{
"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": {}
}
]
}