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Unformatted text preview: C(x) = x . 2] Consider steady 2-dimensional heat conduction in the half-plane 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)  Using separation of variables, decompose the PDE into ODEs in each of the two coordinates. (b)  Solve the ODEs. (c)  Find product solutions that satisfy the homogenous boundary conditions. (d)  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