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+{

+ "metadata": {

+  "name": "",

+  "signature": "sha256:2e72bac4245ea0d7ffb20474fbd7477dd537a5d43e72a324996bb189620d2ad0"

+ },

+ "nbformat": 3,

+ "nbformat_minor": 0,

+ "worksheets": [

+  {

+   "cells": [

+    {

+     "cell_type": "heading",

+     "level": 1,

+     "metadata": {},

+     "source": [

+      "Chapter 5: Principles of Unsteady-State Heat Transfer"

+     ]

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Example 5.2-1, Page number 333"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#Cooling of a Steel Ball\n",

+      "from math import pi, exp\n",

+      "\n",

+      "\n",

+      "#Variable declaration #English Units\n",

+      "r = 1./12           #Radius of a Steel Ball, ft\n",

+      "Tbi = 800.          #Initial uniform temperature of the steel ball, \u00b0F\n",

+      "Tinf = 250.         #Temeperature of a constant temperature bath, \u00b0F\n",

+      "h = 2.0             #Convective Heat Transfer Coefficient, Btu/(h.ft2\u00b0F)\n",

+      "t = 1.              #Time at which temperature of the ball is to be determined, s\n",

+      "k = 25.             #Thermal conductivity of the steel ball, Btu/(h.ft\u00b0F)\n",

+      "rho = 490.          #Density of a steel ball, lbm/ft3\n",

+      "cp = 0.11           #Specific heat of steel ball, Btu/(lbm.\u00b0F)\n",

+      "\n",

+      "#Calculation\n",

+      "\n",

+      "x1 = r/3\n",

+      "NBi = h*x1/k\n",

+      "A = 4*pi*r**2\n",

+      "V = 4*pi*r**3/3.\n",

+      "tau = h*A/(cp*rho*V)\n",

+      "Tb = Tinf + (Tbi - Tinf)*exp(-tau*t)\n",

+      "#Result\n",

+      "print \"Temperature of ball after one hour: \", round(Tb),\"\u00b0F\"\n",

+      "\n",

+      "\n",

+      "#Variable declaration # SI Units\n",

+      "\n",

+      "r = 0.0254                              #Radius of a Steel Ball, m\n",

+      "Tbi = 699.9                             #Initial uniform temperature of the steel ball, K\n",

+      "Tinf = 394.3                            #TEmeperature of a constant temperature bath, K\n",

+      "h = 11.36                               #Convective Heat Transfer Coefficient, W/(m2K)\n",

+      "t = 3600.                               #Time at which temperature of the ball is to be determined, s\n",

+      "k = 43.3                                #Thermal conductivity of the steel ball, W/(mK)\n",

+      "rho = 7849.                             #Density of a steel ball, kg/m3\n",

+      "cp = 460.6                              #Specific heat of steel ball, J/(kg.K)\n",

+      "\n",

+      "#Calculation\n",

+      "\n",

+      "x1 = r/3\n",

+      "NBi = h*x1/k\n",

+      "A = 4*pi*r**2\n",

+      "V = 4*pi*r**3/3.\n",

+      "tau = h*A/(cp*rho*V)\n",

+      "Tb = Tinf + (Tbi - Tinf)*exp(-tau*t)\n",

+      "#Result\n",

+      "print \"Temperature of ball after one hour: \", round(Tb,1),\"\u00b0C\""

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "Temperature of ball after one hour:  395.0 \u00b0F\n",

+        "Temperature of ball after one hour:  474.6 \u00b0C\n"

+       ]

+      }

+     ],

+     "prompt_number": 1

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Example 5.2-2, Page Number 334"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#Total amount of heat in cooling\n",

+      "from math import pi \n",

+      "\n",

+      "#Variable declaration\n",

+      "r = 0.0254                              #Radius of a Steel Ball, m\n",

+      "Tbi = 699.9                             #Initial uniform temperature of the steel ball, K\n",

+      "Tinf = 394.3                            #TEmeperature of a constant temperature bath, K\n",

+      "h = 11.36                               #Convective Heat Transfer Coefficient, W/(m2K)\n",

+      "t = 3600.                               #Time at which temperature of the ball is to be determined, s\n",

+      "k = 43.3                                #Thermal conductivity of the steel ball, W/(mK)\n",

+      "rho = 7849.                             #Density of a steel ball, kg/m3\n",

+      "cp = 460.6                              #Specific heat of steel ball, J/(kg.K)\n",

+      "\n",

+      "#Calculation\n",

+      "\n",

+      "x1 = r/3\n",

+      "NBi = h*x1/k\n",

+      "A = 4*pi*r**2\n",

+      "V = 4*pi*r**3/3.\n",

+      "tau = cp*rho*V/(h*A)\n",

+      "Q = cp*rho*V*(Tbi-Tinf)*(1-exp(-t/tau))\n",

+      "#Result\n",

+      "\n",

+      "print 'Amount of Heat Transffered %6.4e'%(Q),\"J\""

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "Amount of Heat Transffered 5.5901e+04 J\n"

+       ]

+      }

+     ],

+     "prompt_number": 7

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Example 5.3-1, Page number 336"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#Freezing Temperature in the ground\n",

+      "from math import pi, erfc, exp\n",

+      "\n",

+      "# Variable declaration\n",

+      "Ti = 15.6                     #Earths constant temperature, degC\n",

+      "Tc = -17.8                    #Cold wave temperature, deg C\n",

+      "h = 11.36                     #Convective heat transfer coefficient, W/(m2K)\n",

+      "alpha = 4.65e-7               #THermal diffusivity of soil, m2/s\n",

+      "k = 0.865                     #Thermal conductivity of soil, W/(mK)\n",

+      "t = 5*3600                    #Time in seconds\n",

+      "x = 0.                        #Surface position , m\n",

+      "T0 = 0.                       #Freezing temperature for water\n",

+      "\n",

+      "# Calculation SI units\n",

+      "absc = x/(2*sqrt(alpha*t))\n",

+      "param = h*sqrt(alpha*t)/k\n",

+      "corr = erfc(absc) - exp(param*(2*absc+param))*erfc(absc+param)\n",

+      "T = Ti + (Tc - Ti)*(erfc(absc) - exp(param*(2*absc+param))*erfc(absc+param))\n",

+      "\n",

+      "ordi = (T0-Ti)/(Tc-Ti)\n",

+      "abscOrd = .16\n",

+      "x0 = 2*sqrt(alpha*t)*abscOrd\n",

+      "\n",

+      "#Results\n",

+      "print \"(a)   Temperature of the surface after 5 hour:\", round(T,1), \"\u00b0C\"\n",

+      "print \"(b)   Location of Freezing Temperature  after 5 hour:\",round(x0,4),\"m\"\n",

+      "\n",

+      "\n",

+      "# Variable declaration English units\n",

+      "Ti = 60.                     #Earths constant temperature, degF\n",

+      "Tc = -0.                     #Cold wave temperature, deg F\n",

+      "h = 2.                       #Convective heat transfer coefficient, Btu/(ft2Fhr)\n",

+      "alpha = 0.018                #THermal diffusivity of soil, ft2/hr\n",

+      "k = 0.5                      #Thermal conductivity of soil, Btu/(ft F)\n",

+      "t = 5                        #Time in hr\n",

+      "x = 0.                       #Surface position , ft\n",

+      "T0 = 32.                     #Freezing temperature for water\n",

+      "\n",

+      "# Calculation SI units\n",

+      "absc = x/(2*sqrt(alpha*t))\n",

+      "param = h*sqrt(alpha*t)/k\n",

+      "corr = erfc(absc) - exp(param*(2*absc+param))*erfc(absc+param)\n",

+      "T = Ti + (Tc - Ti)*(erfc(absc) - exp(param*(2*absc+param))*erfc(absc+param))\n",

+      "\n",

+      "ordi = (T0-Ti)/(Tc-Ti)\n",

+      "abscOrd = .16\n",

+      "x0 = 2*sqrt(alpha*t)*abscOrd\n",

+      "\n",

+      "#Result\n",

+      "print \"(a)   Temperature of the surface after 5 hour:\", round(T,1), \"\u00b0F\"\n",

+      "print \"(b)   Location of Freezing Temperature  after 5 hour:\",round(x0,4),\"ft\"\n",

+      "print 'The answers are different than book, because of book uses rounded numbers and rounded values of \\ncomplimentary error function whereas code used built in erfc function'"

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "(a)   Temperature of the surface after 5 hour: -5.2 \u00b0C\n",

+        "(b)   Location of Freezing Temperature  after 5 hour: 0.0293 m\n",

+        "(a)   Temperature of the surface after 5 hour: 22.7 \u00b0F\n",

+        "(b)   Location of Freezing Temperature  after 5 hour: 0.096 ft\n",

+        "The answers are different than book, because of book uses rounded numbers and rounded values of \n",

+        "complimentary error function whereas code used built in erfc function\n"

+       ]

+      }

+     ],

+     "prompt_number": 10

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Example 5.3-2, Page number 338"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#Heat Conduction in the slab\n",

+      "\n",

+      "# Variable declaration\n",

+      "x1 = .0462       #Thickness of the slab, m\n",

+      "T0 = 277.6       #Uniform temperature of the slab, K\n",

+      "T1 = 297.1       #Ambient temperature of the fluid, K\n",

+      "h = 8.52         #Convective heat transfer coefficient, W/m2.K\n",

+      "t = 5*3600       #Time, s\n",

+      "rho = 998.       #Density of H2O at 4 deg C (kg/m3)\n",

+      "k = 0.197        #Thermal conductivity of butter, W/m.K\n",

+      "cp = 2300        #Specific heat of butter, J/kg.K\n",

+      "\n",

+      "    \n",

+      "# Calculation\n",

+      "alpha = k/(rho*cp)       #Thermal diffusivity, m2/s\n",

+      "\n",

+      "#PART A Calculation of temperature at the surface\n",

+      "param = k/(h*x2)\n",

+      "X = alpha*t/x2**2\n",

+      "x = 0.0462      #Distance from surface at which temperature needs to be calculated, m\n",

+      "n = x/x2\n",

+      "Y = 0.25    #From fig 5.3-5 \n",

+      "T = T1 - Y*(T1-T0)\n",

+      "\n",

+      "#Result\n",

+      "\n",

+      "print \"Answers to part A\"\n",

+      "print \"Paramenter m for fig 5.3-5:\", round(param,3)\n",

+      "print \"Abscisa X for fig 5.3-2:\", round(X,3) \n",

+      "print \"Parameter n for fig 5.3-2:\", round(n,3)\n",

+      "print \"Temeprature of the surface at .0462 m after 5 hour\", round(T,1), \"K\", round(T-273.2,1), \"\u00b0C\"\n",

+      "\n",

+      "#PART B Calculation of temperature at 25.4 mm below the surface \n",

+      "param = k/(h*x2)\n",

+      "X = alpha*t/x2**2\n",

+      "x = 0.0208       #Distance from surface at which temperature needs to be calculated, m\n",

+      "n = x/x2\n",

+      "Y = 0.45    #From fig 5.3-5 \n",

+      "T = T1 - Y*(T1-T0)\n",

+      "\n",

+      "#Result\n",

+      "\n",

+      "print \"Answers to part B\"\n",

+      "print \"Paramenter m for fig 5.3-5:\", round(param,3)\n",

+      "print \"Abscisa X for fig 5.3-2:\", round(X,3) \n",

+      "print \"Parameter n for fig 5.3-2:\", round(n,3)\n",

+      "print \"Temeprature of the surface at .0208 m after 5 hour\", round(T,1), \"K\", round(T-273.2,1), \"\u00b0C\"\n",

+      "\n",

+      "#PART C Calculation of temperature at 46.2 mm below the surface\n",

+      "param = k/(h*x1)\n",

+      "X = alpha*t/x1**2\n",

+      "n = x/x1\n",

+      "Y = 0.5     #From fig 5.3-5 \n",

+      "T = T1 - Y*(T1-T0)\n",

+      "\n",

+      "#Result\n",

+      "print \"Answers to part B\"\n",

+      "print \"Paramenter m for fig 5.3-5:\", round(param,2)\n",

+      "print \"Abscisa X for fig 5.3-2:\", round(X,2) \n",

+      "print \"Parameter n for fig 5.3-2:\", round(n,1)\n",

+      "print \"Temeprature of the surface at .0462 m after 5 hour\", round(T,1), \"K\", round(T-273.2,1), \"\u00b0C\""

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "Answers to part A\n",

+        "Paramenter m for fig 5.3-5: 0.5\n",

+        "Abscisa X for fig 5.3-2: 0.724\n",

+        "Parameter n for fig 5.3-2: 1.0\n",

+        "Temeprature of the surface at .0462 m after 5 hour 292.2 K 19.0 \u00b0C\n",

+        "Answers to part B\n",

+        "Paramenter m for fig 5.3-5: 0.5\n",

+        "Abscisa X for fig 5.3-2: 0.724\n",

+        "Parameter n for fig 5.3-2: 0.45\n",

+        "Temeprature of the surface at .0208 m after 5 hour 288.3 K 15.1 \u00b0C\n",

+        "Answers to part B\n",

+        "Paramenter m for fig 5.3-5: 0.5\n",

+        "Abscisa X for fig 5.3-2: 0.72\n",

+        "Parameter n for fig 5.3-2: 0.5\n",

+        "Temeprature of the surface at .0462 m after 5 hour 287.4 K 14.2 \u00b0C\n"

+       ]

+      }

+     ],

+     "prompt_number": 21

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Example 5.3-3, Page number 342"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#Transient Heat Conduction in a Can of Pea Puree\n",

+      "\n",

+      "# Variable declaration\n",

+      "D = 0.0681       #Diameter of a Can, m\n",

+      "T0 = 29.4        #Uniform temperature of the slab, deg C\n",

+      "T1 = 115.6       #Ambient temperature of the steam, deg C\n",

+      "h = 4540         #Convective heat transfer coefficient, W/m2.K\n",

+      "t = 0.75*3600    #Time, s\n",

+      "x = 0.0          #Centre of the Can, m\n",

+      "k = 0.830        #Thermal conductivity of butter, W/m.K\n",

+      "alpha = 2.007e-7 #THermal diffusivity, m2/s\n",

+      "  \n",

+      "# Calculation\n",

+      "x1 = D/2.\n",

+      "n = x/x1\n",

+      "param = k/(h*x1)\n",

+      "X = alpha*t/x1**2\n",

+      "Y = 0.13    #From fig 5.3-8\n",

+      "T = T1 - Y*(T1-T0)\n",

+      "   \n",

+      "#Result\n",

+      "print \"Paramenter m for fig 5.3-8:\", round(param,5)\n",

+      "print \"Abscisa X for fig 5.3-8:\", round(X,3) \n",

+      "print \"Parameter n for fig 5.3-8:\", n\n",

+      "print \"Temeprature at the centre after 0.75 hour\", round(T,1),\"\u00b0C \""

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "Paramenter m for fig 5.3-8: 0.00537\n",

+        "Abscisa X for fig 5.3-8: 0.467\n",

+        "Parameter n for fig 5.3-8: 0.0\n",

+        "Temeprature at the centre after 0.75 hour 104.4 \u00b0C \n"

+       ]

+      }

+     ],

+     "prompt_number": 22

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Example 5.3-4, Page number 347"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#Two-Dimensional Conduction in a Short Cylinder \n",

+      "\n",

+      "# Variable declaration\n",

+      "\n",

+      "D = 0.0681       #Diameter of a Can, m\n",

+      "H = 0.1016       #Height of a Can, m\n",

+      "T0 = 29.4        #Uniform temperature of the slab, deg C\n",

+      "T1 = 115.6       #Ambient temperature of the steam, deg C\n",

+      "h = 4540         #Convective heat transfer coefficient, W/m2.K\n",

+      "t = 0.75*3600    #Time, s\n",

+      "x = 0.0          #Centre of the Can in radial direction, m\n",

+      "y = 0.0          #Centre of the Can in axial direction, m\n",

+      "k = 0.830        #Thermal conductivity of butter, W/m.K\n",

+      "alpha = 2.007e-7 #THermal diffusivity, m2/s\n",

+      "\n",

+      "# Calculation\n",

+      "\n",

+      "x1 = D/2.\n",

+      "y1 = H/2.\n",

+      "\n",

+      "#Radial direction\n",

+      "n = x/x1\n",

+      "m = k/(h*x1)\n",

+      "X = alpha*t/x1**2\n",

+      "Yx = 0.13    #From fig 5.3-8\n",

+      "\n",

+      "print \"Prameters for Radial Direction\"\n",

+      "print \"Paramenter m for fig 5.3-8:\", round(m,5)\n",

+      "print \"Abscisa X for fig 5.3-8:\", round(X,4) \n",

+      "print \"Parameter n for fig 5.3-8:\", n\n",

+      "print \"Parameter Yx from figure 5.3-8:\", round(Yx,3)\n",

+      "\n",

+      "#Axial Direction\n",

+      "n = y/y1\n",

+      "m = k/(h*y1)\n",

+      "X = alpha*t/y1**2\n",

+      "Yy = 0.8     #From Fig 5.3.6\n",

+      "\n",

+      "print \"\\nPrameters for Axial Direction\"\n",

+      "print \"Paramenter m for fig 5.3-8:\", round(m,5)\n",

+      "print \"Abscisa X for fig 5.3-8:\", round(X,4) \n",

+      "print \"Parameter n for fig 5.3-8:\", n\n",

+      "print \"Parameter Yy from figure 5.3-8:\", round(Yy,3)\n",

+      "Yxy = Yx*Yy\n",

+      "Txy = T1 - Yxy*(T1-T0)\n",

+      "#Result\n",

+      "\n",

+      "print \"\\nThe Temperature at the Centre of short cylinder:\", round(Txy,1), \"\u00b0C\"  "

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "Prameters for Radial Direction\n",

+        "Paramenter m for fig 5.3-8: 0.00537\n",

+        "Abscisa X for fig 5.3-8: 0.4674\n",

+        "Parameter n for fig 5.3-8: 0.0\n",

+        "Parameter Yx from figure 5.3-8: 0.13\n",

+        "\n",

+        "Prameters for Axial Direction\n",

+        "Paramenter m for fig 5.3-8: 0.0036\n",

+        "Abscisa X for fig 5.3-8: 0.21\n",

+        "Parameter n for fig 5.3-8: 0.0\n",

+        "Parameter Yy from figure 5.3-8: 0.8\n",

+        "\n",

+        "The Temperature at the Centre of short cylinder: 106.6 \u00b0C\n"

+       ]

+      }

+     ],

+     "prompt_number": 16

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Example 5.4-1, Page number 353"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#Unsteady State Conduction and the Schmidt Numerical Method\n",

+      "import matplotlib.pyplot as plt\n",

+      "import copy \n",

+      "\n",

+      "#Variable declaration\n",

+      "thk = 1.0       #Thickness of slab, m\n",

+      "Ti = 100.       #Initial uniform temperature of slab, \u00b0C\n",

+      "Ta = 0.         #Constant Temperature of environment, \u00b0C\n",

+      "alpha = 2.0e-5  #Thermal diffusivity of slab, m2/s\n",

+      "ns = 5          #Number of slices\n",

+      "M = 2.0         #M for Schmidt numerical method\n",

+      "tmax = 6000     #Time at which temperature of the slab at various location to be calculated, s\n",

+      "#Calculation and Result\n",

+      "\n",

+      "dx = thk/ns\n",

+      "x = [0,.2,.4,.6,.8,1.]\n",

+      "dt = dx**2/(alpha*M)\n",

+      "ylim(-1.,110.)\n",

+      "xlim(0,1.1)\n",

+      "#m = tmax/dt\n",

+      "t=0\n",

+      "T = [Ti,Ti,Ti,Ti,Ti,Ti]\n",

+      "plt.plot(x,T,'ko-',label='Initial Temperature Profile')\n",

+      "T[0] = Ta\n",

+      "Tcal = [0,0,0,0,0,0]\n",

+      "for i in range(1,7,1):\n",

+      "    t = int(dt*i)\n",

+      "    for j in range(len(T)):\n",

+      "        if j==0:\n",

+      "            Tcal[j]= Ta\n",

+      "            #print Tcal[j]\n",

+      "        elif j>=1 and j<(len(T)-1):\n",

+      "            Tcal[j]=(T[j-1]+T[j+1])/2.\n",

+      "            #print T[j-1], T[j+1],Tcal[j]\n",

+      "        else:\n",

+      "            Tcal[j]=((M-2)*T[j]+2*T[j-1])/M\n",

+      "            #print Tcal[j]\n",

+      "    T = copy.copy(Tcal)\n",

+      "    plt.plot(x,T, 'o-',label=str(i)+'th iteration Temp. Profile.')\n",

+      "print \"At 6000s\"\n",

+      "for i in range(1,7,1):\n",

+      "    print \"Temperature of the node\",i,\"is\", round(T[i-1],2),\"\u00b0C\"\n",

+      "plt.xlabel('Node number')\n",

+      "plt.ylabel('Temperature, degC')\n",

+      "plt.legend(loc='lower right',fontsize='small' )\n"

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "At 6000s\n",

+        "Temperature of the node 1 is 0.0 \u00b0C\n",

+        "Temperature of the node 2 is 31.25 \u00b0C\n",

+        "Temperature of the node 3 is 54.69 \u00b0C\n",

+        "Temperature of the node 4 is 78.13 \u00b0C\n",

+        "Temperature of the node 5 is 85.94 \u00b0C\n",

+        "Temperature of the node 6 is 93.75 \u00b0C\n"

+       ]

+      },

+      {

+       "metadata": {},

+       "output_type": "pyout",

+       "prompt_number": 7,

+       "text": [

+        "<matplotlib.legend.Legend at 0x8a65e30>"

+       ]

+      },

+      {

+       "metadata": {},

+       "output_type": "display_data",

+       "png": 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4AfjtN8bdvn7GJMjlc4ReK1WUradMVHkKyEG6utjcoUOdU0B+HtPffJ85dNx0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\n4ZKxMZNq3eeOSTBWNvuo16Lo+byCUFlERYURGOjGhAlOBAa6ERUVVqL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+       "text": [

+        "<matplotlib.figure.Figure at 0x8959210>"

+       ]

+      }

+     ],

+     "prompt_number": 7

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Example 5.4-2, Page number 356"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#Unsteady-State Conduction Using the Digital Computer  \n",

+      "\n",

+      "import copy \n",

+      "\n",

+      "#Variable declaration\n",

+      "thk = 1.        #Thickness of slab, m\n",

+      "Ti = 100.       #Initial uniform temperature of slab, \u00b0C\n",

+      "Ta = 0.         #Constant Temperature of environment, \u00b0C\n",

+      "alpha = 2.0e-5  #Thermal diffusivity of slab, m2/s\n",

+      "ns = 20         #Number of slices\n",

+      "M = 2.0         #M for Schmidt numerical method\n",

+      "tmax = 6000     #Time at which temperature of the slab at various location to be calculated, s\n",

+      "\n",

+      "#Calculation and Result\n",

+      "dx = thk/ns\n",

+      "x = range(21)\n",

+      "dt = dx**2/(alpha*M)\n",

+      "m = tmax/dt\n",

+      "\n",

+      "t=0\n",

+      "T = [Ti,Ti,Ti,Ti,Ti,Ti,Ti,Ti,Ti,Ti,Ti,Ti,Ti,Ti,Ti,Ti,Ti,Ti,Ti,Ti,Ti]\n",

+      "T[0] = Ta\n",

+      "Tcal = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]\n",

+      "\n",

+      "for i in range(1,96,1):\n",

+      "    t = int(dt*i)\n",

+      "    for j in range(len(T)):\n",

+      "        if j==0:\n",

+      "            Tcal[j]= Ta\n",

+      "            #print Tcal[j]\n",

+      "        elif j>=1 and j<(len(T)-1):\n",

+      "            Tcal[j]=(T[j-1]+T[j+1])/2.\n",

+      "            #print T[j-1], T[j+1],Tcal[j]\n",

+      "        else:\n",

+      "            Tcal[j]=((M-2)*T[j]+2*T[j-1])/M\n",

+      "            #print Tcal[j]\n",

+      "    T = copy.copy(Tcal)\n",

+      "    #plt.plot(x,T, 'o-',label=str(i)+'th iteration Temp. Profile.')\n",

+      "print \"At 6000s\"\n",

+      "\n",

+      "for i in range(1,22,4):\n",

+      "    print \"Temperature of the node\",i,\"is\", round(T[i-1],2),\"\u00b0C\"\n",

+      "\n",

+      "print 'The difference in the answers is due to rounding error'"

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "At 6000s\n",

+        "Temperature of the node 1 is 0.0 \u00b0C\n",

+        "Temperature of the node 5 is 31.81 \u00b0C\n",

+        "Temperature of the node 9 is 58.72 \u00b0C\n",

+        "Temperature of the node 13 is 77.81 \u00b0C\n",

+        "Temperature of the node 17 is 88.64 \u00b0C\n",

+        "Temperature of the node 21 is 92.08 \u00b0C\n",

+        "The difference in the answers is due to rounding error\n"

+       ]

+      }

+     ],

+     "prompt_number": 25

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Example 5.4-3, Page number 357"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#Unsteady-State conduction with Convective Boundary Conditions\n",

+      "\n",

+      "import copy \n",

+      "\n",

+      "#Variable declaration\n",

+      "thk = 1.0       #Thickness of slab, m\n",

+      "Ti = 100.       #Initial uniform temperature of slab, \u00b0C\n",

+      "Ta = 0.         #Constant Temperature of environment, \u00b0C\n",

+      "alpha = 2.0e-5  #Thermal diffusivity of slab, m2/s\n",

+      "ns = 5          #Number slices\n",

+      "h = 25.0        #Covective coefficient, W/m2K\n",

+      "k = 10.0        #Thermal conductivity of slab, W/mK\n",

+      "M = 2.0         #M for Schmidt numerical method\n",

+      "tmax = 6000     #Time at which temperature of the slab at various location to be calculated, s\n",

+      "\n",

+      "#Calculation and Result\n",

+      "\n",

+      "dx = thk/ns\n",

+      "N = h*dx/k\n",

+      "M = 2*N+2\n",

+      "M =round(M+1)\n",

+      "dt = dx**2/(alpha*M)\n",

+      "m = tmax/dt\n",

+      "T = [Ti,Ti,Ti,Ti,Ti,Ti]\n",

+      "Tcal = [0,0,0,0,0,0]\n",

+      "x = range(6)\n",

+      "\n",

+      "for i in range(1,13,1):\n",

+      "    for j in range(len(T)):\n",

+      "        if j==0:\n",

+      "            Tcal[j]= (1/M)*(2*N*Ta+(M-(2*N+2))*T[j]+2*T[j+1])\n",

+      "        elif j>=1 and j<(len(T)-1):\n",

+      "            Tcal[j]=(1/M)*(T[j+1]+(M-2)*T[j]+T[j-1])\n",

+      "        else:\n",

+      "            Tcal[j]=(1/M)*((M-2)*T[j]+2*T[j-1])\n",

+      "    T = copy.copy(Tcal)\n",

+      "    print 'i:%3d and time %5d s'%(i,i*dt)\n",

+      "    for i in range(len(T)):\n",

+      "        print \"Temperature of the node\",i+1,\"is\", round(T[i],2),\"\u00b0C\""

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "i:  1 and time   500 s\n",

+        "Temperature of the node 1 is 75.0 \u00b0C\n",

+        "Temperature of the node 2 is 100.0 \u00b0C\n",

+        "Temperature of the node 3 is 100.0 \u00b0C\n",

+        "Temperature of the node 4 is 100.0 \u00b0C\n",

+        "Temperature of the node 5 is 100.0 \u00b0C\n",

+        "Temperature of the node 6 is 100.0 \u00b0C\n",

+        "i:  2 and time  1000 s\n",

+        "Temperature of the node 1 is 68.75 \u00b0C\n",

+        "Temperature of the node 2 is 93.75 \u00b0C\n",

+        "Temperature of the node 3 is 100.0 \u00b0C\n",

+        "Temperature of the node 4 is 100.0 \u00b0C\n",

+        "Temperature of the node 5 is 100.0 \u00b0C\n",

+        "Temperature of the node 6 is 100.0 \u00b0C\n",

+        "i:  3 and time  1500 s\n",

+        "Temperature of the node 1 is 64.06 \u00b0C\n",

+        "Temperature of the node 2 is 89.06 \u00b0C\n",

+        "Temperature of the node 3 is 98.44 \u00b0C\n",

+        "Temperature of the node 4 is 100.0 \u00b0C\n",

+        "Temperature of the node 5 is 100.0 \u00b0C\n",

+        "Temperature of the node 6 is 100.0 \u00b0C\n",

+        "i:  4 and time  2000 s\n",

+        "Temperature of the node 1 is 60.55 \u00b0C\n",

+        "Temperature of the node 2 is 85.16 \u00b0C\n",

+        "Temperature of the node 3 is 96.48 \u00b0C\n",

+        "Temperature of the node 4 is 99.61 \u00b0C\n",

+        "Temperature of the node 5 is 100.0 \u00b0C\n",

+        "Temperature of the node 6 is 100.0 \u00b0C\n",

+        "i:  5 and time  2500 s\n",

+        "Temperature of the node 1 is 57.71 \u00b0C\n",

+        "Temperature of the node 2 is 81.84 \u00b0C\n",

+        "Temperature of the node 3 is 94.43 \u00b0C\n",

+        "Temperature of the node 4 is 98.93 \u00b0C\n",

+        "Temperature of the node 5 is 99.9 \u00b0C\n",

+        "Temperature of the node 6 is 100.0 \u00b0C\n",

+        "i:  6 and time  3000 s\n",

+        "Temperature of the node 1 is 55.35 \u00b0C\n",

+        "Temperature of the node 2 is 78.96 \u00b0C\n",

+        "Temperature of the node 3 is 92.41 \u00b0C\n",

+        "Temperature of the node 4 is 98.05 \u00b0C\n",

+        "Temperature of the node 5 is 99.68 \u00b0C\n",

+        "Temperature of the node 6 is 99.95 \u00b0C\n",

+        "i:  7 and time  3500 s\n",

+        "Temperature of the node 1 is 53.31 \u00b0C\n",

+        "Temperature of the node 2 is 76.42 \u00b0C\n",

+        "Temperature of the node 3 is 90.45 \u00b0C\n",

+        "Temperature of the node 4 is 97.05 \u00b0C\n",

+        "Temperature of the node 5 is 99.34 \u00b0C\n",

+        "Temperature of the node 6 is 99.82 \u00b0C\n",

+        "i:  8 and time  4000 s\n",

+        "Temperature of the node 1 is 51.54 \u00b0C\n",

+        "Temperature of the node 2 is 74.15 \u00b0C\n",

+        "Temperature of the node 3 is 88.59 \u00b0C\n",

+        "Temperature of the node 4 is 95.97 \u00b0C\n",

+        "Temperature of the node 5 is 98.89 \u00b0C\n",

+        "Temperature of the node 6 is 99.58 \u00b0C\n",

+        "i:  9 and time  4500 s\n",

+        "Temperature of the node 1 is 49.96 \u00b0C\n",

+        "Temperature of the node 2 is 72.11 \u00b0C\n",

+        "Temperature of the node 3 is 86.83 \u00b0C\n",

+        "Temperature of the node 4 is 94.86 \u00b0C\n",

+        "Temperature of the node 5 is 98.33 \u00b0C\n",

+        "Temperature of the node 6 is 99.23 \u00b0C\n",

+        "i: 10 and time  5000 s\n",

+        "Temperature of the node 1 is 48.54 \u00b0C\n",

+        "Temperature of the node 2 is 70.25 \u00b0C\n",

+        "Temperature of the node 3 is 85.15 \u00b0C\n",

+        "Temperature of the node 4 is 93.72 \u00b0C\n",

+        "Temperature of the node 5 is 97.69 \u00b0C\n",

+        "Temperature of the node 6 is 98.78 \u00b0C\n",

+        "i: 11 and time  5500 s\n",

+        "Temperature of the node 1 is 47.26 \u00b0C\n",

+        "Temperature of the node 2 is 68.55 \u00b0C\n",

+        "Temperature of the node 3 is 83.57 \u00b0C\n",

+        "Temperature of the node 4 is 92.57 \u00b0C\n",

+        "Temperature of the node 5 is 96.97 \u00b0C\n",

+        "Temperature of the node 6 is 98.23 \u00b0C\n",

+        "i: 12 and time  6000 s\n",

+        "Temperature of the node 1 is 46.09 \u00b0C\n",

+        "Temperature of the node 2 is 66.98 \u00b0C\n",

+        "Temperature of the node 3 is 82.06 \u00b0C\n",

+        "Temperature of the node 4 is 91.42 \u00b0C\n",

+        "Temperature of the node 5 is 96.19 \u00b0C\n",

+        "Temperature of the node 6 is 97.6 \u00b0C\n"

+       ]

+      }

+     ],

+     "prompt_number": 29

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Example 5.5-1, Page number 361"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "# Chilling Dressed Beef\n",

+      "\n",

+      "#Variable Declaration\n",

+      "\n",

+      "rho = 1073.                 #Density of a beef, kg/m3\n",

+      "cp = 3480.                  #Specific heat of Beef, J/(kg.K)\n",

+      "k = 0.498                   #Thermal conductivity of beef, W/(m.K)\n",

+      "thk = 0.203                 #Thickness of beef slab, m\n",

+      "Ti = 37.8                   #Initial beef temperature, deg C\n",

+      "Tf = 1.7                    #Uniform fluid temeperature, deg C\n",

+      "T = 10.                     #Temperature of the centre, deg C\n",

+      "h = 39.7                    #Convective heat Transfer coefficient, W/(m2.K)\n",

+      "x = 0\n",

+      "#Calculation\n",

+      "\n",

+      "alpha = k/(rho*cp)          #Thermal diffusivity of beef slab, m2/s\n",

+      "x1 = thk/2                  #Centre of slab, m\n",

+      "n = x/x1\n",

+      "m = k/(h*x1)\n",

+      "Y = (Tf-T)/(Tf-Ti)\n",

+      "X = 0.90               \n",

+      "t = X*x1**2/alpha\n",

+      "#Result\n",

+      "print \"The parameter to be used in association with Fig. 5.3-6\"\n",

+      "print \"n: \", n\n",

+      "print \"m: \", round(m,4)\n",

+      "print \"Y: \", round(Y,4)\n",

+      "print \"Time required to attend 10\u00b0C: \", round(t,1),\"s OR\", round(t/3600,1), \"hr\""

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "The parameter to be used in association with Fig. 5.3-6\n",

+        "n:  0.0\n",

+        "m:  0.1236\n",

+        "Y:  0.2299\n",

+        "Time required to attend 10\u00b0C:  69522.3 s OR 19.3 hr\n"

+       ]

+      }

+     ],

+     "prompt_number": 19

+    },

+    {

+     "cell_type": "heading",

+     "level": 2,

+     "metadata": {},

+     "source": [

+      "Example 5.5-2, Page number 364"

+     ]

+    },

+    {

+     "cell_type": "code",

+     "collapsed": false,

+     "input": [

+      "#Freezing of Meat \n",

+      "\n",

+      "#Variable Declaration\n",

+      "\n",

+      "rho = 1057.                 #Density of a meat, kg/m3\n",

+      "cp = 3480.                  #Specific heat of Beef, J/(kg.K)\n",

+      "k = 1.038                   #Thermal conductivity of meat, W/(m.K)\n",

+      "a = 0.0635                  #Thickness of beef slab, m\n",

+      "Tf = 270.4                  #Initial meat temperature, deg C\n",

+      "T1 = 244.3                  #Uniform air blast temeperature, K\n",

+      "h = 17.0                    #Convective heat Transfer coefficient, W/(m2.K)\n",

+      "Lambdafw = 335000           #Latent heat of fusion of for Water, J/kg\n",

+      "\n",

+      "#Calculations\n",

+      "\n",

+      "Lambdameat = 0.75*Lambdafw\n",

+      "t = Lambdameat*rho/(Tf-T1)*(a/(2*h)+a**2/(8*k))\n",

+      "\n",

+      "#Results\n",

+      "print \"Latent heat of freezing of meat:\", round(Lambdameat/1000,1), \"kJ/kg\"\n",

+      "print 'Time required for freezing:%4.3e s OR %3.2f'%(t,t/3600)"

+     ],

+     "language": "python",

+     "metadata": {},

+     "outputs": [

+      {

+       "output_type": "stream",

+       "stream": "stdout",

+       "text": [

+        "Latent heat of freezing of meat: 251.3 kJ/kg\n",

+        "Time required for freezing:2.394e+04 s OR 6.65\n"

+       ]

+      }

+     ],

+     "prompt_number": 33

+    }

+   ],

+   "metadata": {}

+  }

+ ]

+}
\ No newline at end of file