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mhogg/natural_convection_sphere.ipynb

Created June 28, 2016 23:54
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natural_convection_sphere.ipynb
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from numpy import *"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Natural convective heat loss from sphere"
]
},
{
"cell_type": "code",
"execution_count": 179,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Lc = 0.196350 m\n",
"beta = 0.002309 \n"
]
}
],
"source": [
"d = 0.125 # Sphere diameter (m)\n",
"Lc = 0.5*d*pi # Characteristic length (m) (from textbook version of Cengel)\n",
"#Lc = d # Characteristic length (m) (from online version of Cengel)\n",
"Ts = 160 # Surface temperature (deg C)\n",
"Tinf = 30 # Air temperature (deg C)\n",
"vis = 1.8645e-5 # Air viscosity\n",
"beta = 1.0/(Ts+273.15) # Expansion coefficient of air\n",
"Pr = 0.712 # Prandtl number\n",
"g = 9.8 # Gravity (m/s2)\n",
"k = 0.0263 # Thermal conductivity of air (W/m-K)\n",
"print \"Lc = %f m\" % Lc\n",
"print \"beta = %f \" % beta"
]
},
{
"cell_type": "code",
"execution_count": 180,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Gr = 6.405e+07\n"
]
}
],
"source": [
"Gr = (g*beta*(Ts-Tinf)*(Lc**3.0))/(vis**2.0)\n",
"print \"Gr = %.3e\" % Gr "
]
},
{
"cell_type": "code",
"execution_count": 181,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Ra = 4.560e+07\n"
]
}
],
"source": [
"Ra = Gr*Pr\n",
"print \"Ra = %.3e\" % Ra"
]
},
{
"cell_type": "code",
"execution_count": 182,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Nu = 39.36\n"
]
}
],
"source": [
"Nu = 2 + (0.589*Ra**0.25)/((1+(0.469/Pr)**(9./16.))**(4./9.))\n",
"print \"Nu = %.2f\" % Nu"
]
},
{
"cell_type": "code",
"execution_count": 183,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"5.27 W/m-K\n"
]
}
],
"source": [
"h = k/Lc*Nu\n",
"print \"%.2f W/m-K\" % h"
]
},
{
"cell_type": "code",
"execution_count": 184,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"33.64 W\n"
]
}
],
"source": [
"A = 4*pi*(d/2.)**2\n",
"Q = h*A*(Ts-Tinf)\n",
"print \"%.2f W\" % Q"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.11"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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