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Unformatted text preview: C(x) = x . 2] Consider steady 2dimensional heat conduction in the halfplane defined, in polar coordinates, by ,r 1. Laplace's equation in polar coordinates is 2 T r 2 1 r T r 1 r 2 2 T 2 = 0. The boundary conditions are T = 0, r = 0, T = ,r = 0, T , r = 1 = g (arbitrary differentiable function). Also, the temperature is bounded as r . (a) [10] Using separation of variables, decompose the PDE into ODEs in each of the two coordinates. (b) [10] Solve the ODEs. (c) [15] Find product solutions that satisfy the homogenous boundary conditions. (d) [15] Find a superposition of these solutions that also satisfies the remaining boundary condition....
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This note was uploaded on 08/30/2011 for the course CGN 2200 taught by Professor Glagola during the Spring '11 term at University of Florida.
 Spring '11
 GLAGOLA

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