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Unformatted text preview: 2 = ∇ V (a) Make a contour plot of your solution with the contours labeled (see the ContourPlot help file). Use the AspectRatio>1/2 option in the ContourPlot to scale the geometry properly. (b) Make a 3D plot of your solution. (2) Investigate the 2D transient heat equation on the unit square with homogeneous Dirichlet conditions on all sides and initial temperature distribution C y x T o 100 ) , , ( = . In other words, you’re solving: T t T 2 ∇ = ∂ ∂ α 1V 0V 0V 5V T(x,y) 2 1 T(x,y,t) 0°C 0°C 0°C 0°C 1 1 V(x,y) Let 1 = α . Use 10 Fourier terms for each axis and generate a table of coefficients using the nested “2dimensional” Table command as mentioned above. (a) Plot your solution in 3D for t=0.001. Does your solution match the initial condition? (b) Animate your solution for t=0.001 to 0.1, step 0.001. Pretty cool eh?...
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 Fall '08
 Gordon,M
 Chemistry, Chemical Engineering, The Contours, Johann Peter Gustav Lejeune Dirichlet, Analytical Methods of Chemical Engineering

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