BesselfinalODE.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Importing files"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "n3WdwpcVXeiJ"
   },
   "outputs": [],
   "source": [
    "import scipy.special as s\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import math "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Variables and Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "id": "wVKFNxNUmajG"
   },
   "outputs": [],
   "source": [
    "bi      = 3                      #Biot Number\n",
    "kappa   = 52                     #Thermal Conductivity(cast iron casing a motor generating heat): (W/(mK))\n",
    "alp     = 1.7025e-5              #Thermal Diffusivity: (m2/s)\n",
    "\n",
    "r_0     = 0.2                    #Max radius: (m)\n",
    "\n",
    "q       = 7e4                    #Heat generated/vol: (W/m3)\n",
    "Ti      = 30                     #Initial temp: (degree Celcius)\n",
    "Tinf    = 25                     #Ambient temp: (degree Celcius)\n",
    "delT    = Ti-Tinf\n",
    "\n",
    "k_val   =  32                    #NUmber of bessel summation terms\n",
    "step    = 0.0001                 #Radius steps\n",
    "\n",
    "tmax    = 600                    #Maximum time in: (seconds)\n",
    "tstep   = 10                    \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bessel Fun zeroth & first order: (Jo,J1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "id": "46BC1mfPsyrx"
   },
   "outputs": [],
   "source": [
    "def J0(x2):\n",
    "  bsf1=s.jv(0,x2)\n",
    "  return(bsf1)\n",
    "\n",
    "def J1(x3):\n",
    "  bsf2=s.jv(1,x3)\n",
    "  return(bsf2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Eigen Values for different Bi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "4yWx76sKiMSX",
    "outputId": "dff5fbba-b943-4fda-bfea-790a5271d19b"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "33\n"
     ]
    }
   ],
   "source": [
    "#Lamda values can be solved for using the mth equation in the readme file using function f.solve for a given Biot number.\n",
    "\n",
    "##Bi=1##lam = np.array([1.2557837117946,4.0794777108393,7.1557991746440,10.2709853620793,13.3983974864138,16.5311589326050,19.6667277887128,22.8039505186316,25.9422288398533,29.0812217718691,32.2207208280665,35.3605913932645,38.5007426824640,41.6411112516383,44.7816514290601,47.9223295014823,51.0631200414536,54.2040035097965,57.3449646447644,60.4859913524936,63.6270739257397,66.7682044829213,69.9093765582564,73.0505847975588,76.1918247292276,79.3330925896073,82.4743851882334,85.6156998027256,88.7570340959897,91.8983860503923,95.0397539149845,98.1811361628517,101.3225314563960])/r_0\n",
    "\n",
    "##Bi=3##\n",
    "lam=np.array([1.7886571741034556,4.463371687062525,7.4102697979339265,10.456598813134065,13.543437687744268,16.64985349628233,19.76705067826938,22.890769808457094,26.018720007267877,29.149565359078395,32.282476442581064,35.4169119388982,38.55250391155869,41.68899371534701,44.8261943125047,47.96396714328303, 51.10220740390041, 54.24083572371715, 57.37978487437271, 60.51900923024971, 63.65846576441509, 66.79812391906279, 69.9379538599341, 73.0779357679667, 76.2180501858754, 79.35828141633321, 82.49861655165894, 85.63904303340324, 88.77955228353834, 91.92013548861861, 95.06078532695017, 98.2014954147345, 104.48307463211063])/r_0\n",
    "\n",
    "\n",
    "##Bi=9##lam =np.array([-35.58090661205443, -4.989702929078122, 2.1566066121933813, 4.9897029300394, 7.905056881017777, 10.884181645933715, 13.909031412603078, 16.965035283739006, 20.042197057682266, 23.13399114079144, 26.23616268384973, 29.34588824710337, 32.46124870328023, 35.58090658903461, 38.703907193201005, 41.829553768393104, 44.95732749639535, 48.08683498151535, 51.217773019480305, 54.34990441005031, 57.48304118739001, 60.61703252105408, 63.75175608456559, 66.88711166918512, 70.0230164357018, 73.1594013402616, 76.29620834660287, 79.43338841419276, 82.5708997489792, 85.70870655543673, 88.84677799601506, 91.98508736123622, 95.1236114103184, 98.26232982154872])/r_0\n",
    "\n",
    "\n",
    "print(lam.size)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "0LvZIGISUw3r",
    "outputId": "ca0b1822-e67b-4005-9d91-aa8833a3c0f9"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "33\n"
     ]
    }
   ],
   "source": [
    "a=np.zeros(k_val+1)\n",
    "\n",
    "for i in range(0,k_val+1,1):\n",
    "    \n",
    "  a[i]= (2*lam[i]*r_0)*(delT)*  (  ((bi**2+(lam[i]*r_0)**2)*(J0(lam[i]*r_0))**2)**(-1)   )  * ( (1-(q*r_0**2)*( (0.5/bi)+(1/(lam[i]*r_0))**2 )*(kappa*delT)**(-1)) *(J1(lam[i]*r_0))   +    ( ( q*r_0**2*J0(lam[i]*r_0) )*( kappa*(delT)*lam[i]*r_0)**(-1) ))\n",
    "\n",
    "\n",
    "print(len(a))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# UnsteadySolution Function: (unSol)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "id": "gtY_bFudaree"
   },
   "outputs": [],
   "source": [
    "def unSol(r,t):\n",
    "  asum1=0\n",
    "  asum=0\n",
    "  for k in range(0,k_val+1,1):\n",
    "    asum1= a[k] * (  math.exp(-(lam[k])**2   *alp*t)  )  *  J0( lam[k] * r )\n",
    "    asum=asum+asum1\n",
    "  return(asum)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Computing for all time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "AGQP3YAac-GO",
    "outputId": "dd08acab-5cce-406a-8744-470f020ae85b"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2001 61\n"
     ]
    }
   ],
   "source": [
    "\n",
    "theta=np.ones((int(r_0/step)+1,int(tmax/tstep)+1))\n",
    "t5=0\n",
    "t1=0\n",
    "r1=0\n",
    "while(t5<=tmax):\n",
    "  r=0\n",
    "  r1=0\n",
    "  while(r<=r_0):\n",
    "    theta[r1,t1]= q*r_0**2*(4*kappa*delT)**(-1)*( 1-(r/r_0)**2+(2/bi) )  +  unSol(r,t5)*(delT**(-1))\n",
    "    r=r+step\n",
    "    r1=r1+1\n",
    "  theta[:,0]=1\n",
    "  t5=t5+tstep\n",
    "  t1=t1+1\n",
    "\n",
    "print(r1,t1)\n",
    "#print(theta3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "24WO_p5i_KyT",
    "outputId": "cb2446ad-7cfb-4a5c-dda2-b78b8ac82b4e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(61,)\n"
     ]
    }
   ],
   "source": [
    "radius=np.linspace(0,r_0,int(r_0/step)+1)\n",
    "print(radius.size)\n",
    "\n",
    "time=np.linspace(0,tmax,int(tmax/tstep)+1)\n",
    "print(time.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# DataFrame of Theta(radius,time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "bEyqq0c8FehZ",
    "outputId": "bf49dd54-e3c8-4265-a1a3-46eaaf07d26c"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        0.0       10.0      20.0      30.0      40.0      50.0      60.0   \\\n",
      "0.0000    1.0  2.840708  2.886545  2.932381  2.978218  3.024050  3.069851   \n",
      "0.0001    1.0  2.840708  2.886545  2.932381  2.978218  3.024050  3.069851   \n",
      "0.0002    1.0  2.840708  2.886545  2.932381  2.978218  3.024050  3.069851   \n",
      "0.0003    1.0  2.840708  2.886545  2.932381  2.978218  3.024050  3.069851   \n",
      "0.0004    1.0  2.840708  2.886545  2.932381  2.978218  3.024050  3.069851   \n",
      "...       ...       ...       ...       ...       ...       ...       ...   \n",
      "0.1996    1.0  2.310231  2.161081  2.065115  1.995186  1.941072  1.897666   \n",
      "0.1997    1.0  2.306830  2.157886  2.062056  1.992228  1.938192  1.894849   \n",
      "0.1998    1.0  2.303417  2.154683  2.058992  1.989265  1.935308  1.892028   \n",
      "0.1999    1.0  2.299991  2.151473  2.055921  1.986297  1.932420  1.889204   \n",
      "0.2000    1.0  2.296552  2.148254  2.052845  1.983324  1.929528  1.886376   \n",
      "\n",
      "           70.0      80.0      90.0   ...     510.0     520.0     530.0  \\\n",
      "0.0000  3.115545  3.160984  3.205959  ...  4.063554  4.070559  4.077365   \n",
      "0.0001  3.115545  3.160984  3.205958  ...  4.063554  4.070558  4.077365   \n",
      "0.0002  3.115545  3.160983  3.205958  ...  4.063552  4.070557  4.077363   \n",
      "0.0003  3.115545  3.160983  3.205958  ...  4.063549  4.070554  4.077360   \n",
      "0.0004  3.115545  3.160983  3.205958  ...  4.063545  4.070550  4.077356   \n",
      "...          ...       ...       ...  ...       ...       ...       ...   \n",
      "0.1996  1.862009  1.832221  1.807026  ...  1.670725  1.672127  1.673544   \n",
      "0.1997  1.859244  1.829499  1.804341  ...  1.668238  1.669638  1.671053   \n",
      "0.1998  1.856476  1.826775  1.801654  ...  1.665750  1.667148  1.668561   \n",
      "0.1999  1.853704  1.824047  1.798963  ...  1.663261  1.664657  1.666068   \n",
      "0.2000  1.850929  1.821317  1.796270  ...  1.660771  1.662164  1.663573   \n",
      "\n",
      "           540.0     550.0     560.0     570.0     580.0     590.0     600.0  \n",
      "0.0000  4.083984  4.090427  4.096701  4.102817  4.108783  4.114605  4.120292  \n",
      "0.0001  4.083984  4.090426  4.096701  4.102817  4.108782  4.114605  4.120291  \n",
      "0.0002  4.083982  4.090424  4.096699  4.102815  4.108781  4.114603  4.120290  \n",
      "0.0003  4.083979  4.090421  4.096696  4.102812  4.108778  4.114600  4.120287  \n",
      "0.0004  4.083975  4.090417  4.096692  4.102808  4.108774  4.114596  4.120282  \n",
      "...          ...       ...       ...       ...       ...       ...       ...  \n",
      "0.1996  1.674974  1.676413  1.677860  1.679312  1.680766  1.682222  1.683677  \n",
      "0.1997  1.672481  1.673919  1.675363  1.676813  1.678265  1.679718  1.681171  \n",
      "0.1998  1.669987  1.671422  1.672865  1.674312  1.675762  1.677213  1.678664  \n",
      "0.1999  1.667492  1.668925  1.670365  1.671810  1.673258  1.674707  1.676155  \n",
      "0.2000  1.664995  1.666426  1.667864  1.669307  1.670753  1.672199  1.673646  \n",
      "\n",
      "[2001 rows x 61 columns]\n"
     ]
    }
   ],
   "source": [
    "fordata=pd.DataFrame(theta,columns=time, index=radius)\n",
    "print(fordata)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Contour plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 476
    },
    "id": "VK8Y0C1CAF2D",
    "outputId": "f32739bb-ad03-4493-b406-be1240aaf4a5"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "BIOT NUMBER: 3\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1800x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"BIOT NUMBER:\", bi)\n",
    "plt.figure(figsize=(25,7))\n",
    "plt.title(\"Theta v/s Time at all  radius\")\n",
    "plt.contourf(time, radius, theta , 20, cmap='jet')\n",
    "plt.ylabel(\"Radius: 0.2m\")\n",
    "plt.xlabel(\"Time: 600s\")\n",
    "# plt.ylim(0,101)\n",
    "plt.xlim(0,600)\n",
    "plt.colorbar()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "///Connecting the sharp changes at every time: Exponentially decaying curve can be observed because of the exponentially decaying unsteady term with respect to time///"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 936
    },
    "id": "mMr7NpCiCy2z",
    "outputId": "6ff86890-6f8f-426a-c312-48400e3e5f5d"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "BIOT NUMBER: 3\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1a93ee300a0>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(20,7))\n",
    "plt.title(\"Theta v/s Time\")\n",
    "plt.plot(time[:50],theta[0,:50])\n",
    "#plt.xlim(0,12)\n",
    "plt.xlabel(\"Time: 600s\")\n",
    "plt.ylabel(\"Theta\")\n",
    "print(\"BIOT NUMBER:\", bi)\n",
    "\n",
    "\n",
    "plt.figure(figsize=(20,7))\n",
    "plt.title(\"Theta v/s Radius\")\n",
    "plt.plot(radius,theta[:,0],label='0s')\n",
    "plt.plot(radius,theta[:,20],label='200s')\n",
    "plt.plot(radius,theta[:,30],label='300s')\n",
    "plt.plot(radius,theta[:,40],label='400s')\n",
    "plt.plot(radius,theta[:,60],label='600s')\n",
    "plt.xlabel(\"Radius: 0.2m\")\n",
    "plt.ylabel(\"Theta\")\n",
    "plt.legend()"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}