Answer: A silver plate in the shape of a trapezoid (see the accompanying figure) has

Chapter 12, Problem 5

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A silver plate in the shape of a trapezoid (see the accompanying figure) has heat being uniformly generated at each point at the rate q = 1.5 cal/cm3 s. The steady-state temperature u(x, y) of the plate satisfies the Poisson equation 2u x2 (x, y) + 2u y2 (x, y) = q k , where k, the thermal conductivity, is 1.04 cal/cmdegs. Assume that the temperature is held at 15C on L2, that heat is lost on the slanted edges L1 and L3 according to the boundary condition u/n = 4, and that no heat is lost on L4; that is, u/n = 0. Approximate the temperature of the plate at (1, 0),(4, 0), and 5 2 , 3/2 by using Algorithm 12.5.