a) Consider two identical cylindera overlapped at one third of their circumferences of Intemal radius r1 and externel radius r2 aa shown in Figure Q1 (a) below. Let the inslde and outside surfiace temgerature be t1 and t2 and hot the thermal conductivily of the material be . Derive an expression for the rate of heat transfer per unit length of the cylinders. \{8 marks b) A spherlcal pregsune vessel of 70cm inside diameter is made of 20mm steel plate. The vessel is lagged with a 25mm thickness of vermiculite held in position by 10mm thick gabestos. The heat transfer coelficient for the outside surface is 20Wfm2K, and the thermal confuctivities of sieel, vemicullte and asbestos are 48,0.047 and 0.21W/mK respectively. Neglecting radiation, calculate: i) total thermal resistance, and ii) rate of heat loss from the vessel. 12 marks)