{
 "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": {}
  }
 ]
}