(a) The temperature in a semi-infinite solid is modeled by the boundary-value problem k

Chapter 15, Problem 29

(choose chapter or problem)

(a) The temperature in a semi-infinite solid is modeled by the boundary-value problem k a2u 2 = au ' x > 0, t > 0 ax at u(O, t) = u0, limu(x, t) = 0, t > 0 x-+oo u(x, 0) = 0, x > 0. Solve for u(x, t). Use the solution to determine analytically the value of lim1-+00 u(x, t), x > 0. (b) Use a CAS to graph u(x, t) over the rectangular region defined by 0 ::5 x ::5 10, 0 ::5 t ::5 15. Assume u0 = 100 and k = 1. Indicate the two boundary conditions and initial condition on your graph. Use 2D and 3D plots of u(x, t) to verify your answer to part (a).

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