agoose77/Question_3.ipynb

## Question_3.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from scipy.special import erf\n",
    "from numpy import linspace, sqrt\n",
    "from math import exp\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def c(x, D, cs, c0, t):\n",
    "    return cs - (cs - c0) * erf(x / (2 * sqrt(D * t)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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S58034YgjYOpU+Na30o5GRMpdU2sobQq8+PGETvnvAFsCzxKavqQF7LUX/O//huavv/4V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\nsfg/N8qPZ8JuxPkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x901cd90748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q = 135e3\n",
    "T = 1100 + 273\n",
    "R = 8.3144598\n",
    "\n",
    "# Find D (cm^2)\n",
    "D0 = 0.15\n",
    "D = D0 * exp(-Q/(R*T))\n",
    "\n",
    "# Composition differences (wt%)\n",
    "c0 = 0.15/100 # 0.15wt%\n",
    "cs = 2/100 # 2wt%\n",
    "t = 4 * 60 * 60 \n",
    "\n",
    "x = linspace(0, 0.7, 100000)\n",
    "y = c(x, D, cs, c0, t)\n",
    "\n",
    "plt.plot(x, y)\n",
    "plt.xlabel(\"X (cm)\")\n",
    "plt.ylabel(\"C (wt%C)\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from scipy.special import erfinv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X_eutectoid=0.173cm\n"
     ]
    }
   ],
   "source": [
    "x_eutectoid = erfinv((cs - 0.76/100) / (cs - c0)) * 2 * sqrt(D*t)\n",
    "print(\"X_eutectoid={:.3f}cm\".format(x_eutectoid))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
	{
	"cells": [
	{
	"cell_type": "code",
	"execution_count": 4,
	"metadata": {
	"collapsed": false
	},
	"outputs": [],
	"source": [
	"from scipy.special import erf\n",
	"from numpy import linspace, sqrt\n",
	"from math import exp\n",
	"from matplotlib import pyplot as plt\n",
	"%matplotlib inline "
	]
	},
	{
	"cell_type": "code",
	"execution_count": 5,
	"metadata": {
	"collapsed": false
	},
	"outputs": [],
	"source": [
	"def c(x, D, cs, c0, t):\n",
	" return cs - (cs - c0) * erf(x / (2 * sqrt(D * t)))"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 6,
	"metadata": {
	"collapsed": false
	},
	"outputs": [
	{
	"data": {
	"image/png": 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r9VBERKTlFGOnfKM1Z/Bk2vLFbmZ7mNkLZrbazK5MI8aGFBD/6Wb2erTNMLN9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\nsfg/N8qPZ8JuxPkAAAAASUVORK5CYII=\n",
	"text/plain": [
	"<matplotlib.figure.Figure at 0x901cd90748>"
	]
	},
	"metadata": {},
	"output_type": "display_data"
	}
	],
	"source": [
	"Q = 135e3\n",
	"T = 1100 + 273\n",
	"R = 8.3144598\n",
	"\n",
	"# Find D (cm^2)\n",
	"D0 = 0.15\n",
	"D = D0 * exp(-Q/(R*T))\n",
	"\n",
	"# Composition differences (wt%)\n",
	"c0 = 0.15/100 # 0.15wt%\n",
	"cs = 2/100 # 2wt%\n",
	"t = 4 * 60 * 60 \n",
	"\n",
	"x = linspace(0, 0.7, 100000)\n",
	"y = c(x, D, cs, c0, t)\n",
	"\n",
	"plt.plot(x, y)\n",
	"plt.xlabel(\"X (cm)\")\n",
	"plt.ylabel(\"C (wt%C)\")\n",
	"plt.show()"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 8,
	"metadata": {
	"collapsed": false
	},
	"outputs": [],
	"source": [
	"from scipy.special import erfinv"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 16,
	"metadata": {
	"collapsed": false
	},
	"outputs": [
	{
	"name": "stdout",
	"output_type": "stream",
	"text": [
	"X_eutectoid=0.173cm\n"
	]
	}
	],
	"source": [
	"x_eutectoid = erfinv((cs - 0.76/100) / (cs - c0)) * 2 * sqrt(D*t)\n",
	"print(\"X_eutectoid={:.3f}cm\".format(x_eutectoid))"
	]
	}
	],
	"metadata": {
	"kernelspec": {
	"display_name": "Python 3",
	"language": "python",
	"name": "python3"
	},
	"language_info": {
	"codemirror_mode": {
	"name": "ipython",
	"version": 3
	},
	"file_extension": ".py",
	"mimetype": "text/x-python",
	"name": "python",
	"nbconvert_exporter": "python",
	"pygments_lexer": "ipython3",
	"version": "3.5.0"
	}
	},
	"nbformat": 4,
	"nbformat_minor": 0
	}