Question

You have a rectangular baking tray (0 < x < .5meters and 0 < y < 1meters) that you place in an oven. The heated coils beneath the tray create a nonconstant heating affect. The tray heats up according to ut = c2∆u + h(x, y) where h(x, y) = 5(1 − sin(8πy)) and c2 = 10−4. Assume that u = 200 along each edge. Find the steady state temperature distribution of the tray.