQrMrfrShcWFxJ2MY07sHHze8CEoOohvz37L\njO4zOP2X0+yespt5D82j092dNC8wRu+rS37tGDm71mRNRkNGPcs/My+TL9K+IOZETLlhkxvGbTDM\nsEkhhH1Iu0wjJSXQpo16IqbeT8K81bDJoV5DMXuZGdxxsAybFELnZHaZE9L7Wf63GjZp9jaz+uHV\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": [
+ "%matplotlib inline"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\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",
+ "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",
+ "z=5.0\n",
+ "Tw=32.0\n",
+ "Tbo=-4.0\n",
+ "Tbi=-40.0\n",
+ "L=5.0\n",
+ "\n",
+ "x=2*a*L/((kf*ID/2.0)*(math.log((Tw-Tbo)/(Tw-Tbi)))) #x=V/hl\n",
+ "V=336.0 #ft/h\n",
+ "V_final=V/3600.0 #ft/s\n",
+ "hl_=V_final/(x) #\n",
+ "\n",
+ "Re=(V_final/3600.0)*ID/v\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",
+ "t=144*m_water/(-q*3600)\n",
+ "\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",
+ "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",
+ "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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TQ69evQB44403DHdEL46npycnTpzg1KlT9O/fHy8vL+rWrQvAvXv3GDduHK+88gqOjo6F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\nJPx/NycoLOaJwxIAAAAASUVORK5CYII=\n",
+ "text": [
+ "<matplotlib.figure.Figure at 0x7b9cf28>"
+ ]
+ },
+ {
+ "metadata": {},
+ "output_type": "display_data",
+ "png": 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ZUvHUpt0Y6HOrSqVSicjISNjb2yMqKsooccTFxQnL9vHxqfNyjHqHMqVSiZEj\nRyIiIgKzZ88GAHTq1AlxcXHw9PREeno6wsPD8ddff2kHxXFYOBi41UKF7VstjBUeIcTEpHyHMl9f\nX6xbt65S15CFhQVu3rwJPz+/Wi3v+PHjCA8Ph729vdYOb3R0NEJDQ+sVa4M5RsAYw/Tp09GlSxeh\nCADA6NGjsWHDBsyfPx8bNmzAmDFjdM7voLJEsbIEgL2xQiSEEMGdO3d0Di8tLa3T8gYOHAi1Wl2f\nkEzGaMcITp8+jc2bNyM2NhYhISEICQlBdHQ0FixYgJiYGPj7++PYsWNYsGCBzvmdVBYoVhUbK7wG\ng/qCRZQLEeWCGJLRvhH079+/ymp45MiRGud3oEJACCEmYdRjBHXFcRy2dnfENy2Sce5QO3OHQwgx\nECkfI2hIDH2MQLKXmHBQyVBSSt8ICCHE2CRbCOxVHErUVAioL1hEuRBRLoghSbgQAAr6RkAIIUYn\n2WMEye1cMKr1TtyLG2zucAghBkLHCAyjyRwjsFUyKKlriBBCjK7GQuDo6ChcQ8PGxgYymQzOzs5G\nD8xOxaBgVAioL1hEuRBRLogh1VgI8vPzkZeXh7y8PBQVFWHXrl1aF1UyFluFGioqBIQQEzH0rSor\nLtPJyQnDhw83ULSGVauuIZlMhjFjxiA6OtpY8QhslKVQggpBY7pQV31RLkSUC8Mz9K0qKy4zLy/P\nJJ+ddVHjmcU7d+4UnqvVaiQkJMDOzs6oQQGAtaIUKioEhBAzqHiryu+//x6rVq2CWq3GrVu3arWs\nhnBwvMZvBPv378eBAwdw4MABHD58GE5OTti7d6/RA7MuUVEhAPUFa6JciCgXxmGMW1W+8soraNmy\nJYYNG4ZLly6ZdoP0VOM3AmNdR1sfFihAaSlgQVeiJqTJiIvTfY+S2goLq92eOGMMY8aM0bpV5Ycf\nfojPPvsMCxcuhKurqzCtvh/oW7ZsQbdu3aBWq/Htt99i2LBh+Ouvv+Di4lKr2IytyvMIlixZonuG\nsutqf/LJJ8YLiuNQbGcNj97v4eGhL2Fra7RVEUJMSMrnEVR1PwKZTIabN2+iXbv6X/esc+fO+Oqr\nrzBy5Mh6Lcdk5xE4ODjA0dFR68FxHNatW4cVK1bUekW1pbK1hqNlHt2ukhBidnW9VWVNy5GKKruG\nPvjgA+F5bm4uvvvuO6xfvx4TJkzA3LlzjR5YqY01HC0KmnwhiIuLo1+IlKFciCgX5qXPrSpTU1Nx\n79499Oy+W6gJAAAgAElEQVTZE2q1GqtXr8aTJ0/qfXcyY6j2GMGTJ0+watUq/PLLL5g0aRISExPh\n5uZmksCKHexgz1EhIISYV1334vPy8vD222/j1q1bsLW1RUhICA4dOmSyz9DaqPIYwQcffIDdu3fj\n9ddfx9tvv13pxvNGDYrjcKtbZ0zybIvN/z2EetyTmRAiIVI+RtCQGPoYQZWFQCaTwdraGlZWVjpX\nlpubW+uV6R0UxyE5vA/m2dlg9ao4+PsbbVWEEBOiQmAYJjtYrFarUVxcLJwRp/kwZhEol+/sDFsU\nNfmuIfq9uIhyIaJcEEOS7NVH852cYceKm3whIIQQY5NsISh0doKdmgoB/TJERLkQUS6IIUm3EDg4\nwY6VNPlCQAghxibZQlDg6ATbUioE1BcsolyIKBfEkIxaCKZNmwYPDw907dpVGLZ48WK0bt0aISEh\nCAkJqfKyrIUOjrBTK5p8ISCkMXFzcwPHcfSo58PQ5yLUeNG5+pg6dSreffddTJo0SRjGcRzmzJmD\nOXPmVDtvkZ09bFTKJl8IqC9YRLkQNdRcZGVlmTsEooNRvxEMGDBAZ+XS53euhXYOsC2lQkAIIcZm\nlmMEq1evRnBwMKZPn46cnByd0xTa2cFWpWryhYD6gkWUCxHlQkS5qD+jdg3p8tZbbwmXsP74448x\nd+5crFu3rtJ0B9b8CP97KnC/LkJmphvkcrnwdbj8had202qXk0o85mwnJydLKh5ztpOTkyUVjynb\ncXFxwj1jfOpxLZ4qLzFhKCkpKRg1ahQuX76s9ziO4zDltwMYtHQUct8swTtvVb7MBSGEEG0Gv8SE\nsaSnpwvPd+/erfWLIk3KEks4KmXIL6HbVRJCiDEZtRBMnDgR/fr1w/Xr1+Ht7Y2ff/4Z8+fPR1BQ\nEIKDg3H8+HGsWrVK57wqhSXslDIUKpp2IajYLdKUUS5ElAsR5aL+jHqMYOvWrZWGTZs2Ta95S4tk\nsFdxTb4QEEKIsUn2zGJWxMFByaFI2bQLQfkBIkK50ES5EFEu6k+yhQCFHOxUaPKFgBBCjE2yhYAr\nAOyUQHETLwTU/ymiXIgoFyLKRf1JthBYFqhgq2IoVjXtQkAIIcYm2ULgoCyEVSlQXNq0CwH1f4oo\nFyLKhYhyUX+SLQTNS/NRamGDEvpGQAghRiXZQuDGCqGwsYFCVWjuUMyK+j9FlAsR5UJEuag/yRYC\nZ1aAHEcHMGWuuUMhhJBGTbKFwAH5yHJyBFeSZ+5QzIr6P0WUCxHlQkS5qD/JFgJ7WT6eOjpCpso3\ndyiEENKoSbYQ2Mry8dTJEZbKpv2NgPo/RZQLEeVCRLmoP8kWAkvLfOQ6OsJSWWDuUAghpFEz+v0I\n6oLjOMTMfgnx2dY49dACB6I3mDskQgiRvAZzPwJ9WVjnI8/BEdal9I2AEEKMSbKFAE4FKLZ2hpWq\nyNyRmBX1f4ooFyLKhYhyUX+SLQTMuQAKS2dYlzbtQkAIIcYm2WMER9d3xG/X3oTy9Hb8ePqsuUMi\nhBDJa3THCOBQADXsYaOmaw0RQogxSbYQcPb5YGp72DTxq49S/6eIciGiXIgoF/Un2UIA23yg1Aa2\npSXmjoQQQho1yRYCjlnASg3YqRVITTV3NOZD11ERUS5ElAsR5aL+JFsIoHSCDVOgub0CI0YAuXQR\nUkIIMQrJFgJZqRNsWRGcLZQIDQVefhlQqcwdlelR/6eIciGiXIgoF/Vn1EIwbdo0eHh4oGvXrsKw\nrKwsDBkyBP7+/hg6dChycnJ0B8ZcYMuKYFWiwurV/LCZMwHp/diVEEIaNqMWgqlTpyI6Olpr2PLl\nyzFkyBDcuHEDgwcPxvLly3XOa8k5wxaFsFKoYGkJbN8OnDkDfP21MSOWHur/FFEuRJQLEeWi/oxa\nCAYMGAA3NzetYfv27cPkyZMBAJMnT8aePXt0zmtl4Qo7FMBCoQYAODsDv/8OrFoF7NplzKgJIaRp\nMfkxgoyMDHh4eAAAPDw8kJGRoXM6S0sXOMryAVhCpeYPDnh7A3v3Am+8AVy4YKqIzYv6P0WUCxHl\nQkS5qD9Lc66c4zhwHKdz3KL//AGrHHs4ZFvjk2k9sXLSSgweNBjduwPvvx+HiAggISEMPj7iG6H8\nKyK1G2e7nFTiMWc7OTlZUvGYs52cnCypeEzZjouLQ1RUFADAx8cHdWX0aw2lpKRg1KhRuHz5MgCg\nU6dOiIuLg6enJ9LT0xEeHo6//vpLOyiOw/Vzn+Cv3/5Gx4uP8d4kGVxsXfDL2F9gKeNr13ffAWvW\nAKdPA66uxtwCQghpGBrMtYZGjx6NDRv4G81s2LABY8aM0TmdlZ0rrK0KUMgY9kzYg9ySXPxj5z+g\nLFUCAGbNAgYPBl56CVAqTRY+IYQ0OkYtBBMnTkS/fv1w/fp1eHt7Y/369ViwYAFiYmLg7++PY8eO\nYcGCBTrntXZwh6V1PvI5DraWttj98m4UKAswcedEoRisWgXY2gJvvdV4f1ZasVukKaNciCgXIspF\n/Rn1GMHWrVt1Dj9y5EiN81o7ucHCtgB5cAYA2FraYtf4XRj36zhM2DkB28Ztg5WFFbZuBZ59Flix\nAqiiphBCCKmGZO9HkJ19Eom/vIXMPb4YH7NPGFeiKkHkjkhYyaywLXIbrC2skZYG9O0LrFwJjB9v\nxsAJIcSMGswxAn1ZWroATgUosmvGHxUuY2Npg99e+g0qtQov//YyFKUKeHkB+/fzZx6fpXvYEEJI\nrUi4ELgCjgUonvIO8M03/Kd82VFhG0sb/Db+NzDGMH7HeChKFQgOBjZsAMaOBW7fNnPwBkT9nyLK\nhYhyIaJc1J+EC4ELOPs8lFg4A+fO8Z/uw4cDWVkAAGsLa/z60q/gOA6Rv0aiRFWCiAjgk0+A558X\nJiOEEFIDyR4jUKtLEXfMGgkPEvHBa0FAaSl/NHj3br4fqHNnAICyVImXf3sZSrUSv730G2wsbTB3\nLpCQABw+DFhbm3ljCCHERBrdMQKOk4Ep7cHyn/IDLCyAr74CPv4YGDgQOHgQAGBlYYXtkdthY2GD\ncb+OQ4mqBF9+Cbi5ATNmNN6flRJCiKFIthAAABRO4AorXKZ68mT+gkP//Cf/MyHG+J+RjtsKOys7\njP11LJSsGJs3A9euAZ99Zp7QDYX6P0WUCxHlQkS5qD9pFwKVEyyKn1Ye3rcvcP48sGULMGUKUFwM\nKwsrbBm7BQ5WDnhx+4uwsCnG/v3AunXAL7+YPHJCCGkwpF0ImBMslFXco9LbGzh5EigqAsLDgYcP\n+WIwbgtcbFwwZtsYuDYvxoEDwPvv85M2ROUXmiKUC02UCxHlov4kXQhkzBmWqmpuVuzgwN+xJiIC\n6NULSEyEpcwSm8duhpudG17Y9gLadSzCL7/w1yS6ccN0sRNCSEMh7UIgc4G1Oq/6iTiO/83oqlXA\nsGHAr7/CUmaJTS9uQjO7Znhh2wvoH1aETz8FRowAMjNNE7uhUP+niHIholyIKBf1J+lCYGXpAivU\nUAjKjRsHxMQA//oX8MknsIQMG1/ciJYOLTF622i8MqUQ48YBY8YAxcXGjZsQQhoSyZ5HwBhDfPQc\n3DyZg4mf/6z/zBkZ/OnFHh7Axo0otbfDlL1T8CDvAfa+vB/TXrOHpSV/ALmKe+IQQkiD1OjOIwAA\nO1s3WFnmobQ2G+bhARw7xt+tJjQUFqn3EfVCFLycvDB620j88GMB7twBFi0yXtyEENKQSLsQ2LvD\nwaoQfRITEZ9bzUHjimxs+N+NTpkC9OkDizNnsf6F9Wjj0gYv7RmJLb8V4Jdf+GsTSR31f4ooFyLK\nhYhyUX+SLgQ2ju5wsCnETC8vjLx8GTNv3ECOvrcj4zj+d6NRUcDYsbBYH4V1o9fB19UXU2NG4Nc9\nBZg3D4iNNeomEEKI5En6GMHje9G4tvvfGPhePLKUSiy8fRv7nzzBynbtMLFlyypvfF/J9evAqFHA\n889D/dWXmHHwLfyd/Tfmt/4dU19xRFyccOkiQghpsBrlMQIb52aASwGujL0Cm5sKrOnYEbsCAvDl\nvXt47uJFXC8s1G9BHTvyZyJfuwbZyFH4ccCX6ODeActTn8eSZfkYMQJ49Mi420IIIVIl6UJgae0K\nm44quIS6IDksGX9N/QvyHBvEd++OUc2aITQxER/fuYOi0tKaF+bmxl+ornNnyPr2w1r/uejYrCN+\n4SIQ+UoeXniBP0lZaqj/U0S5EFEuRJSL+pN2IbB0Rak6B95zvdH7Zm/YeNsgvls87rx/C2/beOBi\nz564XliIgD/+wMEnT/RZIH+Tm3/9C7JnB2KN9Vh0ad4FZ3wj4N0uD5MnA2q18beLEEKkRNLHCNRq\nJc6caQlPzynw8poFOztfKB4pcPfzu8jYnAGvd7zgPdcbR1RPMfPmTQQ7OuLb9u3R2ta25pWcPAmM\nHw/1vHl4p/11JGdcBjYfQlhfZyxbZvxtJIQQQ2uUxwhkMiv06HEJHGeNhISeuHIlEkU28Wj/TXv0\nSOyBktQSnPc/jy7rC3AxsBsCHRwgj4/Hf1JToaxp137AAODsWciiovDDbgV6Ng+EasIwbN/7FD/9\nZJrtI4QQKZB0IQAAW1tvtGu3An36pMDVNQx//jkJiYl9kGu3F/7r2kMeK0fumVxc6pyAN47Y4HRQ\nCKKzstA9IQFnnuq4hLUmHx/g9Glw2dn4duVVDHbuDOe3h+HDpU8RE2OSzasR9X+KKBciyoWIclF/\nZusa8vHxgbOzMywsLGBlZYULFy6IQVXz9YaxUmRm7sf9+6tQXJwCL6938cwz/0RRogy3P7yNktQS\n+Hzqg7iBwJzbtxDh7o4V7dqhmZVV1cGo1cCiRWCbNmHF3D7YqLqDh1/9D518XCGTATIZf1qC5t+q\nnht6/IMHcWjTJsxs69dnvKnWeeFCHPr2DTPK8huauLg4uvxyGcqFqK5dQ2YrBL6+vkhISIC7u3ul\ncfpuTG5uPO7fX4WsrEPw8JiE1q1noei0K+4svANWyuDxaVus7JCNbY8fY5mfH6Z4ekJW3X/99u1g\nM2fi5zd6YZXHQ/R2HQ0wDgDH/y17zhgHruwvGAcOMuG55rSswjzieJn2eI3nDBygFudhanH5rHy4\nxnioxXmYsJyy5as1lsvE5WkNU/PTs7LlMHX5MH68uvy5WnMZ/PLVGtOqNf4K06o5qBkHqGXawyo8\n15pPzUFdvvxSMYby+dWlFZ6Xjy+VCcPUFceXissQl8XX//K3mRQKnZTGSzGmxjbeGDsgDbIQxMfH\no1mzZpXG1XZjiovvIy3te6Sn/wRX14Fo3fp9KI76I+XfKbBqaQXlx5541+0BrDgO/+fvj66OjlUv\nLCEBbMwYJEXIkRDUgv+cBqDmGBjjP7fVABjHoAYrew6owcRpwcR5ysaXMjU/TAaoGdOaR2iXTc8v\nl4njy5ala77yeUqZWnxeYTkVp2VgUDM1GGNgYDX+rc20jJVNr+e0xl5+xWmF9xg4cBxX/V+tYbJK\n46A5Xdk4oML00BhW/pzTHs7/lekYVvVfDjJhx6J8ePmDYxrPIe6sCNMwHdNqDBOmrziuwjQVd4zK\nd0Aq7/hw4k4O03zItKct35HRNaxselZpWOWdHWGYWlbluIo7RCjbwRGfa+886d4xkmktR+eOkeay\nSrWnF98rGg9wZTurHGSQCcNlFceXDZNpvGdlnAzpF0IbViHw8/ODi4sLLCws8MYbb2DGjBliUHWs\naipVPjIyNuD+/W9gaekOr1bvQX2oP+4uSYNDsCMSZjlgvl06Jnt6YlHbtnC0tNS9oPR04J13gAcP\n+F3Gqh7lu5T6PuowfZxCgTBLS8OsQ1P5LknFXRR9HmaaPi4/H2HOzvVePpPJ+M8zcGDCcPDPgcrD\nOACcTHiuPZ3GX2i0ZZx2u2w842fVGIaymMrHcWU7FJz4Oaq1Ln7c6QcP0a/1M0IbXNkXSZRPoxkn\n+OWXPy9fvrDzwmmsp/zBaSyn5r9qjgPT2PHhdzjE52oOGusT4xOGQ3vHSXteJk4v7ByJ0167+QAd\nOzwjxqKxAyXsSEFdaUdNe1pWFovGDhS0d84qttUyCDthOnfsKixH2KEDv1NXviNZysTpSjWHl+/Y\nqcWdGTUr26kRdqLEthoMSe+cbViFID09Hc888wweP36MIUOGYPXq1RgwYAAfFMdh8uTJ8PHxAQC4\nurpCLpcL/YDlB4eqasfGHkVu7lm0aXMExcW3cffOcOBcX3j/6g+7wa5YKj+PM/ZFWDN+PMY0b47j\nx49XuzxztjUPhBlk+YwhLjYWYAxhAwfyxaZ8/IAB/PjyfPTvz7dPnODboaH89KdO8fP368ePP32a\nb/fty7fPnOHbffrw0589y7d79+bHnzvHt3v14tvnz/Ptnj212z168O0//hAKWVi3boiLj+fHd+vG\nj4+P58fJ5Xw7MZFvBwfz7aQkvh0UxLeTk/n5u3bl25cu8e3AQL59+TLfDgjQbnfpwrevXuXbnTvz\n7WvX+HanTtrtjh359l9/8W1/f759/Trf7tCBb9+4wbfbtePbN2/y8fr58e2//+bbvr58+9YtJD94\ngNnl+b5zh5+/bVu+nZLCt9u04dt37wJqNcK8vfn2vXv8+Nat+XZqKt/28uLb9+/z07dqxbfT0vjx\nzzzDt8t2kMI8Pfl2ejrfbtmSbz98yMfbogXfzsjg282b8+2y0/jD3N35dmYmP395+8kTvu3mxrez\nsvi2iwvfzs7Wan+Tlga5vT2/k8AY4p4+5cc7OvLt3Fztdl4e33Zw4Nv5+Xzb3p5/vxYU8PHZ2vLj\ny65gEGZjw7fLzjwNs7bmpy8p4ee3suLHKxR8u2wHLk6p5NsWFvz0KhXflsn48aWlfJvj+HbZzlxY\n2f99+SdAWNkOTxxjAMchzMICcYwhquyEWh8LCyxRKhtWIdC0ZMkSODo6Yu7cuQDq/o1Al7y8BKSm\nrkJW1kG0cH8Fsv0vIeMrGVQvumDB2EI097LD6g4d4GtnZ5D1EUKIwejbE1D24Jyc6vTZKTNC6DUq\nLCxEXh5/57GCggIcPnwYXbt2Ncq6nJy6o0uXzejZ8zKsbB2REToWzv9biRZtr+KrVxWYsKYUA+Pi\n8cXdu1DQacWEECkp7/q0sOCvjGBlBVhb85fat7UF7OwAe3v+/u3VHfusgVkKQUZGBgYMGAC5XI7e\nvXtj5MiRGDp0qFHXaWPjBT+/Zejb9y6aeQ5F/pCPYXtgNgKeOYZNU0uh+iYDPU79gdjsbKPGUVv0\nG2kR5UJEuRBRLuqviqOlxuXr64vk5GRzrBoWFg7w8nobrVq9iSdPDuC+3SpYPrsKw0+9jP5Tn8OG\ncVex/lV3fNWpPTysrc0SIyGEmJIkjhFUZMhjBPrIy0vE/furkJlxABZ/DEfOr2Pw07BnkN+u7CQ0\nToxLs635V/hNcBXTaI2vNE7/ebhK6+YqDReey8qf6J6Xk1VYLyrPW2ke8L+24H/WVlUMNcdUcZN1\nxSRMIyyP0950jb/Vjatq3urGVZy3NsttLDHVZrl1iak2y20sMRn7PdHHxaXhHiyuyNSFoFxJSRrS\n0v6LtLtrgb8DwB568j/vKw9F/O1f2V9dw7jK87AK8wi/G6zQ1loW025rrVPHMipMyyrOrzMmaM2j\nNa5SbGXDyk5mq7xNOtrq6uLXFbfY5qrIrebidf+7lJOVTVthOKs8D6swT+VlcRXm01hc1f+WOsZV\nPw/TGlax11ZzudrLrLi8ym3NZci0h5X/xLTC9pX/lLX65Wuvn/+5qvg6l/80Vnue8vUzcVu4yq8V\nY7rmLfu5L9OOXzMfusarNednmiFqxl2WA047Z0wjhvKYND+ZGFd+foQ4rTANp5l7Jvwsl59PM39M\nnFbXv19V/2Y6hv/71/5UCAyltLQAjx/vgkqVjfI0i/FofYpVMw4Vxlc3Tve8jDGcO5eCPn3a1mJe\n48dU83K1YzFUTBcuZKBXz5YVhqvFacuWzyq2NddbxTSVl6HWGFzFuGrXW/0264pJGFdFbJrDExKf\nons35xrXU/vXrPyvfq+ZXq+dzuEVcwcd01TYjirGJSUrECK3qrA+PePWWm9t4q8wDycuqRIdOx8V\n/3KalUBrvI5hTJyHlc9bNmTgc7l1+uw0yzECqbOwcICn52vmDgMAcPduHHx9w8wdhiQ8ehSHLgFh\n5g5DEgqUcegZGmbuMCShlIvDgLJzZqRCVwE1ZkEWC3HlS/bog74REEJII9Eo70dACCHE+KgQSBz9\nRlpEuRBRLkSUi/qjQkAIIU0cHSMghJBGgo4REEIIqRMqBBJH/Z8iyoWIciGiXNQfFQJCCGni6BgB\nIYQ0EnSMgBBCSJ1QIZA46v8UUS5ElAsR5aL+qBAQQkgTR8cICCGkkaBjBIQQQuqECoHEUf+niHIh\nolyIKBf1R4WAEEKaODpGQAghjQQdIyCEEFInZikE0dHR6NSpEzp06IAVK1aYI4QGg/o/RZQLEeVC\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": [
+ "\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",
+ "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",
+ "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",
+ "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",
+ "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": [
+ "\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",
+ "rou_o=.0748\n",
+ "V=10 # average velocity in ft/s\n",
+ "mass_flow=rou_o*A*V\n",
+ "\n",
+ "V_avg=mass_flow/(p*A)\n",
+ "Re=(V_avg*D)/v\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",
+ "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_by_W_S_Janna/CHAPTER7.ipynb b/Engineering_Heat_Transfer_by_W_S_Janna/CHAPTER7.ipynb new file mode 100755 index 00000000..1e2b1047 --- /dev/null +++ b/Engineering_Heat_Transfer_by_W_S_Janna/CHAPTER7.ipynb @@ -0,0 +1,646 @@ +{
+ "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": [
+ "%matplotlib inline"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\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",
+ "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",
+ "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",
+ "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",
+ "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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pKQkWi0XJYctCylzECylzkZ6ejmnTpmHMmDFISEjAE088gVGjRik88tCTMhe/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\nCXXQW9RxAAAAAElFTkSuQmCC\n"
+ }
+ ],
+ "prompt_number": 1
+ },
+ {
+ "cell_type": "heading",
+ "level": 3,
+ "metadata": {},
+ "source": [
+ "Example 7.2 page NO.360"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "%matplotlib inline"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\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",
+ "x1=1\n",
+ "Re1=(V*x1)/v # Reynolds Number at x=1 ft\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",
+ "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",
+ "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",
+ "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": [
+ "\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",
+ "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",
+ "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": [
+ "\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",
+ "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",
+ "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",
+ "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": [
+ "\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",
+ "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",
+ "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": [
+ "\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",
+ "Df=(Cd*rou*V_inf**2*b*L)/(2*gc)\n",
+ "\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": [
+ "\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",
+ "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",
+ "Re5=vel*5*x1/(v)\n",
+ "\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",
+ "Re6=vel*6*x1/(v)\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",
+ "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": [
+ "\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",
+ "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": [
+ "\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",
+ "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",
+ "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": [
+ "\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",
+ "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",
+ "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",
+ "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_by_W_S_Janna/CHAPTER8.ipynb b/Engineering_Heat_Transfer_by_W_S_Janna/CHAPTER8.ipynb new file mode 100755 index 00000000..759f39bd --- /dev/null +++ b/Engineering_Heat_Transfer_by_W_S_Janna/CHAPTER8.ipynb @@ -0,0 +1,481 @@ +{
+ "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": [
+ "\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",
+ "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",
+ "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": [
+ "\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",
+ "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",
+ "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",
+ "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",
+ "Tw2final=q2-T_inf2\n",
+ "Tw1final=10.7\n",
+ "\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": [
+ "\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",
+ "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": [
+ "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",
+ "import math\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": [
+ "\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",
+ "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",
+ "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",
+ "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": [
+ "\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",
+ "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",
+ "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",
+ "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",
+ "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": [
+ "\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",
+ "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",
+ "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": [
+ "\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",
+ "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",
+ "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",
+ "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_by_W_S_Janna/CHAPTER9.ipynb b/Engineering_Heat_Transfer_by_W_S_Janna/CHAPTER9.ipynb new file mode 100755 index 00000000..d66004ef --- /dev/null +++ b/Engineering_Heat_Transfer_by_W_S_Janna/CHAPTER9.ipynb @@ -0,0 +1,482 @@ +{
+ "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": [
+ "\n",
+ "T1=100.0 \n",
+ "T2=75.0\n",
+ "t1=5.0\n",
+ "t2=50.0\n",
+ "\n",
+ "import math\n",
+ "LMTD_counter=((T1-t2)-(T2-t1))/(math.log((T1-t2)/(T2-t1)))\n",
+ "LMTD_parallel=((T1-t1)-(T2-t2))/(math.log((T1-t1)/(T2-t2)))\n",
+ "\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": [
+ "\n",
+ "T1=250\n",
+ "T2=150\n",
+ "t1=100\n",
+ "t2=150\n",
+ "\n",
+ "import math\n",
+ "LMTD_counter=((T1-t2)-(T2-t1))/(math.log((T1-t2)/(T2-t1)));\n",
+ "LMTD_parrelel=0\n",
+ "\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": [
+ "\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",
+ "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",
+ "ID_a=0.1674\n",
+ "ID_p=0.1076\n",
+ "OD_p=1.375/12\n",
+ "A_p=math.pi*ID_p**2/4\n",
+ "A_a=math.pi*((ID_a)**2-(OD_p)**2)/4\n",
+ "\n",
+ "D_h=ID_a-OD_p\n",
+ "D_e=(ID_a**2-OD_p**2)/(OD_p)\n",
+ "\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",
+ "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",
+ "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",
+ "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": [
+ "\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",
+ "t1_air=20+273 \n",
+ "t2_air=80+273\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",
+ "T1_CO2=600 \n",
+ "ID_a=.098\n",
+ "ID_p=.07384\n",
+ "OD_p=.07938\n",
+ "\n",
+ "import math\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",
+ "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",
+ "LMTD_counter=((T1_CO2-t2_air)-(T2_CO2-t1_air))/(log((T1_CO2-t2_air)/(T2_CO2-t1_air)))\n",
+ "D_h=ID_a-OD_p\n",
+ "D_e=(ID_a**2-OD_p**2)/(OD_p)\n",
+ "\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",
+ "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",
+ "\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",
+ "Rd_air=0.0004\n",
+ "Rd_CO2=0.002\n",
+ "\n",
+ "Uo=1/((1/h_1o)+(1/h_2))\n",
+ "Uo=1/((1/Uo)+Rd_air+Rd_CO2)\n",
+ "\n",
+ "A=q_air/(Uo*LMTD_counter)\n",
+ "\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",
+ "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",
+ "V_air=(m_1/3600.0)/(rou_1*A_p)\n",
+ "V_CO2=(m_2/3600.0)/(rou_2*A_a)\n",
+ "\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",
+ "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": [
+ "\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",
+ "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",
+ "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",
+ "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",
+ "import math\n",
+ "At=(Nt*math.pi*ID**2)/(4*Np)\n",
+ "As=(Ds*C*B)/sT\n",
+ "\n",
+ "De=4*((sT/2.0)*(0.86*sT)-(math.pi*OD**2/8.0))/(math.pi*OD/2.0)\n",
+ "\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",
+ "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",
+ "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",
+ "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",
+ "V_t=(m_2/3600.0)/(rou_2*At)\n",
+ "V_s=(m_1/3600.0)/(rou_1*As)\n",
+ "\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",
+ "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": [
+ "\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",
+ "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",
+ "mcp_raw=m_2*cp_2\n",
+ "mcp_distilled=m_1*cp_1\n",
+ "\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",
+ "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": [
+ "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",
+ "T1=190.0\n",
+ "T2=158.0\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",
+ "t1=126.0\n",
+ "t2=166.0\n",
+ "q_air=m_2*cp_2*60*(t2-t1)\n",
+ "q_oil=m_1*cp_1*60*(T1-T2)\n",
+ "\n",
+ "import math\n",
+ "LMTD=((T1-t2)-(T2-t1))/(math.log((T1-t2)/(T2-t1)))\n",
+ "Area_air=(9.82*8)/144.0\n",
+ "Area_oil=(3.25*9.82)/144.0\n",
+ "\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",
+ "UA=q_air/(F*LMTD)\n",
+ "mcp_air=m_2*cp_2*60\n",
+ "mcp_oil=m_1*cp_1*60\n",
+ "\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",
+ "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_by_W_S_Janna/CHAPTER_3.ipynb b/Engineering_Heat_Transfer_by_W_S_Janna/CHAPTER_3.ipynb new file mode 100755 index 00000000..1d13a2b5 --- /dev/null +++ b/Engineering_Heat_Transfer_by_W_S_Janna/CHAPTER_3.ipynb @@ -0,0 +1,301 @@ +{
+ "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": [
+ "\n",
+ "OD=0.02858 # outer diameter in m\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",
+ "q_half=k*S_L*(T1-T2)\n",
+ "q=2*q_half\n",
+ "\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": [
+ "\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": [
+ "\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",
+ "St_A=nA*S1_A # Total shape factor of component A\n",
+ "\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",
+ "S3_C=0.15*0.006\n",
+ "nC=8\n",
+ "St_C=nC*S3_C # Total shape factor of component C\n",
+ "\n",
+ "S2_D=0.54*0.188\n",
+ "nD=4\n",
+ "St_D=nD*S2_D # Total shape factor of component D\n",
+ "\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",
+ "print\"(a)The heat transferred through the walls of the furnace is \",round(q/1000,1),\"kw\"\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": [
+ "\n",
+ "OD=4.5/12.0 # diameter in ft\n",
+ "R=OD/2.0\n",
+ "\n",
+ "import math\n",
+ "L_A=4.5 # length in ft\n",
+ "S_A=(2*math.pi*L_A)/(math.log(2*(L_A)/R))\n",
+ "L_B=18 # length in ft\n",
+ "S_B=(2*math.pi*L_B)/(math.acosh(L_A/R))\n",
+ "S=2*S_A+S_B\n",
+ "\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": [
+ "%matplotlib inline"
+ ],
+ "language": "python",
+ "metadata": {},
+ "outputs": []
+ },
+ {
+ "cell_type": "code",
+ "collapsed": false,
+ "input": [
+ "\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",
+ "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",
+ "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",
+ "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",
+ "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_by_W_S_Janna/README.txt b/Engineering_Heat_Transfer_by_W_S_Janna/README.txt new file mode 100755 index 00000000..0da6ee5a --- /dev/null +++ b/Engineering_Heat_Transfer_by_W_S_Janna/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_by_W_S_Janna/screenshots/heat_transferred.png b/Engineering_Heat_Transfer_by_W_S_Janna/screenshots/heat_transferred.png Binary files differnew file mode 100755 index 00000000..12f4f4a9 --- /dev/null +++ b/Engineering_Heat_Transfer_by_W_S_Janna/screenshots/heat_transferred.png diff --git a/Engineering_Heat_Transfer_by_W_S_Janna/screenshots/length_required.png b/Engineering_Heat_Transfer_by_W_S_Janna/screenshots/length_required.png Binary files differnew file mode 100755 index 00000000..4071c2d2 --- /dev/null +++ b/Engineering_Heat_Transfer_by_W_S_Janna/screenshots/length_required.png diff --git a/Engineering_Heat_Transfer_by_W_S_Janna/screenshots/wall_tempratures.png b/Engineering_Heat_Transfer_by_W_S_Janna/screenshots/wall_tempratures.png Binary files differnew file mode 100755 index 00000000..114869c8 --- /dev/null +++ b/Engineering_Heat_Transfer_by_W_S_Janna/screenshots/wall_tempratures.png |
