A freshly cast metal object is placed in a shallow water bath to cool. The object...
A freshly cast metal object is placed in a shallow water bath to cool. The object is shaped like the intersection of two paraboloids, being the region above z = 1x2 + 1 y2 – 1, and below z=4 – x2 - y2. The water rises to the level z= 0. The object is still rather warm inside, with a temperature distribution T(x, y, z) = 200 – 1022 – 20x2 – 20y2 (a) If the heat flow within the object is given by q = -3VT, determine the outward flux of heat across the submerged portion of the surface. (b) Calculate the average surface temperature on the unsubmerged portion of the surface.