Lab_06-best_fit-model.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import pretty_plots # script to set up LaTex and increase line-width and font size\n",
    "from scipy.optimize import curve_fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "pretty_plots.setdefaults()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Tw(t,T0w,Tinf,L):\n",
    "    '''solution of first order thermal system fluid temperature\n",
    "    inputs are time, t\n",
    "    initial fluid temperature, T0f\n",
    "    final fluid temperature, Tinf\n",
    "    exponent=1/(time constant), L'''\n",
    "    T=(T0w-Tinf)*np.exp(L*t)+Tinf\n",
    "    return T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "data=np.loadtxt('./water-temp.csv',delimiter=',')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f635774a7f0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(data[:,0],data[:,1],'o',label='experiment')\n",
    "plt.xlabel('time (s)')\n",
    "plt.ylabel('Temp (C)')\n",
    "plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "A,pcov=curve_fit(Tw,data[:,0],data[:,1],bounds=([19,21,-0.001],[21,25,0]))\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "1/A[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.plot(data[:,0],data[:,1],'o',label='experiment')\n",
    "plt.plot(data[:,0],Tw(data[:,0],A[0],A[1],A[2]),label='model')\n",
    "plt.xlabel('time (s)')\n",
    "plt.ylabel('Temp (C)')\n",
    "plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
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