{ "cells": [ { "cell_type": "raw", "id": "16e3c3ab-870d-4f06-9535-9942ccb07452", "metadata": {}, "source": [ "Cylindres\n" ] }, { "cell_type": "code", "execution_count": 5, "id": "0b595cac-9254-4ad2-aad5-b37fe261cf94", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0 1\n", "10 2\n", "50 3\n", "100 4\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", "# plate size, mm\n", "w = h = 10.\n", "# intervals in x-, y- directions, mm\n", "dx = dy = 0.1\n", "# Thermal diffusivity of steel, mm2.s-1\n", "D = 8.\n", "\n", "Tcool, Thot = 25, 100\n", "\n", "nx, ny = int(w/dx), int(h/dy)\n", "\n", "dx2, dy2 = dx*dx, dy*dy\n", "dt = dx2 * dy2 / (2 * D * (dx2 + dy2))\n", "\n", "u0 = Tcool * np.ones((nx, ny))\n", "u = np.empty((nx, ny))\n", "\n", "# Initial conditions - ring of inner radius r, width dr centred at (cx,cy) (mm)\n", "r, cx, cy = 2, 5, 5\n", "r2 = r**2\n", "for i in range(nx):\n", " for j in range(ny):\n", " p2 = (i*dx-cx)**2 + (j*dy-cy)**2\n", " if p2 < r2:\n", " u0[i,j] = Thot\n", "\n", "def do_timestep(u0, u):\n", " # Propagate with forward-difference in time, central-difference in space\n", " u[1:-1, 1:-1] = u0[1:-1, 1:-1] + D * dt * (\n", " (u0[2:, 1:-1] - 2*u0[1:-1, 1:-1] + u0[:-2, 1:-1])/dx2\n", " + (u0[1:-1, 2:] - 2*u0[1:-1, 1:-1] + u0[1:-1, :-2])/dy2 )\n", "\n", " u0 = u.copy()\n", " return u0, u\n", "\n", "# Number of timesteps\n", "nsteps = 101000\n", "# Output 4 figures at these timesteps\n", "mfig = [0, 10, 50, 100]\n", "fignum = 0\n", "fig = plt.figure()\n", "for m in range(nsteps):\n", " u0, u = do_timestep(u0, u)\n", " if m in mfig:\n", " fignum += 1\n", " print(m, fignum)\n", " ax = fig.add_subplot(220 + fignum)\n", " im = ax.imshow(u.copy(), cmap=plt.get_cmap('hot'), vmin=Tcool,vmax=Thot)\n", " ax.set_axis_off()\n", " ax.set_title('{:.1f} ms'.format(m*dt*1000))\n", "fig.subplots_adjust(right=0.85)\n", "cbar_ax = fig.add_axes([0.9, 0.15, 0.03, 0.7])\n", "cbar_ax.set_xlabel('$T$ / K', labelpad=20)\n", "fig.colorbar(im, cax=cbar_ax)\n", "plt.show()" ] }, { "cell_type": "raw", "id": "f37c5e1c-189a-4ee3-8397-12fbae485947", "metadata": {}, "source": [ "Fourier square sans prod" ] }, { "cell_type": "code", "execution_count": 2, "id": "dfe6a61e-b016-404d-8407-ddcd135df9e5", "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", "# Initialize the grid with a 100 degree wall on the left side\n", "nx = 100 # Number of grid points in x direction\n", "ny = 1000 # Number of grid points in y direction\n", "dx = 1.0 # Spacing between grid points in x direction\n", "dy = 1 # Spacing between grid points in y direction\n", "dt = 0.1 # Time step\n", "k = 238 # Thermal conductivity\n", "rho= 2.700 #Density\n", "Cp= 929 #Cp\n", "\n", "\n", "grid = np.zeros((nx, ny))+25\n", "grid[:, 0] = 100.0\n", "\n", "# Time-stepping loop\n", "for t in range(10000):\n", " grid[1:-1, 1:-1] = grid[1:-1, 1:-1] + (dt) * k /(rho * Cp) * (\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", "\n", "# Plot the final temperature distribution\n", "plt.imshow(grid, cmap='turbo', interpolation='nearest')\n", "plt.colorbar()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 18, "id": "90ef1d54-4939-43d8-9235-fff2ae835236", "metadata": {}, "outputs": [ { "ename": "SyntaxError", "evalue": "invalid syntax (1590047439.py, line 20)", "output_type": "error", "traceback": [ "\u001b[0;36m Input \u001b[0;32mIn [18]\u001b[0;36m\u001b[0m\n\u001b[0;31m plt.title('1D Diffusion Convecction')\u001b[0m\n\u001b[0m ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n" ] } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "nx = 100 # length\n", "dx=1 #grid space\n", "dt = 100 # Time step\n", "k = 1 # Thermal conductivity\n", "rho=1\n", "Cp=1\n", "\n", "T = np.ones(nx) +25\n", "\n", "for n in range(dt+1): #time marching\n", " un = u.copy() \n", " for i in range(1, nx-1): #Space marching\n", " T[i] = T[i] + dt * k * ((T(i+1) - 2 * T(i) + T(i-1))/dx**2,\n", "\n", " \n", "plt.plot(np.linspace(0,2,nx), T, label='Numerical Solution')\n", "plt.title('1D Diffusion Convecction')\n", "plt.xlabel('Grid Space')\n", "plt.ylabel('Velocity')\n", "plt.legend()\n", "plt.show() " ] }, { "cell_type": "code", "execution_count": 6, "id": "9013bf9e-0998-4d66-baca-1ca300644670", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Solving 1D Diffusion Equation using Finite Difference Method\n", "\n", "------------------------------------------------\n", "Computing Innitial Solution...\n", "Printing Innitial Solution...\n", "------------------------------------------------\n", "[1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 1. 1. 1.\n", " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]\n", "------------------------------------------------\n", "Calculating Numerical Solution......\n", "------------------------------------------------\n", "------------------------------------------------\n", "Printing Numerical Solution......\n", "------------------------------------------------\n", "[1. 1.01 1.03 1.06 1.09 1.14 1.2 1.27 1.36 1.45 1.54 1.63 1.71 1.77\n", " 1.81 1.82 1.81 1.77 1.71 1.63 1.54 1.45 1.36 1.27 1.2 1.14 1.09 1.06\n", " 1.03 1.02 1.01 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. ]\n", "------------------------------------------------\n", "Plotting Innitial & Numerical Solution\n", "------------------------------------------------\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy #here we load numpy library that provides a bunch of useful matrix operations akin to MATLAB\n", "from matplotlib import pyplot #2D plotting library that we will use to plot our results\n", "\n", "lineSingle = '------------------------------------------------'\n", "\n", "print(\"Solving 1D Diffusion Equation using Finite Difference Method\\n\")\n", "\n", "#setting the grid\n", "\n", "nx = 41 #grid points\n", "dx = 2 / (nx - 1) #grid spacing \n", "nt = 20 #number of timesteps\n", "nu = 0.3 #viscosity\n", "cfl = 0.4 \n", "dt = cfl*dx**2/nu #based on von neumaan stability analysis\n", "\n", "#innitial condition\n", "\n", "print(lineSingle)\n", "print(\"Computing Innitial Solution...\")\n", "\n", "\n", "u = numpy.ones(nx) \n", "u[int(0.5/dx):int(1/dx+1)] = 2 #Square Wave Profile\n", "\n", "print(\"Printing Innitial Solution...\")\n", "print(lineSingle)\n", "\n", "print(u)\n", "\n", "pyplot.plot(numpy.linspace(0,2,nx), u, label='Initial Solution')\n", "\n", "#discritization\n", "\n", "print(lineSingle)\n", "print(\"Calculating Numerical Solution......\")\n", "print(lineSingle)\n", "\n", "un = numpy.ones(nx) \n", "\n", "for n in range(nt+1): #time marching\n", " un = u.copy() \n", " for i in range(1, nx-1): #Space marching\n", " \n", " u[i] = un[i] + nu * dt/dx**2 *(un[i+1] - 2*un[i] + un[i-1]) #Central Differnece Scheme\n", "\n", "print(lineSingle)\n", "print(\"Printing Numerical Solution......\")\n", "print(lineSingle)\n", " \n", "print(u)\n", "\n", "print(lineSingle)\n", "print(\"Plotting Innitial & Numerical Solution\")\n", "print(lineSingle)\n", "\n", "pyplot.plot(numpy.linspace(0,2,nx), u, label='Numerical Solution')\n", "pyplot.title('1D Diffusion Convecction')\n", "pyplot.xlabel('Grid Space')\n", "pyplot.ylabel('Velocity')\n", "\n", "pyplot.legend()\n", "pyplot.show()" ] }, { "cell_type": "raw", "id": "86e71482-ed47-46a2-9fe9-f74ca32ec678", "metadata": {}, "source": [ "Fourier 2D avec prod " ] }, { "cell_type": "code", "execution_count": 42, "id": "3ab6b45f-32ab-482d-9a46-b9bba47b684c", "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", "nx = 40 # Number of grid points in x direction = height of the bar \n", "ny = 100 # Number of grid points in y direction = length of the bar \n", "dt = 0.1 # Time step\n", "dx = 1 # Spacing between grid points in x direction \n", "dy = 1 # Spacing between grid points in y direction\n", "k = 238 # Thermal conductivity\n", "rho= 2.700 #Density\n", "Cp= 929 #Cp\n", "P=50 # Puissance spécifique\n", "\n", "\n", "grid = np.zeros((nx, ny))+ 100\n", "grid[:, 0] = 300.0\n", "\n", "# Time-stepping loop\n", "for t in range(100000):\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", "\n", "# Plot the final temperature distribution\n", "plt.imshow(grid, cmap='turbo', interpolation='nearest')\n", "plt.colorbar()\n", "plt.show()" ] }, { "cell_type": "raw", "id": "e544a378-be41-47bf-879e-68c489398f7c", "metadata": {}, "source": [ "Fourier 1D" ] }, { "cell_type": "code", "execution_count": 54, "id": "330851c3-14b2-4648-9f50-ca47be578866", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "time=\n", "10000.0\n", "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", "dt = 0.1 \n", "dx = 1 \n", "dy = 1 \n", "\n", "#Parametrès à varier\n", "nx = 40 #Hauteur de la barre \n", "ny = 100 #Largeur de la barre\n", "k = 238 #Coefficient de conduction \n", "rho= 27 #Densité\n", "Cp= 929 #chaleur massique\n", "P=0 # Puissance spécifique\n", "a=98.8*10**(-6)\n", "tmax=100000 #nombre d'itérations (=1/10 du temps final)\n", "\n", "grid = np.zeros((nx, ny))+ 25\n", "grid[:, 0] = 1000.0\n", "\n", "# Time-stepping loop\n", "for t in range(tmax):\n", " grid[1:-1, 1:-1] = grid[1:-1, 1:-1] + (dt) /(rho * Cp) * (P + k * (\n", " (grid[1:-1, 2:] - 2 * grid[1:-1, 1:-1] + grid[1:-1, :-2]) / dy**2))\n", "\n", "u=tmax*dt\n", "# Plot the final temperature distribution\n", "print('time=') \n", "print(u) \n", "print('s')\n", "plt.imshow(grid, cmap='turbo', interpolation='nearest')\n", "plt.colorbar()\n", "plt.show()" ] }, { "cell_type": "raw", "id": "2904809c-b8ab-49fc-a8cb-42863aa169b2", "metadata": {}, "source": [ "Stationary 2D sans prod" ] }, { "cell_type": "code", "execution_count": 2, "id": "33563bfc-b1a8-4d18-af32-865a8707b045", "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", "nx = 10 # Number of grid points in x direction = height of the bar \n", "ny = 100 # Number of grid points in y direction = length of the bar \n", "dx = 1 # Spacing between grid points in x direction \n", "dy = 1 # Spacing between grid points in y direction\n", "k = 238 # Thermal conductivity\n", "rho= 2.700 #Density\n", "Cp= 929 #Cp\n", "P=5 # Puissance spécifique\n", "\n", "\n", "grid = np.zeros((nx, ny))\n", "grid[:, 0] = 100.0\n", "grid[1:-1, 1:-1] = grid[1:-1, 1:-1] - P / k * (dx**2 + dy**2)\n", "\n", "\n", "# Plot the final temperature distribution\n", "plt.imshow(grid, cmap='turbo', interpolation='nearest')\n", "plt.colorbar()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 51, "id": "ae1f7ecb-3cfa-4e31-891b-9b88a73e6fac", "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", "# PHYSICAL PARAMETERS\n", "\n", "L = 1.0 #Domain size\n", "Time = 10 #Integration time\n", "k = 238 # Thermal conductivity\n", "rho= 2702 #Density\n", "Cp= 929 #Cp\n", "P=50 # Puissance spécifique\n", "a=k/(rho*Cp)\n", "# NUMERICAL PARAMETERS\n", "NX = 100 #Number of grid points\n", "NT = 100000 #Number of time steps\n", "\n", "dx = L/(NX-1) #Grid step (space)\n", "dt = Time/NT #Grid step (time)\n", "\n", "\n", "### MAIN PROGRAM ###\n", "\n", "# Initialisation\n", "x = np.linspace(0,1,NX)\n", "T = np.zeros((NX))\n", "T[0]=100\n", "RHS = np.zeros((NX))\n", "\n", "plt.figure()\n", "\n", "# Main loop\n", "for n in range(0,NT):\n", "\n", " for j in range (1, NX-1):\n", " RHS[j] = dt*(P/(rho*Cp)+a*(T[j-1]-2*T[j]+T[j+1])/(dx**2))\n", "\n", " for j in range (1, NX-1):\n", " T[j] += RHS[j]\n", "\n", "#Plot every 100 time steps\n", " if (n%10000 == 0):\n", " plotlabel = \"t = %1.2f\" %(n * dt)\n", " plt.plot(x,T, label=plotlabel,color = plt.get_cmap('copper')(float(n)/NT))\n", " \n", "\n", "plt.xlabel(u'$x$', fontsize=26)\n", "plt.ylabel(u'$T$', fontsize=26, rotation=0)\n", "plt.title(u'Equation de la chaleur 1D')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "raw", "id": "f8ccd957-804a-4e48-8585-c12d560f52f3", "metadata": {}, "source": [ "2D fourier " ] }, { "cell_type": "code", "execution_count": null, "id": "3ecbf9ab-fe65-47fb-b18b-59f6667ea2ad", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "# PHYSICAL PARAMETERS\n", "Lx = 1.0 #Domain size\n", "Ly= 1\n", "Time = 0.1 #Integration time\n", "k = 238 # Thermal conductivity\n", "rho= 2.700 #Density\n", "Cp= 929 #Cp\n", "P=50 # Puissance spécifique\n", "a=k/(rho*Cp)\n", "\n", "# NUMERICAL PARAMETERS\n", "NX = 100 #Number of grid points\n", "NY=100\n", "NT = 1000 #Number of time steps\n", "\n", "dx = Lx/(NX-1)\n", "dy = Ly/(NY-1)#Grid step (space)\n", "dt = Time/NT #Grid step (time)\n", "\n", "grid = np.zeros((NX, NY))\n", "grid[:, 0] = 100.0\n", "\n", "### MAIN PROGRAM ###\n", "\n", "# Initialisation\n", "x = np.linspace(0.0,1.0,NX)\n", "T = np.sin(2*np.pi*x)\n", "RHS = np.zeros((NX))\n", "\n", "plt.figure()\n", "\n", "# Main loop\n", "for n in range(0,NT):\n", " \n", " for j in range(1,NX-1):\n", " grid[1:-1, 1:-1] = grid[1:-1, 1:-1] + (dt) * (P/(rho * Cp) + k * a * (\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", "\n", " \n", "# Plot the final temperature distribution\n", "plt.imshow(grid, cmap='turbo', interpolation='nearest')\n", "plt.colorbar()\n", "plt.show()" ] }, { "cell_type": "raw", "id": "db1c7eed-c32a-4dd1-adf0-7cac9f6c9ea1", "metadata": {}, "source": [ "1D fourier complete " ] }, { "cell_type": "code", "execution_count": 1, "id": "c4151747-bd55-4ac6-ac90-813945372663", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Time= 10.0 s\n" ] }, { "data": { "image/png": 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\n", 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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", "# PHYSICAL PARAMETERS\n", "\n", "Lx = 0.1 #Domain size\n", "Ly= 1\n", "Time = 10 #Integration time\n", "k = 238 # Thermal conductivity\n", "rho= 2702 #Density\n", "Cp= 929 #Cp\n", "P=0 # Puissance spécifique\n", "a=k/(rho*Cp)\n", "\n", "# NUMERICAL PARAMETERS\n", "NX = 10 #Number of grid points\n", "NY=100\n", "NT = 10000 #Number of time steps\n", "\n", "dx = Lx/(NX-1)\n", "dy = Ly/(NY-1)#Grid step (space)\n", "dt = Time/NT #Grid step (time)\n", "\n", "grid = np.zeros((NX, NY))\n", "grid[:, 0] = 100.0\n", "\n", "\n", "plt.figure()\n", "\n", "\n", "for n in range(0,NT):\n", " \n", " for j in range(1,NX-1):\n", " grid[1:-1, 1:-1] = grid[1:-1, 1:-1] + (dt) * (P/(rho * Cp) + a * (\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'$x$', fontsize=26)\n", "plt.ylabel(u'$T$', fontsize=26, rotation=0)\n", "plt.colorbar()\n", "plt.show()\n", "\n", "x = np.linspace(0,Ly,NX)\n", "T = np.zeros((NX))\n", "T[0]=100\n", "RHS = np.zeros((NX))\n", "\n", "plt.figure()\n", "\n", "\n", "for n in range(0,NT):\n", "\n", " for j in range (1, NX-1):\n", " RHS[j] = dt*(P/(rho*Cp)+a*(T[j-1]-2*T[j]+T[j+1])/(dx**2))\n", "\n", " for j in range (1, NX-1):\n", " T[j] += RHS[j]\n", "\n", "\n", " if (n%(NT/10) == 0):\n", " plotlabel = \"t = %1.2f\" %(n * dt)\n", " plt.plot(x,T, label=plotlabel,color = plt.get_cmap('copper')(float(n)/NT))\n", " \n", "\n", "plt.xlabel(u'$x$', fontsize=26)\n", "plt.ylabel(u'$T$', fontsize=26, rotation=0)\n", "plt.title(u'Equation de la chaleur 1D')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "raw", "id": "9cb83e50-7d65-456f-be36-03e1ee719679", "metadata": {}, "source": [ "Simulation profil mur " ] }, { "cell_type": "code", "execution_count": 1, "id": "968d685d-881b-484f-b4fd-c01e8872f243", "metadata": {}, "outputs": [ { "ename": "NameError", "evalue": "name 'T1' is not defined", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mNameError\u001b[0m Traceback (most recent call last)", "Input \u001b[0;32mIn [1]\u001b[0m, in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 31\u001b[0m fig \u001b[38;5;241m=\u001b[39m plt\u001b[38;5;241m.\u001b[39mfigure()\n\u001b[1;32m 32\u001b[0m ax \u001b[38;5;241m=\u001b[39m plt\u001b[38;5;241m.\u001b[39maxes()\n\u001b[0;32m---> 33\u001b[0m plt\u001b[38;5;241m.\u001b[39mplot([\u001b[38;5;241m0\u001b[39m, \u001b[38;5;241m0\u001b[39m, e1,e1, e1\u001b[38;5;241m+\u001b[39me2, e1\u001b[38;5;241m+\u001b[39me2, e1\u001b[38;5;241m+\u001b[39me2], [Tint, Tmuri, \u001b[43mT1\u001b[49m, Tinside, T2, Tmure, Text])\n\u001b[1;32m 34\u001b[0m plt\u001b[38;5;241m.\u001b[39mxlabel(\u001b[38;5;124mu\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124m$EPAISSEUR [m]$\u001b[39m\u001b[38;5;124m'\u001b[39m)\n\u001b[1;32m 35\u001b[0m plt\u001b[38;5;241m.\u001b[39mylabel(\u001b[38;5;124mu\u001b[39m\u001b[38;5;124m'\u001b[39m\u001b[38;5;124m$T[°C]$\u001b[39m\u001b[38;5;124m'\u001b[39m, rotation\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m0\u001b[39m)\n", "\u001b[0;31mNameError\u001b[0m: name 'T1' is not defined" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "#Paramètres\n", "Tint=25\n", "Text=5\n", "hint=7\n", "hext=2\n", "h12=1\n", "e1=0.1\n", "k1=1\n", "e2=0.02\n", "k2=.1\n", "\n", "#Calcul du flux\n", "q=(Tint-Text)/(1/hint+e1/k1+1/h12+e2/k2+1/hext)\n", "\n", "#Différentes températures avec un flux constant\n", "for d in range(0,int(e1+e2+1)):\n", " if (d==0):\n", " Tmuri=-q/hint+Tint\n", " if (0