{ "cells": [ { "cell_type": "raw", "id": "a2b61891-2900-468e-a69d-7b2d0ffdf41e", "metadata": {}, "source": [ "2D cas stationaire sans production de chaleur" ] }, { "cell_type": "code", "execution_count": 4, "id": "a9c9b6c8-918b-4dee-b6b7-942bd231fda6", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "\n", "L = 1.0 \n", "W = 1.0 \n", "nx = 51 \n", "ny = 51 \n", "dx = L / (nx - 1)\n", "dy = W / (ny - 1)\n", "k = 1.0\n", "\n", "T_top = 100.0 \n", "T_bottom = 0 \n", "T_left = 10 \n", "T_right = 0.0 \n", "\n", "\n", "x = np.linspace(0.0, L, nx)\n", "y = np.linspace(0.0, W, ny)\n", "X, Y = np.meshgrid(x, y)\n", "\n", "\n", "T = np.zeros((ny, nx))\n", "\n", "\n", "T[0, :] = T_top\n", "T[ny-1, :] = T_bottom\n", "T[:, 0] = T_left\n", "T[:, nx-1] = T_right\n", "\n", "\n", "convergence = 1e-4\n", "residual = 1.0\n", "while residual > convergence:\n", " T_old = np.copy(T)\n", " for i in range(1, ny-1):\n", " for j in range(1, nx-1):\n", " T[i, j] = (T[i-1, j] + T[i+1, j] + T[i, j-1] + T[i, j+1]) / 4.0\n", " residual = np.max(np.abs(T - T_old))\n", "\n", "\n", "plt.contourf(X, Y, T, cmap='coolwarm')\n", "plt.colorbar()\n", "plt.xlabel('x')\n", "plt.ylabel('y', rotation=0)\n", "plt.title('2D cas stationaire sans production de chaleur')\n", "plt.show()" ] }, { "cell_type": "raw", "id": "a958e5f0-7dba-4223-8233-fb38b42b290c", "metadata": {}, "source": [ "2D cas stationaire avec production de chaleur" ] }, { "cell_type": "code", "execution_count": 8, "id": "26ca060b-20df-4595-b5eb-879f1ea8fa39", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "# Define the size of the plate\n", "L = 1.0 # length\n", "W = 1.0 # width\n", "\n", "# Define the number of grid points\n", "nx = 51 # number of points in x-direction\n", "ny = 51 # number of points in y-direction\n", "\n", "# Define the grid spacing\n", "dx = L / (nx - 1)\n", "dy = W / (ny - 1)\n", "\n", "# Define the thermal conductivity of the plate\n", "k = 1.0\n", "\n", "# Define the internal heat production\n", "Q = np.zeros((ny, nx))\n", "Q[25:31, 25:31] = 100.0\n", "\n", "# Define the boundary conditions\n", "T_top = 100.0 # temperature at the top boundary\n", "T_bottom = 0.0 # temperature at the bottom boundary\n", "T_left = 0.0 # temperature at the left boundary\n", "T_right = 0.0 # temperature at the right boundary\n", "\n", "# Create the grid\n", "x = np.linspace(0.0, L, nx)\n", "y = np.linspace(0.0, W, ny)\n", "X, Y = np.meshgrid(x, y)\n", "\n", "# Initialize the temperature array\n", "T = np.zeros((ny, nx))\n", "\n", "# Apply the boundary conditions\n", "T[0, :] = T_top\n", "T[ny-1, :] = T_bottom\n", "T[:, 0] = T_left\n", "T[:, nx-1] = T_right\n", "\n", "# Define the convergence criterion\n", "convergence = 1e-4\n", "\n", "# Initialize the residual\n", "residual = 1.0\n", "\n", "# Perform the iterations\n", "while residual > convergence:\n", " T_old = np.copy(T)\n", " for i in range(1, ny-1):\n", " for j in range(1, nx-1):\n", " Qij = Q[i, j]\n", " T[i, j] = (T[i-1, j] + T[i+1, j] + T[i, j-1] + T[i, j+1] + dx**2 * Qij / k) / 4.0\n", " residual = np.max(np.abs(T - T_old))\n", "\n", "# Plot the results\n", "plt.contourf(X, Y, T)\n", "plt.colorbar()\n", "plt.xlabel('x')\n", "plt.ylabel('y', rotation=0)\n", "plt.title('2D cas stationaire avec production de chaleur')\n", "plt.show()" ] }, { "cell_type": "raw", "id": "b0a22bb7-2b06-42c3-b01a-270bfc8eed28", "metadata": {}, "source": [ "Cas non stationaire avec production de chaleur" ] }, { "cell_type": "code", "execution_count": 9, "id": "d0b81191-f14e-48f0-8327-ea55e602cb4e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Time= 500.0 s\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "#Paramètres à varier\n", "\n", "Lx = 1 \n", "Ly= 1\n", "Time = 500 #Temps \n", "k = 238 # Conductivité thermique\n", "rho= 2702 #Densité\n", "Cp= 929 #Chaleur massique\n", "P=0 # Puissance spécifique\n", "a=k/(rho*Cp) #diffusivité thermique\n", "T0=100 #Température T0\n", "\n", "# Paramètres de la grille\n", "NX = 100 #Nombres de divisions en x\n", "NY=100 #Nombres de divisions en y\n", "NT = 10000 #Nombre de pas\n", "\n", "dx = Lx/(NX-1) #Pas de la grille (en x)\n", "dy = Ly/(NY-1) #Pas de la grille (en y)\n", "dt = Time/NT #Pas de la grille (temps)\n", "\n", "grid = np.zeros((NX, NY))\n", "grid[:, 0] = T0\n", "\n", "\n", "plt.figure()\n", "\n", "\n", "for n in range(0,NT):\n", " grid[1:-1, 1:-1] = grid[1:-1, 1:-1] + (dt) /(rho * Cp) * (P + k * (\n", " (grid[2:, 1:-1] - 2 * grid[1:-1, 1:-1] + grid[:-2, 1:-1]) / dx**2 +\n", " (grid[1:-1, 2:] - 2 * grid[1:-1, 1:-1] + grid[1:-1, :-2]) / dy**2))\n", "tfin=NT*dt \n", "print('Time=', tfin, 's' ) \n", "\n", "plt.imshow(grid, cmap='turbo', interpolation='nearest')\n", "plt.xlabel(u'$x$')\n", "plt.ylabel(u'$y$', rotation=0)\n", "plt.title('2D cas instationaire avec production de chaleur')\n", "plt.colorbar()\n", "plt.show()\n", "\n" ] }, { "cell_type": "code", "execution_count": null, "id": "cff4dea5-5950-4ba2-ab58-9f7d7e660582", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python", "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": "3.8.10" } }, "nbformat": 4, "nbformat_minor": 5 }