2d battery.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [],
   "source": [
    "from fenics import *\n",
    "from mshr import *\n",
    "import matplotlib.pyplot as plt\n",
    "#%matplotlib inline \n",
    "#% matplotlib notebook\n",
    "from IPython.display import Image\n",
    "from IPython.display import set_matplotlib_formats\n",
    "set_matplotlib_formats('png', 'pdf')\n",
    "import numpy as np\n",
    "import sympy as sym"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Start battery model with simple rectangle mesh geometry. Will add more complex internal geometry once the model is run succesfully. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/pdf": 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\n",
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "originx = 0.0\n",
    "originy = 0.0\n",
    "cornerx = 2.0\n",
    "cornery = 5.0\n",
    "\n",
    "#mesh = RectangleMesh(Point(originx,originy), Point(cornerx,cornery), 20, 20)\n",
    "domain = Rectangle(dolfin.Point(originx,originy), dolfin.Point(cornerx,cornery))\n",
    "mesh = generate_mesh(domain, 20)\n",
    "V = FunctionSpace(mesh, 'CG', 1)\n",
    "\n",
    "plot(mesh)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define function that describes the heat generation in the battery \n",
    "def q(u) : \n",
    "    I = 2 # current of the battery (Amps)\n",
    "    Vol = 8#9.7e-7 # volume of the battery (cm^2)\n",
    "    R = 10 # Internal Resistance of the battery (Ohms)\n",
    "    V = .3#-0.4337 # coefficient voltage variation with temperatur in battery cell\n",
    "    return (I/Vol)*(I*R + V*u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [],
   "source": [
    "gD = Constant(1.0) #Expression('x[1]*x[1]', degree = 1) # Constant(100.0) # Dirichlet Boundaeies :top and bottom of battery are exposed to ambient temperature\n",
    "u_int = Expression('exp(-a*pow(x[0], 2) - a*pow(x[1], 2))',\n",
    "                 degree=2, a=1)\n",
    "#u_int = Expression('exp(-10*(x[0]*x[0] + x[1]*x[1]))', degree = 1) # Constant(1.0) #Expression('sin(x[0] + x[1])', degree = 1)#Constant(1.0) # Initial condition :begin at same temp as outside\n",
    "u0 = interpolate(u_int, V)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [],
   "source": [
    "# defining parts of the boundaries by creating classes\n",
    "class Left (SubDomain):\n",
    "    def inside (self , x , on_boundary):\n",
    "        return near(x[0], originx)\n",
    "class Right (SubDomain):\n",
    "    def inside (self , x , on_boundary):\n",
    "        return near(x[0], cornerx)\n",
    "class Bottom (SubDomain):\n",
    "    def inside (self , x , on_boundary):\n",
    "        return near(x[1], originy)\n",
    "class Top (SubDomain):\n",
    "    def inside (self , x , on_boundary):\n",
    "        return near(x[1], cornery)\n",
    "\n",
    "#create each instance of the classess created above\n",
    "left = Left()\n",
    "right = Right()\n",
    "top = Top()\n",
    "bottom = Bottom()\n",
    "\n",
    "# Initialize mesh function for boundary domains and mark\n",
    "boundaries = MeshFunction(\"size_t\", mesh , 1) #\n",
    "boundaries.set_all(0) #\n",
    "\n",
    "left.mark(boundaries , 1)\n",
    "top.mark(boundaries , 2)\n",
    "right.mark(boundaries , 3)\n",
    "bottom.mark(boundaries , 4)\n",
    "\n",
    "ds = Measure(\"ds\", domain = mesh, subdomain_data = boundaries) #\n",
    "\n",
    "bc = DirichletBC(V, gD, boundaries, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "left.mark(boundaries, 1)\n",
    "right.mark(boundaries, 2)\n",
    "front.mark(boundaries, 3)\n",
    "back.mark(boundaries, 4)\n",
    "top.mark(boundaries, 5)\n",
    "#bottom.mark(boundaries, 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Heat flux from batteries on boundaries\n",
    "gN_left = Constant(10.0) \n",
    "gN_right = Constant(10.0)\n",
    "#declare neumann for top and bottom boundaries if necessary.\n",
    "#gN_top = Constant(50)\n",
    "#gN_bottom = Constant(50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [],
   "source": [
    "#define time interval and step size\n",
    "num_steps = 1000\n",
    "T = 10.0\n",
    "dt = T/num_steps\n",
    "t = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [],
   "source": [
    "#variational problem\n",
    "u = TrialFunction(V)\n",
    "v = TestFunction(V)\n",
    "#f = q(u) #Constant(1.0)\n",
    "f = Expression('-exp(-x[0]*x[0] - x[1]*x[1])', degree = 1)\n",
    "\n",
    "#f = Expression(f_code, degree = 1)\n",
    "#f = Expression('sin(x[0] + x[1])', degree = 2)#Constant(1.0)\n",
    "#f = Expression('(I/Vol)*(I*R + V*u)', I = I, Vol = Vol, R = R, Volt = Volt, u = u degree = 1) # This is where the heat source will go (q) function of Temp."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [],
   "source": [
    "up = u0 #store u(t=0) in new var\n",
    "\n",
    "F =  u*v*dx + dt*dot(grad(u), grad(v))*dx - (u0 + dt*f)*v*dx - dt*gN_left*v*ds(1) - dt*gN_right*v*ds(3)\n",
    "\n",
    "a = lhs(F) #left hand side\n",
    "L = rhs(F) #right hand side"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = assemble(a)\n",
    "u = Function(V)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [],
   "source": [
    "vtkfile = File('output/battery_test.pvd')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t =  0.01\n",
      "t =  0.02\n",
      "t =  0.03\n",
      "t =  0.04\n",
      "t =  0.05\n",
      "t =  0.060000000000000005\n",
      "t =  0.07\n",
      "t =  0.08\n",
      "t =  0.09\n",
      "t =  0.09999999999999999\n",
      "t =  0.10999999999999999\n",
      "t =  0.11999999999999998\n",
      "t =  0.12999999999999998\n",
      "t =  0.13999999999999999\n",
      "t =  0.15\n",
      "t =  0.16\n",
      "t =  0.17\n",
      "t =  0.18000000000000002\n",
      "t =  0.19000000000000003\n",
      "t =  0.20000000000000004\n",
      "t =  0.21000000000000005\n",
      "t =  0.22000000000000006\n",
      "t =  0.23000000000000007\n",
      "t =  0.24000000000000007\n",
      "t =  0.25000000000000006\n",
      "t =  0.26000000000000006\n",
      "t =  0.2700000000000001\n",
      "t =  0.2800000000000001\n",
      "t =  0.2900000000000001\n",
      "t =  0.3000000000000001\n",
      "t =  0.3100000000000001\n",
      "t =  0.3200000000000001\n",
      "t =  0.3300000000000001\n",
      "t =  0.34000000000000014\n",
      "t =  0.35000000000000014\n",
      "t =  0.36000000000000015\n",
      "t =  0.37000000000000016\n",
      "t =  0.38000000000000017\n",
      "t =  0.3900000000000002\n",
      "t =  0.4000000000000002\n",
      "t =  0.4100000000000002\n",
      "t =  0.4200000000000002\n",
      "t =  0.4300000000000002\n",
      "t =  0.4400000000000002\n",
      "t =  0.45000000000000023\n",
      "t =  0.46000000000000024\n",
      "t =  0.47000000000000025\n",
      "t =  0.48000000000000026\n",
      "t =  0.49000000000000027\n",
      "t =  0.5000000000000002\n",
      "t =  0.5100000000000002\n",
      "t =  0.5200000000000002\n",
      "t =  0.5300000000000002\n",
      "t =  0.5400000000000003\n",
      "t =  0.5500000000000003\n",
      "t =  0.5600000000000003\n",
      "t =  0.5700000000000003\n",
      "t =  0.5800000000000003\n",
      "t =  0.5900000000000003\n",
      "t =  0.6000000000000003\n",
      "t =  0.6100000000000003\n",
      "t =  0.6200000000000003\n",
      "t =  0.6300000000000003\n",
      "t =  0.6400000000000003\n",
      "t =  0.6500000000000004\n",
      "t =  0.6600000000000004\n",
      "t =  0.6700000000000004\n",
      "t =  0.6800000000000004\n",
      "t =  0.6900000000000004\n",
      "t =  0.7000000000000004\n",
      "t =  0.7100000000000004\n",
      "t =  0.7200000000000004\n",
      "t =  0.7300000000000004\n",
      "t =  0.7400000000000004\n",
      "t =  0.7500000000000004\n",
      "t =  0.7600000000000005\n",
      "t =  0.7700000000000005\n",
      "t =  0.7800000000000005\n",
      "t =  0.7900000000000005\n",
      "t =  0.8000000000000005\n",
      "t =  0.8100000000000005\n",
      "t =  0.8200000000000005\n",
      "t =  0.8300000000000005\n",
      "t =  0.8400000000000005\n",
      "t =  0.8500000000000005\n",
      "t =  0.8600000000000005\n",
      "t =  0.8700000000000006\n",
      "t =  0.8800000000000006\n",
      "t =  0.8900000000000006\n",
      "t =  0.9000000000000006\n",
      "t =  0.9100000000000006\n",
      "t =  0.9200000000000006\n",
      "t =  0.9300000000000006\n",
      "t =  0.9400000000000006\n",
      "t =  0.9500000000000006\n",
      "t =  0.9600000000000006\n",
      "t =  0.9700000000000006\n",
      "t =  0.9800000000000006\n",
      "t =  0.9900000000000007\n",
      "t =  1.0000000000000007\n",
      "t =  1.0100000000000007\n",
      "t =  1.0200000000000007\n",
      "t =  1.0300000000000007\n",
      "t =  1.0400000000000007\n",
      "t =  1.0500000000000007\n",
      "t =  1.0600000000000007\n",
      "t =  1.0700000000000007\n",
      "t =  1.0800000000000007\n",
      "t =  1.0900000000000007\n",
      "t =  1.1000000000000008\n",
      "t =  1.1100000000000008\n",
      "t =  1.1200000000000008\n",
      "t =  1.1300000000000008\n",
      "t =  1.1400000000000008\n",
      "t =  1.1500000000000008\n",
      "t =  1.1600000000000008\n",
      "t =  1.1700000000000008\n",
      "t =  1.1800000000000008\n",
      "t =  1.1900000000000008\n",
      "t =  1.2000000000000008\n",
      "t =  1.2100000000000009\n",
      "t =  1.2200000000000009\n",
      "t =  1.2300000000000009\n",
      "t =  1.2400000000000009\n",
      "t =  1.2500000000000009\n",
      "t =  1.260000000000001\n",
      "t =  1.270000000000001\n",
      "t =  1.280000000000001\n",
      "t =  1.290000000000001\n",
      "t =  1.300000000000001\n",
      "t =  1.310000000000001\n",
      "t =  1.320000000000001\n",
      "t =  1.330000000000001\n",
      "t =  1.340000000000001\n",
      "t =  1.350000000000001\n",
      "t =  1.360000000000001\n",
      "t =  1.370000000000001\n",
      "t =  1.380000000000001\n",
      "t =  1.390000000000001\n",
      "t =  1.400000000000001\n",
      "t =  1.410000000000001\n",
      "t =  1.420000000000001\n",
      "t =  1.430000000000001\n",
      "t =  1.440000000000001\n",
      "t =  1.450000000000001\n",
      "t =  1.460000000000001\n",
      "t =  1.470000000000001\n",
      "t =  1.480000000000001\n",
      "t =  1.490000000000001\n",
      "t =  1.500000000000001\n",
      "t =  1.5100000000000011\n",
      "t =  1.5200000000000011\n",
      "t =  1.5300000000000011\n",
      "t =  1.5400000000000011\n",
      "t =  1.5500000000000012\n",
      "t =  1.5600000000000012\n",
      "t =  1.5700000000000012\n",
      "t =  1.5800000000000012\n",
      "t =  1.5900000000000012\n",
      "t =  1.6000000000000012\n",
      "t =  1.6100000000000012\n",
      "t =  1.6200000000000012\n",
      "t =  1.6300000000000012\n",
      "t =  1.6400000000000012\n",
      "t =  1.6500000000000012\n",
      "t =  1.6600000000000013\n",
      "t =  1.6700000000000013\n",
      "t =  1.6800000000000013\n",
      "t =  1.6900000000000013\n",
      "t =  1.7000000000000013\n",
      "t =  1.7100000000000013\n",
      "t =  1.7200000000000013\n",
      "t =  1.7300000000000013\n",
      "t =  1.7400000000000013\n",
      "t =  1.7500000000000013\n",
      "t =  1.7600000000000013\n",
      "t =  1.7700000000000014\n",
      "t =  1.7800000000000014\n",
      "t =  1.7900000000000014\n",
      "t =  1.8000000000000014\n",
      "t =  1.8100000000000014\n",
      "t =  1.8200000000000014\n",
      "t =  1.8300000000000014\n",
      "t =  1.8400000000000014\n",
      "t =  1.8500000000000014\n",
      "t =  1.8600000000000014\n",
      "t =  1.8700000000000014\n",
      "t =  1.8800000000000014\n",
      "t =  1.8900000000000015\n",
      "t =  1.9000000000000015\n",
      "t =  1.9100000000000015\n",
      "t =  1.9200000000000015\n",
      "t =  1.9300000000000015\n",
      "t =  1.9400000000000015\n",
      "t =  1.9500000000000015\n",
      "t =  1.9600000000000015\n",
      "t =  1.9700000000000015\n",
      "t =  1.9800000000000015\n",
      "t =  1.9900000000000015\n",
      "t =  2.0000000000000013\n",
      "t =  2.010000000000001\n",
      "t =  2.020000000000001\n",
      "t =  2.0300000000000007\n",
      "t =  2.0400000000000005\n",
      "t =  2.0500000000000003\n",
      "t =  2.06\n",
      "t =  2.07\n",
      "t =  2.0799999999999996\n",
      "t =  2.0899999999999994\n",
      "t =  2.099999999999999\n",
      "t =  2.109999999999999\n",
      "t =  2.1199999999999988\n",
      "t =  2.1299999999999986\n",
      "t =  2.1399999999999983\n",
      "t =  2.149999999999998\n",
      "t =  2.159999999999998\n",
      "t =  2.1699999999999977\n",
      "t =  2.1799999999999975\n",
      "t =  2.1899999999999973\n",
      "t =  2.199999999999997\n",
      "t =  2.209999999999997\n",
      "t =  2.2199999999999966\n",
      "t =  2.2299999999999964\n",
      "t =  2.239999999999996\n",
      "t =  2.249999999999996\n",
      "t =  2.259999999999996\n",
      "t =  2.2699999999999956\n",
      "t =  2.2799999999999954\n",
      "t =  2.289999999999995\n",
      "t =  2.299999999999995\n",
      "t =  2.3099999999999947\n",
      "t =  2.3199999999999945\n",
      "t =  2.3299999999999943\n",
      "t =  2.339999999999994\n",
      "t =  2.349999999999994\n",
      "t =  2.3599999999999937\n",
      "t =  2.3699999999999934\n",
      "t =  2.3799999999999932\n",
      "t =  2.389999999999993\n",
      "t =  2.399999999999993\n",
      "t =  2.4099999999999926\n",
      "t =  2.4199999999999924\n",
      "t =  2.429999999999992\n",
      "t =  2.439999999999992\n",
      "t =  2.4499999999999917\n",
      "t =  2.4599999999999915\n",
      "t =  2.4699999999999913\n",
      "t =  2.479999999999991\n",
      "t =  2.489999999999991\n",
      "t =  2.4999999999999907\n",
      "t =  2.5099999999999905\n",
      "t =  2.5199999999999902\n",
      "t =  2.52999999999999\n",
      "t =  2.53999999999999\n",
      "t =  2.5499999999999896\n",
      "t =  2.5599999999999894\n",
      "t =  2.569999999999989\n",
      "t =  2.579999999999989\n",
      "t =  2.5899999999999888\n",
      "t =  2.5999999999999885\n",
      "t =  2.6099999999999883\n",
      "t =  2.619999999999988\n",
      "t =  2.629999999999988\n",
      "t =  2.6399999999999877\n",
      "t =  2.6499999999999875\n",
      "t =  2.6599999999999873\n",
      "t =  2.669999999999987\n",
      "t =  2.679999999999987\n",
      "t =  2.6899999999999866\n",
      "t =  2.6999999999999864\n",
      "t =  2.709999999999986\n",
      "t =  2.719999999999986\n",
      "t =  2.7299999999999858\n",
      "t =  2.7399999999999856\n",
      "t =  2.7499999999999853\n",
      "t =  2.759999999999985\n",
      "t =  2.769999999999985\n",
      "t =  2.7799999999999847\n",
      "t =  2.7899999999999845\n",
      "t =  2.7999999999999843\n",
      "t =  2.809999999999984\n",
      "t =  2.819999999999984\n",
      "t =  2.8299999999999836\n",
      "t =  2.8399999999999834\n",
      "t =  2.849999999999983\n",
      "t =  2.859999999999983\n",
      "t =  2.869999999999983\n",
      "t =  2.8799999999999826\n",
      "t =  2.8899999999999824\n",
      "t =  2.899999999999982\n",
      "t =  2.909999999999982\n",
      "t =  2.9199999999999817\n",
      "t =  2.9299999999999815\n",
      "t =  2.9399999999999813\n",
      "t =  2.949999999999981\n",
      "t =  2.959999999999981\n",
      "t =  2.9699999999999807\n",
      "t =  2.9799999999999804\n",
      "t =  2.9899999999999802\n",
      "t =  2.99999999999998\n",
      "t =  3.00999999999998\n",
      "t =  3.0199999999999796\n",
      "t =  3.0299999999999794\n",
      "t =  3.039999999999979\n",
      "t =  3.049999999999979\n",
      "t =  3.0599999999999787\n",
      "t =  3.0699999999999785\n",
      "t =  3.0799999999999783\n",
      "t =  3.089999999999978\n",
      "t =  3.099999999999978\n",
      "t =  3.1099999999999777\n",
      "t =  3.1199999999999775\n",
      "t =  3.1299999999999772\n",
      "t =  3.139999999999977\n",
      "t =  3.149999999999977\n",
      "t =  3.1599999999999766\n",
      "t =  3.1699999999999764\n",
      "t =  3.179999999999976\n",
      "t =  3.189999999999976\n",
      "t =  3.1999999999999758\n",
      "t =  3.2099999999999755\n",
      "t =  3.2199999999999753\n",
      "t =  3.229999999999975\n",
      "t =  3.239999999999975\n",
      "t =  3.2499999999999747\n",
      "t =  3.2599999999999745\n",
      "t =  3.2699999999999743\n",
      "t =  3.279999999999974\n",
      "t =  3.289999999999974\n",
      "t =  3.2999999999999736\n",
      "t =  3.3099999999999734\n",
      "t =  3.319999999999973\n",
      "t =  3.329999999999973\n",
      "t =  3.3399999999999728\n",
      "t =  3.3499999999999726\n",
      "t =  3.3599999999999723\n",
      "t =  3.369999999999972\n",
      "t =  3.379999999999972\n",
      "t =  3.3899999999999717\n",
      "t =  3.3999999999999715\n",
      "t =  3.4099999999999713\n",
      "t =  3.419999999999971\n",
      "t =  3.429999999999971\n",
      "t =  3.4399999999999706\n",
      "t =  3.4499999999999704\n",
      "t =  3.45999999999997\n",
      "t =  3.46999999999997\n",
      "t =  3.47999999999997\n",
      "t =  3.4899999999999696\n",
      "t =  3.4999999999999694\n",
      "t =  3.509999999999969\n",
      "t =  3.519999999999969\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t =  3.5299999999999687\n",
      "t =  3.5399999999999685\n",
      "t =  3.5499999999999683\n",
      "t =  3.559999999999968\n",
      "t =  3.569999999999968\n",
      "t =  3.5799999999999677\n",
      "t =  3.5899999999999674\n",
      "t =  3.5999999999999672\n",
      "t =  3.609999999999967\n",
      "t =  3.619999999999967\n",
      "t =  3.6299999999999666\n",
      "t =  3.6399999999999664\n",
      "t =  3.649999999999966\n",
      "t =  3.659999999999966\n",
      "t =  3.6699999999999657\n",
      "t =  3.6799999999999655\n",
      "t =  3.6899999999999653\n",
      "t =  3.699999999999965\n",
      "t =  3.709999999999965\n",
      "t =  3.7199999999999647\n",
      "t =  3.7299999999999645\n",
      "t =  3.7399999999999642\n",
      "t =  3.749999999999964\n",
      "t =  3.759999999999964\n",
      "t =  3.7699999999999636\n",
      "t =  3.7799999999999634\n",
      "t =  3.789999999999963\n",
      "t =  3.799999999999963\n",
      "t =  3.8099999999999627\n",
      "t =  3.8199999999999625\n",
      "t =  3.8299999999999623\n",
      "t =  3.839999999999962\n",
      "t =  3.849999999999962\n",
      "t =  3.8599999999999617\n",
      "t =  3.8699999999999615\n",
      "t =  3.8799999999999613\n",
      "t =  3.889999999999961\n",
      "t =  3.899999999999961\n",
      "t =  3.9099999999999606\n",
      "t =  3.9199999999999604\n",
      "t =  3.92999999999996\n",
      "t =  3.93999999999996\n",
      "t =  3.9499999999999598\n",
      "t =  3.9599999999999596\n",
      "t =  3.9699999999999593\n",
      "t =  3.979999999999959\n",
      "t =  3.989999999999959\n",
      "t =  3.9999999999999587\n",
      "t =  4.009999999999959\n",
      "t =  4.019999999999959\n",
      "t =  4.0299999999999585\n",
      "t =  4.039999999999958\n",
      "t =  4.049999999999958\n",
      "t =  4.059999999999958\n",
      "t =  4.069999999999958\n",
      "t =  4.079999999999957\n",
      "t =  4.089999999999957\n",
      "t =  4.099999999999957\n",
      "t =  4.109999999999957\n",
      "t =  4.119999999999957\n",
      "t =  4.129999999999956\n",
      "t =  4.139999999999956\n",
      "t =  4.149999999999956\n",
      "t =  4.159999999999956\n",
      "t =  4.1699999999999555\n",
      "t =  4.179999999999955\n",
      "t =  4.189999999999955\n",
      "t =  4.199999999999955\n",
      "t =  4.209999999999955\n",
      "t =  4.2199999999999545\n",
      "t =  4.229999999999954\n",
      "t =  4.239999999999954\n",
      "t =  4.249999999999954\n",
      "t =  4.259999999999954\n",
      "t =  4.269999999999953\n",
      "t =  4.279999999999953\n",
      "t =  4.289999999999953\n",
      "t =  4.299999999999953\n",
      "t =  4.3099999999999525\n",
      "t =  4.319999999999952\n",
      "t =  4.329999999999952\n",
      "t =  4.339999999999952\n",
      "t =  4.349999999999952\n",
      "t =  4.3599999999999515\n",
      "t =  4.369999999999951\n",
      "t =  4.379999999999951\n",
      "t =  4.389999999999951\n",
      "t =  4.399999999999951\n",
      "t =  4.40999999999995\n",
      "t =  4.41999999999995\n",
      "t =  4.42999999999995\n",
      "t =  4.43999999999995\n",
      "t =  4.4499999999999496\n",
      "t =  4.459999999999949\n",
      "t =  4.469999999999949\n",
      "t =  4.479999999999949\n",
      "t =  4.489999999999949\n",
      "t =  4.4999999999999485\n",
      "t =  4.509999999999948\n",
      "t =  4.519999999999948\n",
      "t =  4.529999999999948\n",
      "t =  4.539999999999948\n",
      "t =  4.549999999999947\n",
      "t =  4.559999999999947\n",
      "t =  4.569999999999947\n",
      "t =  4.579999999999947\n",
      "t =  4.589999999999947\n",
      "t =  4.599999999999946\n",
      "t =  4.609999999999946\n",
      "t =  4.619999999999946\n",
      "t =  4.629999999999946\n",
      "t =  4.6399999999999455\n",
      "t =  4.649999999999945\n",
      "t =  4.659999999999945\n",
      "t =  4.669999999999945\n",
      "t =  4.679999999999945\n",
      "t =  4.689999999999944\n",
      "t =  4.699999999999944\n",
      "t =  4.709999999999944\n",
      "t =  4.719999999999944\n",
      "t =  4.729999999999944\n",
      "t =  4.739999999999943\n",
      "t =  4.749999999999943\n",
      "t =  4.759999999999943\n",
      "t =  4.769999999999943\n",
      "t =  4.7799999999999425\n",
      "t =  4.789999999999942\n",
      "t =  4.799999999999942\n",
      "t =  4.809999999999942\n",
      "t =  4.819999999999942\n",
      "t =  4.8299999999999415\n",
      "t =  4.839999999999941\n",
      "t =  4.849999999999941\n",
      "t =  4.859999999999941\n",
      "t =  4.869999999999941\n",
      "t =  4.87999999999994\n",
      "t =  4.88999999999994\n",
      "t =  4.89999999999994\n",
      "t =  4.90999999999994\n",
      "t =  4.9199999999999395\n",
      "t =  4.929999999999939\n",
      "t =  4.939999999999939\n",
      "t =  4.949999999999939\n",
      "t =  4.959999999999939\n",
      "t =  4.9699999999999385\n",
      "t =  4.979999999999938\n",
      "t =  4.989999999999938\n",
      "t =  4.999999999999938\n",
      "t =  5.009999999999938\n",
      "t =  5.019999999999937\n",
      "t =  5.029999999999937\n",
      "t =  5.039999999999937\n",
      "t =  5.049999999999937\n",
      "t =  5.0599999999999365\n",
      "t =  5.069999999999936\n",
      "t =  5.079999999999936\n",
      "t =  5.089999999999936\n",
      "t =  5.099999999999936\n",
      "t =  5.1099999999999355\n",
      "t =  5.119999999999935\n",
      "t =  5.129999999999935\n",
      "t =  5.139999999999935\n",
      "t =  5.149999999999935\n",
      "t =  5.159999999999934\n",
      "t =  5.169999999999934\n",
      "t =  5.179999999999934\n",
      "t =  5.189999999999934\n",
      "t =  5.199999999999934\n",
      "t =  5.209999999999933\n",
      "t =  5.219999999999933\n",
      "t =  5.229999999999933\n",
      "t =  5.239999999999933\n",
      "t =  5.2499999999999325\n",
      "t =  5.259999999999932\n",
      "t =  5.269999999999932\n",
      "t =  5.279999999999932\n",
      "t =  5.289999999999932\n",
      "t =  5.299999999999931\n",
      "t =  5.309999999999931\n",
      "t =  5.319999999999931\n",
      "t =  5.329999999999931\n",
      "t =  5.339999999999931\n",
      "t =  5.34999999999993\n",
      "t =  5.35999999999993\n",
      "t =  5.36999999999993\n",
      "t =  5.37999999999993\n",
      "t =  5.3899999999999295\n",
      "t =  5.399999999999929\n",
      "t =  5.409999999999929\n",
      "t =  5.419999999999929\n",
      "t =  5.429999999999929\n",
      "t =  5.4399999999999284\n",
      "t =  5.449999999999928\n",
      "t =  5.459999999999928\n",
      "t =  5.469999999999928\n",
      "t =  5.479999999999928\n",
      "t =  5.489999999999927\n",
      "t =  5.499999999999927\n",
      "t =  5.509999999999927\n",
      "t =  5.519999999999927\n",
      "t =  5.5299999999999265\n",
      "t =  5.539999999999926\n",
      "t =  5.549999999999926\n",
      "t =  5.559999999999926\n",
      "t =  5.569999999999926\n",
      "t =  5.5799999999999255\n",
      "t =  5.589999999999925\n",
      "t =  5.599999999999925\n",
      "t =  5.609999999999925\n",
      "t =  5.619999999999925\n",
      "t =  5.629999999999924\n",
      "t =  5.639999999999924\n",
      "t =  5.649999999999924\n",
      "t =  5.659999999999924\n",
      "t =  5.6699999999999235\n",
      "t =  5.679999999999923\n",
      "t =  5.689999999999923\n",
      "t =  5.699999999999923\n",
      "t =  5.709999999999923\n",
      "t =  5.7199999999999225\n",
      "t =  5.729999999999922\n",
      "t =  5.739999999999922\n",
      "t =  5.749999999999922\n",
      "t =  5.759999999999922\n",
      "t =  5.769999999999921\n",
      "t =  5.779999999999921\n",
      "t =  5.789999999999921\n",
      "t =  5.799999999999921\n",
      "t =  5.809999999999921\n",
      "t =  5.81999999999992\n",
      "t =  5.82999999999992\n",
      "t =  5.83999999999992\n",
      "t =  5.84999999999992\n",
      "t =  5.8599999999999195\n",
      "t =  5.869999999999919\n",
      "t =  5.879999999999919\n",
      "t =  5.889999999999919\n",
      "t =  5.899999999999919\n",
      "t =  5.909999999999918\n",
      "t =  5.919999999999918\n",
      "t =  5.929999999999918\n",
      "t =  5.939999999999918\n",
      "t =  5.949999999999918\n",
      "t =  5.959999999999917\n",
      "t =  5.969999999999917\n",
      "t =  5.979999999999917\n",
      "t =  5.989999999999917\n",
      "t =  5.9999999999999165\n",
      "t =  6.009999999999916\n",
      "t =  6.019999999999916\n",
      "t =  6.029999999999916\n",
      "t =  6.039999999999916\n",
      "t =  6.0499999999999154\n",
      "t =  6.059999999999915\n",
      "t =  6.069999999999915\n",
      "t =  6.079999999999915\n",
      "t =  6.089999999999915\n",
      "t =  6.099999999999914\n",
      "t =  6.109999999999914\n",
      "t =  6.119999999999914\n",
      "t =  6.129999999999914\n",
      "t =  6.1399999999999135\n",
      "t =  6.149999999999913\n",
      "t =  6.159999999999913\n",
      "t =  6.169999999999913\n",
      "t =  6.179999999999913\n",
      "t =  6.1899999999999125\n",
      "t =  6.199999999999912\n",
      "t =  6.209999999999912\n",
      "t =  6.219999999999912\n",
      "t =  6.229999999999912\n",
      "t =  6.239999999999911\n",
      "t =  6.249999999999911\n",
      "t =  6.259999999999911\n",
      "t =  6.269999999999911\n",
      "t =  6.2799999999999105\n",
      "t =  6.28999999999991\n",
      "t =  6.29999999999991\n",
      "t =  6.30999999999991\n",
      "t =  6.31999999999991\n",
      "t =  6.3299999999999095\n",
      "t =  6.339999999999909\n",
      "t =  6.349999999999909\n",
      "t =  6.359999999999909\n",
      "t =  6.369999999999909\n",
      "t =  6.379999999999908\n",
      "t =  6.389999999999908\n",
      "t =  6.399999999999908\n",
      "t =  6.409999999999908\n",
      "t =  6.419999999999908\n",
      "t =  6.429999999999907\n",
      "t =  6.439999999999907\n",
      "t =  6.449999999999907\n",
      "t =  6.459999999999907\n",
      "t =  6.4699999999999065\n",
      "t =  6.479999999999906\n",
      "t =  6.489999999999906\n",
      "t =  6.499999999999906\n",
      "t =  6.509999999999906\n",
      "t =  6.519999999999905\n",
      "t =  6.529999999999905\n",
      "t =  6.539999999999905\n",
      "t =  6.549999999999905\n",
      "t =  6.559999999999905\n",
      "t =  6.569999999999904\n",
      "t =  6.579999999999904\n",
      "t =  6.589999999999904\n",
      "t =  6.599999999999904\n",
      "t =  6.6099999999999035\n",
      "t =  6.619999999999903\n",
      "t =  6.629999999999903\n",
      "t =  6.639999999999903\n",
      "t =  6.649999999999903\n",
      "t =  6.659999999999902\n",
      "t =  6.669999999999902\n",
      "t =  6.679999999999902\n",
      "t =  6.689999999999902\n",
      "t =  6.699999999999902\n",
      "t =  6.709999999999901\n",
      "t =  6.719999999999901\n",
      "t =  6.729999999999901\n",
      "t =  6.739999999999901\n",
      "t =  6.7499999999999005\n",
      "t =  6.7599999999999\n",
      "t =  6.7699999999999\n",
      "t =  6.7799999999999\n",
      "t =  6.7899999999999\n",
      "t =  6.7999999999998995\n",
      "t =  6.809999999999899\n",
      "t =  6.819999999999899\n",
      "t =  6.829999999999899\n",
      "t =  6.839999999999899\n",
      "t =  6.849999999999898\n",
      "t =  6.859999999999898\n",
      "t =  6.869999999999898\n",
      "t =  6.879999999999898\n",
      "t =  6.8899999999998975\n",
      "t =  6.899999999999897\n",
      "t =  6.909999999999897\n",
      "t =  6.919999999999897\n",
      "t =  6.929999999999897\n",
      "t =  6.9399999999998965\n",
      "t =  6.949999999999896\n",
      "t =  6.959999999999896\n",
      "t =  6.969999999999896\n",
      "t =  6.979999999999896\n",
      "t =  6.989999999999895\n",
      "t =  6.999999999999895\n",
      "t =  7.009999999999895\n",
      "t =  7.019999999999895\n",
      "t =  7.0299999999998946\n",
      "t =  7.039999999999894\n",
      "t =  7.049999999999894\n",
      "t =  7.059999999999894\n",
      "t =  7.069999999999894\n",
      "t =  7.0799999999998935\n",
      "t =  7.089999999999893\n",
      "t =  7.099999999999893\n",
      "t =  7.109999999999893\n",
      "t =  7.119999999999893\n",
      "t =  7.129999999999892\n",
      "t =  7.139999999999892\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t =  7.149999999999892\n",
      "t =  7.159999999999892\n",
      "t =  7.169999999999892\n",
      "t =  7.179999999999891\n",
      "t =  7.189999999999891\n",
      "t =  7.199999999999891\n",
      "t =  7.209999999999891\n",
      "t =  7.2199999999998905\n",
      "t =  7.22999999999989\n",
      "t =  7.23999999999989\n",
      "t =  7.24999999999989\n",
      "t =  7.25999999999989\n",
      "t =  7.269999999999889\n",
      "t =  7.279999999999889\n",
      "t =  7.289999999999889\n",
      "t =  7.299999999999889\n",
      "t =  7.309999999999889\n",
      "t =  7.319999999999888\n",
      "t =  7.329999999999888\n",
      "t =  7.339999999999888\n",
      "t =  7.349999999999888\n",
      "t =  7.3599999999998875\n",
      "t =  7.369999999999887\n",
      "t =  7.379999999999887\n",
      "t =  7.389999999999887\n",
      "t =  7.399999999999887\n",
      "t =  7.4099999999998865\n",
      "t =  7.419999999999886\n",
      "t =  7.429999999999886\n",
      "t =  7.439999999999886\n",
      "t =  7.449999999999886\n",
      "t =  7.459999999999885\n",
      "t =  7.469999999999885\n",
      "t =  7.479999999999885\n",
      "t =  7.489999999999885\n",
      "t =  7.4999999999998845\n",
      "t =  7.509999999999884\n",
      "t =  7.519999999999884\n",
      "t =  7.529999999999884\n",
      "t =  7.539999999999884\n",
      "t =  7.5499999999998835\n",
      "t =  7.559999999999883\n",
      "t =  7.569999999999883\n",
      "t =  7.579999999999883\n",
      "t =  7.589999999999883\n",
      "t =  7.599999999999882\n",
      "t =  7.609999999999882\n",
      "t =  7.619999999999882\n",
      "t =  7.629999999999882\n",
      "t =  7.6399999999998816\n",
      "t =  7.649999999999881\n",
      "t =  7.659999999999881\n",
      "t =  7.669999999999881\n",
      "t =  7.679999999999881\n",
      "t =  7.6899999999998805\n",
      "t =  7.69999999999988\n",
      "t =  7.70999999999988\n",
      "t =  7.71999999999988\n",
      "t =  7.72999999999988\n",
      "t =  7.739999999999879\n",
      "t =  7.749999999999879\n",
      "t =  7.759999999999879\n",
      "t =  7.769999999999879\n",
      "t =  7.779999999999879\n",
      "t =  7.789999999999878\n",
      "t =  7.799999999999878\n",
      "t =  7.809999999999878\n",
      "t =  7.819999999999878\n",
      "t =  7.8299999999998775\n",
      "t =  7.839999999999877\n",
      "t =  7.849999999999877\n",
      "t =  7.859999999999877\n",
      "t =  7.869999999999877\n",
      "t =  7.879999999999876\n",
      "t =  7.889999999999876\n",
      "t =  7.899999999999876\n",
      "t =  7.909999999999876\n",
      "t =  7.919999999999876\n",
      "t =  7.929999999999875\n",
      "t =  7.939999999999875\n",
      "t =  7.949999999999875\n",
      "t =  7.959999999999875\n",
      "t =  7.9699999999998745\n",
      "t =  7.979999999999874\n",
      "t =  7.989999999999874\n",
      "t =  7.999999999999874\n",
      "t =  8.009999999999874\n",
      "t =  8.019999999999873\n",
      "t =  8.029999999999873\n",
      "t =  8.039999999999873\n",
      "t =  8.049999999999873\n",
      "t =  8.059999999999873\n",
      "t =  8.069999999999872\n",
      "t =  8.079999999999872\n",
      "t =  8.089999999999872\n",
      "t =  8.099999999999872\n",
      "t =  8.109999999999872\n",
      "t =  8.119999999999871\n",
      "t =  8.129999999999871\n",
      "t =  8.139999999999871\n",
      "t =  8.14999999999987\n",
      "t =  8.15999999999987\n",
      "t =  8.16999999999987\n",
      "t =  8.17999999999987\n",
      "t =  8.18999999999987\n",
      "t =  8.19999999999987\n",
      "t =  8.20999999999987\n",
      "t =  8.21999999999987\n",
      "t =  8.229999999999869\n",
      "t =  8.239999999999869\n",
      "t =  8.249999999999869\n",
      "t =  8.259999999999868\n",
      "t =  8.269999999999868\n",
      "t =  8.279999999999868\n",
      "t =  8.289999999999868\n",
      "t =  8.299999999999867\n",
      "t =  8.309999999999867\n",
      "t =  8.319999999999867\n",
      "t =  8.329999999999867\n",
      "t =  8.339999999999867\n",
      "t =  8.349999999999866\n",
      "t =  8.359999999999866\n",
      "t =  8.369999999999866\n",
      "t =  8.379999999999866\n",
      "t =  8.389999999999866\n",
      "t =  8.399999999999865\n",
      "t =  8.409999999999865\n",
      "t =  8.419999999999865\n",
      "t =  8.429999999999865\n",
      "t =  8.439999999999864\n",
      "t =  8.449999999999864\n",
      "t =  8.459999999999864\n",
      "t =  8.469999999999864\n",
      "t =  8.479999999999864\n",
      "t =  8.489999999999863\n",
      "t =  8.499999999999863\n",
      "t =  8.509999999999863\n",
      "t =  8.519999999999863\n",
      "t =  8.529999999999863\n",
      "t =  8.539999999999862\n",
      "t =  8.549999999999862\n",
      "t =  8.559999999999862\n",
      "t =  8.569999999999862\n",
      "t =  8.579999999999862\n",
      "t =  8.589999999999861\n",
      "t =  8.599999999999861\n",
      "t =  8.60999999999986\n",
      "t =  8.61999999999986\n",
      "t =  8.62999999999986\n",
      "t =  8.63999999999986\n",
      "t =  8.64999999999986\n",
      "t =  8.65999999999986\n",
      "t =  8.66999999999986\n",
      "t =  8.67999999999986\n",
      "t =  8.68999999999986\n",
      "t =  8.699999999999859\n",
      "t =  8.709999999999859\n",
      "t =  8.719999999999859\n",
      "t =  8.729999999999858\n",
      "t =  8.739999999999858\n",
      "t =  8.749999999999858\n",
      "t =  8.759999999999858\n",
      "t =  8.769999999999857\n",
      "t =  8.779999999999857\n",
      "t =  8.789999999999857\n",
      "t =  8.799999999999857\n",
      "t =  8.809999999999857\n",
      "t =  8.819999999999856\n",
      "t =  8.829999999999856\n",
      "t =  8.839999999999856\n",
      "t =  8.849999999999856\n",
      "t =  8.859999999999856\n",
      "t =  8.869999999999855\n",
      "t =  8.879999999999855\n",
      "t =  8.889999999999855\n",
      "t =  8.899999999999855\n",
      "t =  8.909999999999854\n",
      "t =  8.919999999999854\n",
      "t =  8.929999999999854\n",
      "t =  8.939999999999854\n",
      "t =  8.949999999999854\n",
      "t =  8.959999999999853\n",
      "t =  8.969999999999853\n",
      "t =  8.979999999999853\n",
      "t =  8.989999999999853\n",
      "t =  8.999999999999853\n",
      "t =  9.009999999999852\n",
      "t =  9.019999999999852\n",
      "t =  9.029999999999852\n",
      "t =  9.039999999999852\n",
      "t =  9.049999999999851\n",
      "t =  9.059999999999851\n",
      "t =  9.069999999999851\n",
      "t =  9.07999999999985\n",
      "t =  9.08999999999985\n",
      "t =  9.09999999999985\n",
      "t =  9.10999999999985\n",
      "t =  9.11999999999985\n",
      "t =  9.12999999999985\n",
      "t =  9.13999999999985\n",
      "t =  9.14999999999985\n",
      "t =  9.15999999999985\n",
      "t =  9.169999999999849\n",
      "t =  9.179999999999849\n",
      "t =  9.189999999999849\n",
      "t =  9.199999999999848\n",
      "t =  9.209999999999848\n",
      "t =  9.219999999999848\n",
      "t =  9.229999999999848\n",
      "t =  9.239999999999847\n",
      "t =  9.249999999999847\n",
      "t =  9.259999999999847\n",
      "t =  9.269999999999847\n",
      "t =  9.279999999999847\n",
      "t =  9.289999999999846\n",
      "t =  9.299999999999846\n",
      "t =  9.309999999999846\n",
      "t =  9.319999999999846\n",
      "t =  9.329999999999846\n",
      "t =  9.339999999999845\n",
      "t =  9.349999999999845\n",
      "t =  9.359999999999845\n",
      "t =  9.369999999999845\n",
      "t =  9.379999999999844\n",
      "t =  9.389999999999844\n",
      "t =  9.399999999999844\n",
      "t =  9.409999999999844\n",
      "t =  9.419999999999844\n",
      "t =  9.429999999999843\n",
      "t =  9.439999999999843\n",
      "t =  9.449999999999843\n",
      "t =  9.459999999999843\n",
      "t =  9.469999999999843\n",
      "t =  9.479999999999842\n",
      "t =  9.489999999999842\n",
      "t =  9.499999999999842\n",
      "t =  9.509999999999842\n",
      "t =  9.519999999999841\n",
      "t =  9.529999999999841\n",
      "t =  9.539999999999841\n",
      "t =  9.54999999999984\n",
      "t =  9.55999999999984\n",
      "t =  9.56999999999984\n",
      "t =  9.57999999999984\n",
      "t =  9.58999999999984\n",
      "t =  9.59999999999984\n",
      "t =  9.60999999999984\n",
      "t =  9.61999999999984\n",
      "t =  9.62999999999984\n",
      "t =  9.639999999999839\n",
      "t =  9.649999999999839\n",
      "t =  9.659999999999838\n",
      "t =  9.669999999999838\n",
      "t =  9.679999999999838\n",
      "t =  9.689999999999838\n",
      "t =  9.699999999999838\n",
      "t =  9.709999999999837\n",
      "t =  9.719999999999837\n",
      "t =  9.729999999999837\n",
      "t =  9.739999999999837\n",
      "t =  9.749999999999837\n",
      "t =  9.759999999999836\n",
      "t =  9.769999999999836\n",
      "t =  9.779999999999836\n",
      "t =  9.789999999999836\n",
      "t =  9.799999999999836\n",
      "t =  9.809999999999835\n",
      "t =  9.819999999999835\n",
      "t =  9.829999999999835\n",
      "t =  9.839999999999835\n",
      "t =  9.849999999999834\n",
      "t =  9.859999999999834\n",
      "t =  9.869999999999834\n",
      "t =  9.879999999999834\n",
      "t =  9.889999999999834\n",
      "t =  9.899999999999833\n",
      "t =  9.909999999999833\n",
      "t =  9.919999999999833\n",
      "t =  9.929999999999833\n",
      "t =  9.939999999999833\n",
      "t =  9.949999999999832\n",
      "t =  9.959999999999832\n",
      "t =  9.969999999999832\n",
      "t =  9.979999999999832\n",
      "t =  9.989999999999831\n",
      "t =  9.999999999999831\n"
     ]
    }
   ],
   "source": [
    "# time travel\n",
    "for n in range(num_steps) :\n",
    "    t += dt\n",
    "    \n",
    "    print(\"t = \", t)\n",
    "    \n",
    "    b = assemble(L)\n",
    "    bc.apply(A,b)\n",
    "    solve(A, u.vector(), b)\n",
    "    #solve(a == L, u, bcs)\n",
    "    \n",
    "    n = FacetNormal(mesh)\n",
    "    \n",
    "    # compute the power transfer through each boundary\n",
    "    \n",
    "    flux = inner(grad(u0), n)*ds(4) #flux through bottom \n",
    "    power_bottom = assemble(flux) #integrate flux to get power\n",
    "    \n",
    "    flux = inner(grad(u0), n)*ds(2) #flux through top boundary\n",
    "    power_top = assemble(flux) #integrate flux to get power\n",
    "    \n",
    "    flux = inner(grad(u0), n)*ds(3) #flux through right boundary\n",
    "    power_right = assemble(flux) #integrate flux to get power\n",
    "    \n",
    "    flux = inner(grad(u0), n)*ds(1) #flux through left boundary\n",
    "    power_left = assemble(flux) #integrate flux to get power\n",
    "    \n",
    "    #update\n",
    "    up.assign(u)\n",
    "    vtkfile << (u,t) #save"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/pdf": 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\n",
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(u)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The power transfer through the bottom boundary is -0.031295110530862376 Joules\n",
      "The power transfer through the top boundary is 0.003290718024276279 Joules\n",
      "The power transfer through the right boundary is -49.07798699910465 Joules\n",
      "The power transfer through the left boundary is 49.92405522894218 Joules\n"
     ]
    }
   ],
   "source": [
    "print(\"The power transfer through the bottom boundary is {}\".format(power_bottom), \"Joules\")\n",
    "print(\"The power transfer through the top boundary is {}\".format(power_top), \"Joules\")\n",
    "print(\"The power transfer through the right boundary is {}\".format(power_right), \"Joules\")\n",
    "print(\"The power transfer through the left boundary is {}\".format(power_left), \"Joules\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "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",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}