A problem concerning the diffusion of gas through a
Chapter , Problem 17(choose chapter or problem)
A problem concerning the diffusion of gas through a membrane leads to the boundary value problem ut D kuxx (00); u.0; t / D ut.L; t / C hkux.L; t / D 0; u.x; 0/ D 1: Derive the solution u.x; t / D 4 X1 nD1 1 cos n 2n sin 2n exp 2 nkt L2 ! sin nx L ; where fng 1 1 are the positive roots of the equation x tan x D hL. 1
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