The outer surface of a hollow sphere of radius r2 is sub- jected to a uniform heat flux q2". The inner surface at r1 is held at a constant temperature Ts,1.

(a) Develop an expression for the temperature distribu- tion T(r) in the sphere wall in terms of q2", Ts,1, r1,r2, and the thermal conductivity of the wall material k.

(b) If the inner and outer tube radii are r1 = 50 mm and r2 = 100 mm, what heat flux q2" is required to main- tain the outer surface at Ts,2 = 50°C, while the inner surface is at Ts,1 = 20°C? The thermal conductivity of the wall material is k = 10 W/m · K.