Suppose that current flowing through a laterally insulated

Chapter , Problem 20

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Suppose that current flowing through a laterally insulated rod generates heat at a constant rate; then yields the equation @u @t D k @2u @x2 C C: Assume the boundary conditions u.0; t / D u.L; t / D 0 and u.x; 0/ D f .x/. (a) Find the steady-state temperature uss.x/ determined by 0 D k d 2uss dx2 C C; uss.0/ D uss.L/ D 0: (b) Show that the transient temperature utr.x; t / D u.x; t / uss.x/

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