The glass dome of a futuristic greenhouse is shaped like the surface z = 8 2x 2 2y2. The
Chapter 7, Problem 28(choose chapter or problem)
The glass dome of a futuristic greenhouse is shaped like the surface z = 8 2x 2 2y2. The greenhouse has a flat dirt floor at z = 0. Suppose that the temperature T , at points in and around the greenhouse, varies as T (x, y,z) = x 2 + y2 + 3(z 2)2 . Then the temperature gives rise to a heat flux density field H given by H = kT . (Here k is a positive constant that depends on the insulating properties of the particular medium.) Find the total heat flux outward across the dome and the surface of the ground if k = 1 on the glass and k = 3 on the ground.
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