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{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 5 : Diffusion"
]
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 5.1 Page No. 114"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"Ca=1.2 #Concentration at A in kg/m**3\n",
"Cb=0.8 #Concentration at B in kg/m**3\n",
"xa=5*10**-3 #Position 1 in m\n",
"xb=10*10**-3 #Position 2 in m\n",
"\n",
"D=3*10**-11 #Diffusion coefficient in m**2/s\n",
"J=-D*(Ca-Cb)/(xa-xb)\n",
"\n",
"print\"Diffusion flux is \",J,\"kg/m**2-s\"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Diffusion flux is 2.4e-09 kg/m**2-s\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 5.2 Page No. 117"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from scipy.optimize import fsolve\n",
"Co=0.25 #Initial Conc. in wt%\n",
"Cs=1.2 #Surface conc. in wt%\n",
"Cx=0.8 #Conc. at any x in wt%\n",
"x=5*10**-4 #Position in m\n",
"D=1.6*10**-11 #Diffusion coeff in m**2/s\n",
"\n",
"import math\n",
"C=1-((Cx-Co)/(Cs-Co))\n",
"\n",
"def f(z):\n",
" return(0.4210-math.erf(z))\n",
"z=fsolve(f,1)\n",
"t=x**2/(4.0*D*z**2.0)\n",
"\n",
"print\"Time required is \",round(t/3600.0,1),\"h\"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Time required is 7.0 h\n"
]
}
],
"prompt_number": 15
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 5.3 Page No. 118"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"D500=4.8*10**-14 #Diffusion coefficient at 500 C\n",
"D600=5.3*10**-13 #Diffusion coefficient at 600 C\n",
"t600=10 #Time in hours to diffuse\n",
"\n",
"t500=D600*t600/D500\n",
"\n",
"print\"Time to diffuse at 500 C is \",round(t500,1),\"h\"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Time to diffuse at 500 C is 110.4 h\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 5.4 Page No. 121"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"T=550+273 #in K\n",
"D0=1.2*10**-4 #Temperature independent preexponential in m**2/s\n",
"Qd=131000 #Activation energy in J/mol-K\n",
"R=8.31 #Universal Gas constt\n",
"\n",
"import math\n",
"D=D0*math.exp(-Qd/(R*T))\n",
"\n",
"print\"Diffusion coefficient is \",round(D,14),\"m**2/s\"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Diffusion coefficient is 5.8e-13 m**2/s\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Example 5.5 Page No.121"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"inv_T1=0.8*10**-3 #Reciprocal of temp. in K**-1\n",
"inv_T2=1.1*10**-3 #Reciprocal of temp. in K**-1\n",
"logD1=-12.4\n",
"logD2=-15.45\n",
"R=8.31 #Gas law Constant in J/mol-K\n",
"\n",
"Qd=-2.3*R*(logD1-logD2)/(inv_T1-inv_T2)\n",
"print\"Activation energy is\",round(Qd/1000,0),\"KJ\"\n",
"\n",
"D0=10**(logD2+(Qd*inv_T2/(2.3*R)))\n",
"print\"Preexponential factor is\",round(D0,6),\"m**2/s\"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Activation energy is 194.0 KJ\n",
"Preexponential factor is 5.4e-05 m**2/s\n"
]
}
],
"prompt_number": 15
},
{
"cell_type": "heading",
"level": 3,
"metadata": {},
"source": [
"Design Example 5.1, Page No.122"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"C0=0.2 #Initial concentration in wt%\n",
"Cs=1 #Surface conc in wt%\n",
"Cx=0.6 #Conc at any position X in wt%\n",
"x=7.5*10**-4 #Position in m\n",
"D0=2.3*10**-5 #Preexponential factor in m**2/s\n",
"R=8.31 #Gas law constant in J/mol-K\n",
"Qd=148000 #Activation energy in J/mol\n",
"\n",
"C=1-((Cx-C0)/(Cs-C0))\n",
"z=0.4747\n",
"Dt=(x/(2*z))**2\n",
"\n",
"D=Dt/D0\n",
"\n",
"T1=900.0\n",
"T2=950.0\n",
"T3=1000.0\n",
"T4=1050.0\n",
"t1=D/math.exp(-Qd/(R*(T1+273)))/3600.0\n",
"t2=D/math.exp(-Qd/(R*(T2+273)))/3600.0\n",
"t3=D/math.exp(-Qd/(R*(T3+273)))/3600.0\n",
"t4=D/math.exp(-Qd/(R*(T4+273)))/3600.0\n",
"\n",
"print\"Temperature in Celcius are\",T1,T2,T3,T4\n",
"print\"Time is respectively \",round(t1,1),\"h,\",round(t2,1),\"h,\",round(t3,1),\"h,\",round(t4,1),\"h\"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Temperature in Celcius are 900.0 950.0 1000.0 1050.0\n",
"Time is respectively 29.6 h, 15.9 h, 9.0 h, 5.3 h\n"
]
}
],
"prompt_number": 23
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
|
