diff options
Diffstat (limited to 'Engineering_Heat_Transfer/CHAPTER4.ipynb')
| -rw-r--r-- | Engineering_Heat_Transfer/CHAPTER4.ipynb | 60 |
1 files changed, 0 insertions, 60 deletions
diff --git a/Engineering_Heat_Transfer/CHAPTER4.ipynb b/Engineering_Heat_Transfer/CHAPTER4.ipynb index 918045d0..a15cf189 100644 --- a/Engineering_Heat_Transfer/CHAPTER4.ipynb +++ b/Engineering_Heat_Transfer/CHAPTER4.ipynb @@ -27,9 +27,7 @@ "cell_type": "code",
"collapsed": false,
"input": [
- "# determination of response time\n",
"\n",
- "#Given\n",
"k=12.0 # thermal conductivity in BTU/(hr.ft.degree Rankine) \n",
"c=0.1 # specific heat in BTU/(lbm.degree Rankine) \n",
"D=0.025/12.0 # diameter in ft\n",
@@ -40,15 +38,11 @@ "As=3.14*D**2 # surface area in sq.ft\n",
"Vs=3.14*D**(0.5) # volume in cu.ft\n",
"\n",
- "#calculation\n",
- "#As/Vs=6/D\n",
"import math\n",
"reciprocal_timeconstant=(hc*6)/(density*D*c)\n",
- "# selecting T=139 F as T=140 gives an infinite time through the equation (T-T_inf)/(T_i-T_inf)=exp(-hc*As/density*Vs*c)t\n",
"T=139\n",
"t=math.log((T-T_inf)/(T_i-T_inf))/(-reciprocal_timeconstant)\n",
"\n",
- "#result\n",
"print\"The response time of the junction is %.1f s\",round(t*3600,2),\"s\"\n"
],
"language": "python",
@@ -76,10 +70,7 @@ "cell_type": "code",
"collapsed": false,
"input": [
- "# Determination of temperature of metal and cumulative heat rate\n",
- "# properties of aluminium from appendix table B1\n",
"\n",
- "#Given\n",
"k=236.0 # thermal conductivity in W/(m.K)\n",
"Cp=896.0 # specific heat in J/(kg.K)\n",
"sp_gr=2.702 # specific gravity\n",
@@ -88,13 +79,11 @@ "L=0.60 # length in m\n",
"hc=550.0 # unit surface conductance between the metal and the bath in W/(K.sq.m)\n",
"\n",
- "#calculation\n",
"import math\n",
"Vs=(math.pi*D**2*L)/4.0 # Volume in cu.m\n",
"As=(2*math.pi*D**2/4.0)+(math.pi*D*L) # surface area in sq.m\n",
"import math\n",
"Bi=(hc*Vs)/(k*As) # Biot Number\n",
- "# Biot number is less than 1 hence lump capacitance equations apply\n",
"T_i=50.0 # initial temperature in degree celsius\n",
"T_inf=2.0 # temperature of ice water bath in degree celsius\n",
"t=60.0 # time=1 minute=60 s\n",
@@ -102,7 +91,6 @@ "T=T_inf+(T_i-T_inf)*math.exp(-(hc*As_*t)/(density*Vs*Cp))\n",
"Q=density*Vs*Cp*(T_inf-T_i)*(1-math.exp(-(hc*As_*t)/(density*Vs*Cp)))\n",
"\n",
- "#result\n",
"print\"(a)The temperature of aluminium is\",round(T,1),\"C\"\n",
"print\"(b)The cumulative heat transferred is \",round(-Q/1000,1),\"KJ\"\n"
],
@@ -132,9 +120,7 @@ "cell_type": "code",
"collapsed": false,
"input": [
- "#Determine the time required and temprature profile\n",
"\n",
- "#Given\n",
"hc=30\n",
"L=0.24\n",
"k=1.25 #Conductivity\n",
@@ -142,7 +128,6 @@ "rou=550\n",
"Fo=0.4 #Fourier no\n",
"\n",
- "#Calculation\n",
"Bi=hc*L/k\n",
"alpha=k/(rou*c)\n",
"Tc=150\n",
@@ -150,7 +135,6 @@ "T_i=50\n",
"t=(L**2*Fo)/(alpha)\n",
"TC1=0.82 #Centreline temprature\n",
- "#from table at x/l=0.4\n",
"T=0.71*(T_i-T_inf)*TC1\n",
"x=0.4*L\n",
"Ti=149\n",
@@ -182,7 +166,6 @@ "cell_type": "code",
"collapsed": false,
"input": [
- "#Calculate the time required\n",
"hc=6 #Surface Conductance\n",
"D=0.105 #Orange Diameter\n",
"k=0.431 #Thermal conductivity \n",
@@ -190,11 +173,9 @@ "rou=998 #Density\n",
"Fo=1.05 #Fourier no.\n",
"\n",
- "#Calculation\n",
"import math\n",
"Vs=math.pi*D**3/6\n",
"As=math.pi*D**2\n",
- "# calculating Biot Number for lumped capacitance approach\n",
"Bi=hc*Vs/(k*As)\n",
"Bi_=hc*(D/2)/(k)\n",
"alpha=k/(rou*c)\n",
@@ -205,7 +186,6 @@ "a=Bi_**2*Fo\n",
"Q=0.7*rou*c*(math.pi/6.0*(Fo**3))*(T_i-T_inf)\n",
"\n",
- "#Result\n",
"print\"The time required is \",round(t/3600,2),\"hr\"\n",
"print\"The heat transfered is\",round(Q/1000,2),\"kj\""
],
@@ -235,7 +215,6 @@ "cell_type": "code",
"collapsed": false,
"input": [
- "#Estimate the depth of freeze line\n",
" \n",
"D=0.105 #diameter\n",
"k=0.3 #Thermal conductivity \n",
@@ -245,8 +224,6 @@ "alpha=k/(sp_gr*rou_water*c)\n",
"t=3*30*24\n",
"\n",
- "#Calculation\n",
- "# Bi_math.sqrt(Fo) is infinite\n",
"T_inf=10\n",
"Ts=10\n",
"T=32\n",
@@ -255,7 +232,6 @@ "variable_fig4_12=0.38 #The value of x/(2*(alpha*t)**0.5) from figure 4.12\n",
"x=2*math.sqrt(alpha*t)*variable_fig4_12\n",
"\n",
- "#result\n",
"print\"The depth of the freeze line in soil is ft\",round(x,2),\"ft\"\n"
],
"language": "python",
@@ -283,18 +259,14 @@ "cell_type": "code",
"collapsed": false,
"input": [
- "# properties of aluminium from appendix table B1\n",
"\n",
- "#Given\n",
"k_al=236\n",
"p_al=2.7*1000\n",
"c_al=896\n",
- "# properties of oak from appendix table B3\n",
"k_oak=0.19\n",
"p_oak=0.705*1000\n",
"c_oak=2390\n",
"\n",
- "#Calculation\n",
"import math\n",
"math.sqrt_kpc_al=math.sqrt(k_al*p_al*c_al)\n",
"kpc_R=4\n",
@@ -304,7 +276,6 @@ "math.sqrt_kpc_oak=math.sqrt(k_oak*p_oak*c_oak)\n",
"T_oak=(T_Li*(math.sqrt_kpc_oak)+T_Ri*math.sqrt(kpc_R))/(math.sqrt_kpc_oak+math.sqrt(kpc_R))\n",
"\n",
- "#Result\n",
"print\"The temperature of aluminium is felt as \",round(T_al,2),\"C\"\n",
"print\"The temperature of oak is felt as %.1f degree celsius\",round(T_oak,1),\"C\"\n",
"print\"So oak will feel warmer to the touch than will the aluminium\"\n"
@@ -336,10 +307,7 @@ "cell_type": "code",
"collapsed": false,
"input": [
- "# properties of water at 68 degree fahrenheit from appendix table C11\n",
"\n",
- "#Given\n",
- "# The given properties are\n",
"rou=62.46\n",
"cp=0.9988\n",
"k=0.345\n",
@@ -347,7 +315,6 @@ "D=2.5/12.0\n",
"L=4.75/12.0\n",
"\n",
- "#Calculation\n",
"Vs=math.pi*D**2*L/4\n",
"As=(math.pi*D*L)+(math.pi*D**2)/2\n",
"Lc=Vs/As\n",
@@ -355,19 +322,16 @@ "Bi=hc*Lc/k\n",
"t=4\n",
"\n",
- "# for the cylinder solution\n",
"Fo_cylinder=alpha*t/(D/2)**2\n",
"Bi_cylinder=hc*(D/2)/k\n",
"reciprocal_Bi_cylinder=1/Bi_cylinder\n",
"dim_T_cylinder=0.175 #The value of dimensionless temperature of cylinder from figure 4.7a at corresponding values of Fo and 1/Bi\n",
"\n",
- "# for the infinite plate solution\n",
"Fo_plate=alpha*t/(L/2)**2\n",
"Bi_plate=hc*L/(2*k)\n",
"reciprocal_Bi_plate=1/Bi_plate\n",
"dim_T_plate=0.55 #The value of dimensionless temperature of infinite plate from figure 4.7a at corresponding values of Fo and 1/Bi\n",
"\n",
- "# For short cylinder problem\n",
"dim_T_shortcylinder=dim_T_cylinder*dim_T_plate\n",
"T_inf=30\n",
"T_i=72\n",
@@ -377,7 +341,6 @@ "dim_Tw_shortcylinder=dim_Tw_cylinder*dim_Tw_plate\n",
"Tw=dim_Tw_shortcylinder*(Tc-T_inf)+T_inf\n",
"\n",
- "#Result\n",
"print\"The temperature at centre of can is %.1f degree celsius\",round(Tc,0),\"F\"\n",
"print\"The bear temperature near the metal of the can is\",round(Tw,0),\"F\"\n",
"\n"
@@ -408,15 +371,11 @@ "cell_type": "code",
"collapsed": false,
"input": [
- "#Determine the time to reach centre temp. 50 C\n",
"\n",
- "#Given Data\n",
- "#The given properties are\n",
"rou=7817 #Density\n",
"c=461 #Specific heat \n",
"k=14.4 #Thermal conductivity \n",
"alpha=.387e-5\n",
- "#The dimension are\n",
"L1=0.03\n",
"L2=0.03\n",
"L3=0.04\n",
@@ -424,19 +383,14 @@ "T_i=95 #Internal temprature \n",
"T_inf=17 #Temprature at infinity\n",
"\n",
- "#Calculation\n",
- "# for infinite plate\n",
"L=L1/2\n",
"hc=50\n",
"reciprocal_Bi_plate=k/(hc*L)\n",
"Tinf=0.085 #Temprature distribution for infinite plate\n",
"Tsi=0.225 #Temprature distribution for semi infinite plate\n",
- "#Temprature at a depth of 4 cm\n",
"T=(Tinf**2)*(1-Tsi)*(T_i-T_inf)+T_inf\n",
- "#From the table\n",
"t=350\n",
"\n",
- "#Result\n",
"print\"At a time 3000s The temprature is \",round(T,1),\"C\"\n",
"print\"From the table The time requires to reach tempratue 50C is \",t,\"s\""
],
@@ -476,19 +430,14 @@ "cell_type": "code",
"collapsed": false,
"input": [
- "#Determine the time that will pass before the heat added\n",
"\n",
- "#Given\n",
"rou=0.5*1000\n",
"cp=837\n",
"k=0.128\n",
"alpha=0.049e-5\n",
"Ti=20 #Initial temprature\n",
- "# let Fo=0.5 and dx=0.05\n",
"dt=0.5*(0.05)**2/alpha\n",
"\n",
- "#Calculation\n",
- "#Temprature at 1<m<6 and p>0 till T6>20\n",
"p=0\n",
"T0=200\n",
"m=1\n",
@@ -504,7 +453,6 @@ "m=6\n",
"T61=(Ti+Ti)/2.0\n",
"\n",
- "#For next time interval\n",
"p=1\n",
"m=1\n",
"T12=(Ti+T0)/2.0\n",
@@ -518,11 +466,9 @@ "T52=(Ti+T41)/2.0\n",
"m=6\n",
"T62=(Ti+T51)/2.0\n",
- "#Repeating it\n",
"t=4.97\n",
"print\"The time that will pass before the heat added\",t,\"hr\"\n",
"\n",
- "#Plot\n",
"import matplotlib.pyplot as plt\n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(111)\n",
@@ -567,24 +513,18 @@ "cell_type": "code",
"collapsed": false,
"input": [
- "# determination of time required to cool to a certain temperature\n",
"\n",
- "#Given\n",
- "#The properties are\n",
"rou=7.817*62.4 #density\n",
"c=0.110\n",
"k=8.32\n",
"alpha=0.417e-4\n",
"dx=1/12.0\n",
- "# taking Fo=1\n",
"Fo=1\n",
"\n",
- "#Calculation\n",
"dt=Fo*dx**2/alpha\n",
"n=8 #Enter the number of time intervals from Saulev plot\n",
"time=n*dt\n",
"\n",
- "#result\n",
"print\"The required time is hr\",round(time/3600,2),\"hr\"\n"
],
"language": "python",
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