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Final - EGM 4313 NAME Spring 2010 Final Exam Open...

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Unformatted text preview: EGM 4313 NAME:_____________________________ Spring 2010 Final Exam Open book/Closed notes/No calculators or computers 2 hour time limit (1) Solve the following unsteady 1-dimensional heat equation problem: ( 29 ( 29 ( 29 ( 29 2 2 3 , 0, 10, , 20 , ,0 10 3cos 2 u u u x t u t u x x t x x π π π ∂ ∂ ∂ = = = = + + ∂ ∂ ∂ . First find the steady-state solution: ( 29 ( 29 ( 29 ( 29 ( 29 , 10 10, 20 10 10 ss ss ss ss u x Ax B u A u B u x x π π π π ′ = + = ⇒ = = ⇒ = = + Now let ( 29 ( 29 ( 29 ( 29 ( 29 , , 10 , ss u x t u x x t x x t φ π φ = + = + + The problem for ( 29 , x t φ is now: ( 29 ( 29 ( 29 2 2 3 , 0, 0, , 0, ,0 3cos 2 x t t x t x x φ φ φ φ π φ ∂ ∂ ∂ = = = = ∂ ∂ ∂ Separating variables gives ( 29 ( 29 ( 29 ( 29 ( 29 2 1 2 , cos sin X T x t X x T t X C x C x X T φ λ λ λ ′′ ′ = ⇒ = = - ⇒ = + Applying the boundary condition at x=0 gives C 2 =0. The other boundary condition gives ( 29 1 1 3 5 cos , , 2 2 2...
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Final - EGM 4313 NAME Spring 2010 Final Exam Open...

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