{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t= 0 sec; dT =  0.4778972520908005 T= 20.477897252090802 m= 1\n",
      "t= 20 sec; dT =  0.47789252016255496 T= 30.03582092132473 m= 1\n",
      "t= 40 sec; dT =  0.47782154971663565 T= 39.593143202467914 m= 1\n",
      "t= 60 sec; dT =  0.4775141988966611 T= 49.14694082100387 m= 1\n",
      "t= 80 sec; dT =  0.47668824613363947 T= 58.68970682496618 m= 1\n",
      "t= 100 sec; dT =  0.4749539916600158 T= 68.20714921745714 m= 1\n",
      "t= 120 sec; dT =  0.47182571850976235 T= 77.676146799768 m= 1\n",
      "t= 140 sec; dT =  0.46674446315535334 T= 87.06304524228844 m= 1\n",
      "t= 160 sec; dT =  0.4591164807782781 T= 96.32256690089059 m= 1\n",
      "t= 169 sec; dT =  0.45469810619281387 T= 100.43301020202186 m= 1\n"
     ]
    }
   ],
   "source": [
    "liT=[]\n",
    "m=1\n",
    "mmax=1\n",
    "mpers=0.0\n",
    "c=4185\n",
    "dq=2000\n",
    "q=0\n",
    "Tini=20\n",
    "T=Tini\n",
    "sig=5.67e-8\n",
    "for t in range(280):\n",
    "    # add water\n",
    "    if (m<mmax):\n",
    "        m=m+mpers\n",
    "    else:\n",
    "        mpers=0\n",
    "    # mix temperatures\n",
    "    T=(T*c*(m-mpers)+Tini*c*mpers)/m/c\n",
    "    # \n",
    "    dtemp=dq/m/c - sig*(T-20)**4 *0.01\n",
    "    T=T+dtemp\n",
    "    liT.append(T)\n",
    "    if ( t % 20 ==0):\n",
    "        print('t=',t,'sec; dT = ',dtemp, 'T=',T,'m=',m)\n",
    "    if ( T>=100):\n",
    "        print('t=',t,'sec; dT = ',dtemp, 'T=',T,'m=',m)\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t= 0 sec; dT =  23.894862604540023 T= 43.89486260454002 m= 0.02\n",
      "t= 20 sec; dT =  1.1376985644894024 T= 43.89342210679046 m= 0.4200000000000001\n",
      "t= 40 sec; dT =  0.5826341570895881 T= 43.891628811564765 m= 0.8200000000000004\n",
      "t= 60 sec; dT =  0.4775143215188033 T= 49.144646269763946 m= 1.0000000000000004\n",
      "t= 80 sec; dT =  0.4766885360168304 T= 58.68741632632058 m= 1.0000000000000004\n",
      "t= 100 sec; dT =  0.4749545546158589 T= 68.20486718884294 m= 1.0000000000000004\n",
      "t= 120 sec; dT =  0.47182668123137317 T= 77.67388000302022 m= 1.0000000000000004\n",
      "t= 140 sec; dT =  0.46674596601836416 T= 87.06080313201579 m= 1.0000000000000004\n",
      "t= 160 sec; dT =  0.4591186664420722 T= 96.32036178592037 m= 1.0000000000000004\n",
      "t= 169 sec; dT =  0.4547006427272458 T= 100.4308264936212 m= 1.0000000000000004\n"
     ]
    }
   ],
   "source": [
    "liTm=[]\n",
    "m=0\n",
    "mmax=1\n",
    "mpers=0.02\n",
    "c=4185\n",
    "dq=2000\n",
    "q=0\n",
    "Tini=20\n",
    "T=Tini\n",
    "sig=5.67e-8\n",
    "for t in range(280):\n",
    "    # add water\n",
    "    if (m<mmax):\n",
    "        m=m+mpers\n",
    "    else:\n",
    "        mpers=0\n",
    "    # mix temperatures\n",
    "    T=(T*c*(m-mpers)+Tini*c*mpers)/m/c\n",
    "    # \n",
    "    dtemp=dq/m/c - sig*(T-20)**4 *0.01\n",
    "    T=T+dtemp\n",
    "    liTm.append(T)\n",
    "    if ( t % 20 ==0):\n",
    "        print('t=',t,'sec; dT = ',dtemp, 'T=',T,'m=',m)\n",
    "    if ( T>=100):\n",
    "        print('t=',t,'sec; dT = ',dtemp, 'T=',T,'m=',m)\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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RALGxscHE8F3pcYNFxY5HLuvCsJQ2RGncoIiEkKAK3zlXBPQ0s4bANKDzcTx2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\n9/oAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6ef0ed8d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.plot( liT )\n",
    "plt.plot( liTm )\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}