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Unformatted text preview: HOMEWORK 7: THE FINITE ELEMENT METHOD IN 2D â€¢ Solve the following boundary value problem, on an archshaped domain, using COMSOL: âˆ‡ Â· ( k âˆ‡ T ) + f = 0 , T = T along Î¸ = Ï€ âˆ’ k âˆ‡ T Â· n = q ( r ) along Î¸ = 0 âˆ’ k âˆ‡ T Â· n = 0 along r = r i , r o k = k 1 for  x âˆ’ x c  â‰¤ r k = k 2 for  x âˆ’ x c  > r These equations describe a thermal physics problem in the twophase structure that is shown in Figure 1. Note that in COMSOL you will need to use the relationship between cartesian and polar coordinates in order to define the circular inclusion, as well as the flux, q o , and source term, f.k Î¤ . n = qk Î¤ . n = 0 Î¤=Î¤ c r r Î¸ r r i o x c Figure 1: â€¢ You are to generate a mesh of the domain for r i = 2 and r o = 3. Use N r Ã— N Î¸ bilinear elements. For example, in Figure 2, N r = 3 and N Î¸ = 12. You may need to increase the integration order of the elements to resolve the material discontinuity....
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This note was uploaded on 08/01/2008 for the course ME 180 taught by Professor Zohdi during the Spring '08 term at Berkeley.
 Spring '08
 ZOHDI

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