Question

2072 A hollow cylindrical conductor of length L (like the insulation around a pipe) has inside radius a and outside radius b. The inside surface temperature is T, and the outside surface temperature is T T, and T, remain fixed. Unlikely as it seems, the conductivity of the insulating material is not constant but increases as the square of the radius, according to K(r) K,r , where K, is a constant. Find the heat flow rate ( in cal/sec), in terms of L, K, , a, b, T, and Tb, from the inside to the outside surface of the cylinder. (T.> Tb) b* la
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