{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import seaborn as sn\n", "\n", "import pycollocation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider the following boundary value problem:\n", "\\begin{align}\n", " \\frac{d T_1}{d_A} =& -q,\\ T_1(0) = T_{1,0} \\\\\n", " \\frac{d T_2}{d_A} =& -\\frac{1}{2}q,\\ T_2(A_{hx}) = T_{2,A_{hx}} \\\\\n", "\\end{align}\n", "where $q = (T_1 - T_2)U$.\n", "\n", "This boundary value problem describes a counter current heat exchanger; a hot liquid enters a device and exchanges heat across a metal plate with a cold liquid traveling through the device in the opposite direction. Here, $T_1$ is the temperature of the hot stream, $T_2$ is the temperature of the cold stream, $q$ is the rate of heat transfer from the hot fluid to the cold fluid, $U$ is the overall heat transfer coefficient and $A_hx$ is the total area of the heat exchanger." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# provide numerical values for the parameters\n", "params = {'T10': 130, 'T2Ahx': 70, 'U': 1.0}\n", "\n", "def q(T1, T2, U):\n", " return (T1 - T2) * U\n", "\n", "def rhs(A, T1, T2, U, **params):\n", " return [-q(T1, T2, U), -0.5 * q(T1, T2, U)]\n", "\n", "def bcs_lower(A, T1, T2, T10, **params):\n", " return [T1 - T10]\n", "\n", "def bcs_upper(A, T1, T2, T2Ahx, **params):\n", " return [T2 - T2Ahx]" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "problem = pycollocation.problems.TwoPointBVP(bcs_lower, bcs_upper, 1, 2, params, rhs)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def initial_mesh(domain, num, problem):\n", " As = np.linspace(domain[0], domain[1], num)\n", " T1s = np.repeat(0.5 * (problem.params['T10'] + problem.params['T2Ahx']), num)\n", " return As, T1s, T1s\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [], "source": [ "polynomial_basis = pycollocation.basis_functions.PolynomialBasis()\n", "solver = pycollocation.solvers.Solver(polynomial_basis)\n", "\n", "basis_kwargs = {'kind': 'Chebyshev', 'domain': [0, 5.0], 'degree': 15}\n", "\n", "As, T1s, T2s = initial_mesh(basis_kwargs['domain'], 1000, problem)\n", "T1_poly = polynomial_basis.fit(As, T1s, **basis_kwargs)\n", "T2_poly = polynomial_basis.fit(As, T2s, **basis_kwargs)\n", "initial_coefs = np.hstack([T1_poly.coef, T2_poly.coef])\n", "\n", "solution = solver.solve(basis_kwargs, initial_coefs, problem)\n" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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6bDz12HjqcXgolC9DedM+nj/8B1r62ki1e7hxwnLmx9jqU9rRRiYYDLFuZw1r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\njvv9AzS0DoV18+DIur61l8a2HnyB4Fn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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "T1_soln, T2_soln = solution.evaluate_solution(As)\n", "plt.plot(As, T1_soln)\n", "plt.plot(As, T2_soln)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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KWqHioaR7We6fRnV3LX/K/jt9lv4xPXd96uCxmKngc7KwhZZ2I6uSA/D3nFsX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\nYNAmIiJqE/8fsBZlPfjmi3IAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "T1_normalized_resids, T2_normalized_resids = solution.normalize_residuals(As)\n", "plt.plot(As, np.abs(T1_normalized_resids))\n", "plt.plot(As, np.abs(T2_normalized_resids))\n", "plt.yscale('log')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.10" } }, "nbformat": 4, "nbformat_minor": 0 }