Solved: 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 ^ = 1.5 cal/cm3 s. The steady-state temperature u(x, y) of the plate satisfies the Poisson equation 9 m 9 m q where A:, the thermal conductivity, is 1.04 cal/cm deg-s. Assume that the temperature is held at 150 C on L2, that heat is lost on the slanted edges L| and L3 according to the boundary condition du/dn 4, and that no heat is lost on L4; that is, 3u/dn 0. Approximate the temperature of the plate at (1,0), (4, 0), and (|, -