assignment7 - k i , j 1 u k i , j − 1 (3) Before the...

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ME 372 Computer-Aided Mechanical Engineering Instructor: Dr. Emre Alpman Assignment #7 Due Date: Final Exam 1 Problem Statement Steady state temperature distribution on a plate can be obtained by solving the Laplace equation for  temperature. 2 u x 2 2 u y 2 = 0 (1) where u is temperature. Suppose that plate has a shape of a square and each side is 1m  long. The  boundary conditions of the plate are given as: u 0, y = 20, u 1, y = 50 u x , 0 = 20, u x , 1 = 100 (2) Dividing the plate in both   x   and   y   directions in to 40 equal segments   find the steady state  temperature distribution on the plate by solving equation (1) using Jacobi method.  u k 1 i , j = 0.25 u k i 1, j u k i 1, j u
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Unformatted text preview: k i , j 1 u k i , j − 1 (3) Before the iterations start initialize the temperature of internal points to 20. Stop iterations when ∑ j = 2 N y ∑ i = 2 Nx ∣ u k 1 i , j − u k i , j ∣ tol (4) where k is the iteration level and tol is 1 . Plot temperature contours on the plate. Hints: The boundary conditions may be applied as follows: u :, 1 = 20, u :, N y 1 = 50 u 1, : = 20, u N x 1, : = 100 (5) For contour plot [x, y] = meshgrid([0:dx:1],[0:dy:1]); contour(x,y,u); where dx and dy are mesh spacing in x and y directions respectively....
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