A1 m radioactive rod (k= 0.45 W/m.K) whose diameter is 3 cm is to be covered with material X (k = 1.5 W/m.K). The rod generates heat g with wall temperature of 60C and is placed at a surrounding T = 28.5C with convective coefficient of h = 88 W/m.K. Assume the heat flows only in radial direction at steady state. a. From the energy balance for cylindrical geometry, show the derivation (integration) for temperature distribution with heat generation. State all the boundary conditions. Calculate the temperature at r=0 and r=0.8 cm in the radioactive rod. 1 a(,0 1 a 7 a T 20+ g 1 K a a rar or b. Determine the thickness of material X, if the heat loss to the surrounding is to be maximized. Calculate the heat loss and outer surface temperature. C. The rod is now encapsulated with material x with thickness from (b). 200 circular aluminum fins (k = 160 W/m.C) of 1.5 cm length and thickness t = 2 mm are attached to material X. Determine the increase of heat loss as a result of adding the fins, and the outer surface temperature