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{
"metadata": {
"name": "CHAPTER 3"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 3:Steady-State Conduction in Multiple Dimensions"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 3.1 Page No.132"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Determination of the heat-flow rate from one tube \n",
"# specifications of 1 standard type K from table F2\n",
"\n",
"#iven\n",
"OD=0.02858 # outer diameter in m\n",
"# from figure 3.11\n",
"M=8.0 # total number of heat-flow lanes\n",
"N=6.0 # number of squares per lane\n",
"S_L=M/N # conduction shape factor\n",
"k=0.128 # thermal conductivity in W/(m.K) for concrete from appendix table B3\n",
"T1=85 # temperature of tube surface\n",
"T2=0 # temperature of ground beneath the slab\n",
"\n",
"#Calculation\n",
"q_half=k*S_L*(T1-T2)\n",
"q=2*q_half\n",
"\n",
"#Result\n",
"print\"The total heat flow per tube is\",round(q,0),\" W/m\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The total heat flow per tube is 29.0 W/m\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 3.2 Page No.134"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Determination of the heat transferred from the buried pipe per unit length\n",
"# shape factor number 8 is selected from table 3.1\n",
"# specifications of 10 nominal, schedule 80 pipe from table F1\n",
"\n",
"#Given\n",
"import math\n",
"OD=10.74/12 # diameter in ft\n",
"R=OD/2\n",
"T1=140.0\n",
"T2=65.0\n",
"k=0.072 # thermal conductivity in BTU/(hr-ft. degree R)\n",
"d=18.0/12.0 # distance from centre-line\n",
"S_L=(2*math.pi)/(math.acosh(d/R))\n",
"q_L=k*S_L*(T1-T2)\n",
"print\"The heat transferred from the buried pipe per unit length is \",round(q_L,2),\"BTU/(hr.ft)\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The heat transferred from the buried pipe per unit length is 18.05 BTU/(hr.ft)\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 3.3 Page No.135"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Determination of the heat lost through the walls, using the shape-factor method. \n",
"#(b) Repeat the calculations but neglect the effects of the corners that is, . \n",
"\n",
"#Given\n",
"k = 1.07 # thermal conductivity of silica brick from appendix table B3 in W/(m.K)\n",
"S1_A=0.138*0.138/0.006\n",
"nA=2\n",
"\n",
"# Calculation of total shape factor\n",
"# From figure 3.12, for component A\n",
"St_A=nA*S1_A # Total shape factor of component A\n",
"\n",
"# For component B\n",
"S1_B=0.138*0.188/0.006\n",
"nB=4\n",
"St_B=nB*S1_B # Total shape factor of component B\n",
"\n",
"# For component C\n",
"S3_C=0.15*0.006\n",
"nC=8\n",
"St_C=nC*S3_C # Total shape factor of component C\n",
"\n",
"# For component D\n",
"S2_D=0.54*0.188\n",
"nD=4\n",
"St_D=nD*S2_D # Total shape factor of component D\n",
"\n",
"# For component E\n",
"S2_E=0.138*0.54\n",
"nE=8\n",
"St_E=nE*S2_E # Total shape factor of component E\n",
"\n",
"S=St_A+St_B+St_C+St_D+St_E\n",
"T1=550\n",
"T2=30\n",
"q=k*S*(T1-T2)\n",
"S=St_A+St_B\n",
"q_1=k*S*(T1-T2)\n",
"Error=(q-q_1)/q\n",
"\n",
"#result\n",
"print\"(a)The heat transferred through the walls of the furnace is \",round(q/1000,1),\"kw\"\n",
"# Neglecting the effects of the edges and corners, the shape factor for all walls is found as \n",
"print\"(b The heat transferred is\",q_1/1000,1,\"kw\"\n",
"print\" The error introduced by neglecting heat flow through the edges and corners is \",round(Error*100,1),\" percent\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)The heat transferred through the walls of the furnace is 13.7 kw\n",
"(b The heat transferred is 13.1555216 1 kw\n",
" The error introduced by neglecting heat flow through the edges and corners is 4.1 percent\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 3.4 Page No. 142"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Determination of the conduction shape factor for the underground portion of the configuration\n",
"# specifications of 4 nominal, schedule 40 pipe from table F1\n",
"\n",
"#Given\n",
"OD=4.5/12.0 # diameter in ft\n",
"R=OD/2.0\n",
"\n",
"# For pipe A\n",
"#calculation\n",
"import math\n",
"L_A=4.5 # length in ft\n",
"# shape factor number 9 is selected from table 3.1\n",
"S_A=(2*math.pi*L_A)/(math.log(2*(L_A)/R))\n",
"# For pipe B\n",
"L_B=18 # length in ft\n",
"# shape factor number 9 is selected from table 3.1\n",
"S_B=(2*math.pi*L_B)/(math.acosh(L_A/R))\n",
"S=2*S_A+S_B\n",
"\n",
"#Result\n",
"print\"The total conduction shape factor for the system is\",round(S,1)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The total conduction shape factor for the system is 43.8\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 3.5 Page No. 151"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%pylab inline"
],
"language": "python",
"metadata": {},
"outputs": []
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#(a)plot graph the temperature distribution existing within the rod. \n",
"#(b) Use the numerical formulation of this section to obtain the temperature distribution.\n",
"#(c) Compare the two models to determine how well the numerical results approximate the exact results\n",
"\n",
"#Given\n",
"h=1.1 # convective coefficient in BTU/(hr.ft^2. degree R)\n",
"Tw=200.0\n",
"T_inf=68.0 # ambient temperature\n",
"k=0.47 # thermal conductivity in BTU/(hr.ft.degree R) from table B3\n",
"D=0.25/12 # diameter in ft\n",
"\n",
"#Calculation\n",
"A=math.pi*D**(2)/4.0 # cross sectional area in ft^2\n",
"P=math.pi*D # perimeter in ft\n",
"L=6/12.0 # length in ft\n",
"mL=L*((h*P)/(k*A))**(0.5)\n",
"dz=1.0\n",
"L=4.0\n",
"de=dz/L\n",
"K=2+(mL*de)**2\n",
"\n",
"#Tempature can be calculated as\n",
"T4=T_inf+(Tw-T_inf)*(2/(K**4-4*K**2+2))\n",
"T3=T_inf+(Tw-T_inf)*(K/(K**4-4*K**2+2))\n",
"T2=T_inf+(Tw-T_inf)*((K**2-1)/(K**4-4*K**2+2))\n",
"T1=T_inf+(Tw-T_inf)*((K**3-3*K)/(K**4-4*K**2+2))\n",
"\n",
"#result\n",
"print\"The temprature distribution is T4=\",round(T4,2),\"F\"\n",
"print\"The temprature distribution is T3=\",round(T3,2),\"F\"\n",
"print\"The temprature distribution is T2=\",round(T2,2),\"F\"\n",
"print\"The temprature distribution is T1=\",round(T1,2),\"F\"\n",
"\n",
"#(b)plot\n",
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"T=[200.0,77.33,68.66,68.05,68]\n",
"z=[0,1.5,3,4.5,6]\n",
"xlim(0,6)\n",
"ylim(50,200)\n",
"plt.ylabel('T (C)')\n",
"plt.xlabel('z (in)')\n",
"plt.annotate('Numeric approximation using 4 nodes', xy=(2,82), xytext=(0,30),\n",
" arrowprops=dict(facecolor='black', shrink=0.05),\n",
" )\n",
"a=plot(z,T)\n",
"\n",
"T1=[200.0,82.81,69.66,68.19,68.04]\n",
"plt.ylabel('T1 (F)')\n",
"plt.xlabel('z (in)')\n",
"plt.annotate('exact solution', xy=(1.5,80), xytext=(0,60),\n",
" arrowprops=dict(facecolor='black', shrink=0.05),\n",
" )\n",
"a=plot(z,T1)\n",
"show(a)\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The temprature distribution is T4= 68.04 F\n",
"The temprature distribution is T3= 68.19 F\n",
"The temprature distribution is T2= 69.68 F\n",
"The temprature distribution is T1= 82.82 F\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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nhs/kvd3vUVhcqG4wIUSVJQWhGps6FebPB0WBDm4daOnUkpijMWrHEkJUUVIQ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\nVq147rnnOHv2LB4eHqxZs4Z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"text": [
"<matplotlib.figure.Figure at 0x752b7f0>"
]
}
],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
|
