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"name": "",
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Introduction to conduction"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.1 Page 68"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"def alpha(p, Cp, k):\n",
" a=k/(p*Cp); #[m^2/s]\n",
" return a;\n",
"\n",
"p = 2702.; \t\t#[Kg/m^3] - Density Of Material \n",
"Cp = 903.; \t\t\t#[J/kg.K] - Specific heat of Material\n",
"k = 237.; \t\t#[W/m.k] - Thermal Conductivity of Material\n",
"\n",
"print '%s %.2e %s' %(\"\\n (a) Thermal Diffuisivity of Pure Aluminium at 300K = \",alpha(p, Cp, k),\" m^2/s\\n\");\n",
"\n",
"#(b) Pure Aluminium at 700K\n",
"# From Appendix A, Table A.1\n",
"\n",
"p = 2702.; \t\t#[Kg/m^3] - Density Of Material \n",
"Cp = 1090.; \t\t#[J/kg.K] - Specific heat of Material\n",
"k = 225.; \t\t#[W/m.k] - Thermal Conductivity of Material\n",
"\n",
"print '%s %.2e %s' %(\"\\n (b) Thermal Diffuisivity of Pure Aluminium at 700K =\",alpha(p, Cp, k),\" m^2/s\\n\");\n",
"\n",
"#(c) Silicon Carbide at 1000K\n",
"# From Appendix A, Table A.2\n",
"\n",
"p = 3160.; \t\t#[Kg/m^3] - Density Of Material \n",
"Cp = 1195.; \t\t#[J/kg.K] - Specific heat of Material\n",
"k = 87.; \t\t#[W/m.k] - Thermal Conductivity of Material\n",
"\n",
"print '%s %.2e %s' %(\"\\n (c) Thermal Diffuisivity of Silicon Carbide at 1000K =\",alpha(p, Cp, k),\" m^2/s\\n\");\n",
"\n",
"#(d) Paraffin at 300K\n",
"# From Appendix A, Table A.3\n",
"\n",
"p = 900.; \t\t\t#[Kg/m^3] - Density Of Material \n",
"Cp = 2890.; \t\t#[J/kg.K] - Specific heat of Material\n",
"k = .24; \t\t#[W/m.k] - Thermal Conductivity of Material\n",
"\n",
"print '%s %.2e %s' %(\"\\n (d) Thermal Diffuisivity of Paraffin at 300K = \",alpha(p, Cp, k),\"m^2/s\");\n",
"#END\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" (a) Thermal Diffuisivity of Pure Aluminium at 300K = 9.71e-05 m^2/s\n",
"\n",
"\n",
" (b) Thermal Diffuisivity of Pure Aluminium at 700K = 7.64e-05 m^2/s\n",
"\n",
"\n",
" (c) Thermal Diffuisivity of Silicon Carbide at 1000K = 2.30e-05 m^2/s\n",
"\n",
"\n",
" (d) Thermal Diffuisivity of Paraffin at 300K = 9.23e-08 m^2/s\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.2 Page 75"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"\n",
"a = 900.; \t\t\t#[degC]\n",
"b = -300.; \t\t\t#[degC/m]\n",
"c = -50.; \t\t\t#[degC/m^2]\n",
"\n",
"q = 1000.; \t\t\t#[W/m^2.K] - Uniform heat Generation\n",
"A = 10. ; \t\t\t#[m^2] - Wall Area\n",
"#Properties of Wall\n",
"p = 1600.; \t\t\t#[kg/m^3] - Density\n",
"k = 40.; \t\t\t#[W/m] - Thermal Conductivity\n",
"Cp = 4000.; \t\t\t#[J/kg.K] - Specific Heat\n",
"L = 1; \t\t\t #[m] - Length of wall\n",
"#calculations and results\n",
"\n",
"#(i) Rate of Heat Transfer entering the wall and leaving the wall\n",
"# From Eqn 2.1\n",
"# qin = -kA(dT/dx)|x=0 = -kA(b)\n",
"\n",
"qin= - b*k*A;\n",
"\n",
"# Similarly\n",
"# qout = -kA(dT/dx)|x=L = -kA(b+2cx)|x=L\n",
"\n",
"qout= - k*A*(b+2*c*L);\n",
"\n",
"print '%s %d %s' %(\"\\n (i) Rate of Heat Transfer entering the wall =\",qin,\" W \");\n",
"print '%s %d %s' %(\"\\n And leaving the wall =\",qout,\"W \");\n",
"\n",
"#(ii) Rate of change Of Energy Storage in Wall E`st\n",
"# Applying Overall Energy Balance across the Wall\n",
"#E`st = E`in + E`g + E`out = qin + q`AL - qout\n",
"Est = qin + q*A*L - qout;\n",
"\n",
"print '%s %d %s' %(\"\\n (ii) Rate of change Of Energy Storage in Wall =\",Est,\" W\\n\");\n",
"\n",
"#(iii) Time rate of Temperature change at x= 0, 0.25 and .5m\n",
"#Using Eqn 2.19\n",
"# T`= dT/dt = (k/p*Cp)*d(dT/dx)/dx + q`/p*Cp\n",
"#As d(dT/dx)/dx = d(b + 2cx)/dx = 2c - Independent of x\n",
"T = (k/(p*Cp))*(2*c)+ q/(p*Cp);\n",
"print '%s %.6f %s' %(\"\\n (iii) Time rate of Temperature change independent of x =\",T,\" degC/s\\n\");\n",
"\n",
"#END\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" (i) Rate of Heat Transfer entering the wall = 120000 W \n",
"\n",
" And leaving the wall = 160000 W \n",
"\n",
" (ii) Rate of change Of Energy Storage in Wall = -30000 W\n",
"\n",
"\n",
" (iii) Time rate of Temperature change independent of x = -0.000469 degC/s\n",
"\n"
]
}
],
"prompt_number": 2
}
],
"metadata": {}
}
]
}
|
