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FinalExam

# FinalExam - EGM 4313 Spring 2009 Final Exam NAME Open...

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EGM 4313 NAME:_____________________________ Spring 2009 Final Exam Open book/Closed notes/No calculators or computers 2 hour time limit (1) Solve the following heat equation problem: ( 29 ( 29 ( 29 ( 29 2 2 5 , 0, 10, , 20 , ,0 10 5cos 2 u u u x t u t u x x t x x π π π = = = = + + ÷ . First find the steady-state solution that meets the boundary conditions: ( 29 ( 29 ( 29 ( 29 ( 29 0 10 10 20 10 10 ss ss ss ss u x Ax B du A dx u B u x x π π π π = + = = = = = + ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 , , 5 , 0, 0, , 0, ,0 5cos 2 ss u x t u x x t x t t x t x x φ φ φ φ φ π φ = + = = = = ÷ The problem is greatly simplified if you notice that the initial condition on φ meets the boundary conditions and is in the form that one gets from separation of variables hence you should look for a solution of the form: ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 25 25 4 4 25 4 5 5 125 5 , 5cos 0 1, 5cos cos 2 2 4 2 25 5 , 5cos 4 2 5 , 10 5cos 2 t t t x x x x t T t T T t T t T t x T t e x t e T t x u x t x e φ φ π - - - = = = - ÷ ÷ ÷

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