{ "cells": [ { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[20.0, 19.3, 19.1, 19.0, 18.6, 18.0]\n", "[20.0, 19.346, 19.11, 18.97, 18.58, 18.0]\n", "[20.0, 19.466, 19.15, 18.899, 18.519, 18.0]\n", "[20.0, 19.562, 19.173, 18.832, 18.441, 18.0]\n" ] } ], "source": [ "#Heat Flow exercise on February 18, 2019\n", "kappa = .001 #cm^2/s\n", "dx1 = 1 #cm\n", "dt = 10 #seconds\n", "T = [[20.0, 19.3, 19.1, 19.0, 18.6, 18.0]] #degrees C\n", "\n", "def temperature(k, i):\n", " result = (kappa * dt /dx1**2)\n", " result = result * (T[k-1][i+1] - 2*T[k-1][i] + T[k-1][i-1])\n", " result = result + T[k-1][i]\n", " return float(\"{0:.3f}\".format(result)) #just three decimal places position\n", " #return result\n", "\n", "for t in range(1, 130): #march through time\n", " T.append([20.0, 19.3, 19.1, 19.0, 18.6, 18.0])\n", " for i in range(1, 5): #match through the nodes\n", " T[t][i] = temperature(t, i)\n", "\n", "#print out the resulting ending matrix:\n", "#for t in range(0, 130):\n", "# print(T[t])\n", "\n", "print(T[0])\n", "print(T[10])\n", "print(T[50])\n", "print(T[129])" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#plot the curves over time:\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import math\n", "\n", "fig = plt.figure(figsize=(12, 8))\n", "ax = plt.axes()\n", "\n", "i = [1, 2, 3, 4, 5, 6]\n", "plt.plot(i, T[0], color='#0000ff', linewidth=4)\n", "plt.plot(i, T[10], color='#6000a0')\n", "plt.plot(i, T[50], color='#a00060')\n", "plt.plot(i, T[129], color='#ff0000', linewidth=4)\n" ] }, { "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": "3.6.8" } }, "nbformat": 4, "nbformat_minor": 2 }