A special coating, which is applied to the inner surface of a plastic tube, is cured by placing a cylindrical radiation heat source within the tube. The space between the tube and the source is evacuated, and the source delivers a uniform flux, q, which is absorbed at the inner surface of the tube. The outer surface of the tube is maintained at a uniform temperature, T2. Develop an expression for the temperature distribution T(r) in the wall in terms of q1, T2, r1, r2, and k. If the inner and outer tube radii are r1 = 25 mm and r2 = 38 mm, what is the power required per unit length of the radiation source to maintain the inner surface at T1 = 150°C, while the outer surface is fixed at T2 = 25°C? The tube wall thermal conductivity is k = 10 W/m-K.