Question

18. A cylinder of radius r and made of a material of thermal conductivity kiis surrounded by a cylindrical shell of inner radius r and outer radius 2r. This outer shell is made of a material of thermal conductivity k2. The two ends of the combined system are maintained at two different temperatures. Under steady state conditions and no loss of heat across the cylindrical surface, the effective thermal conductivity of the arrangement would be: (a) k,+k2 (6) kk kitk, (d) 3k, tk, 19. The heat flow equation through a sphere of inner radius and outer radius ra is to be written in the same form as that for heat flow through a plane wall. For wall thickness (r2-ra), the equivalent mean radius for the spherical shell is: (b) C (d) It, 20. log.(2/9) A thin cylinder of radius ris lagged to an outer radius r, with an insulating layer of thermal conductivity k. If he is the film coefficient at the outer surface of lagging, then minimum resistance and consequently the maximum heat flow rate occurs when ra equals: 21. (6) k/h. (c) 2k/h (d) h / Critical thickness of insulation for spheres is given by: (a) k/h (b) k/476h (c) h/2k (d) 2k/h Fins are provided on heat transferring surfaces in order to increase (a) Heat transfer area (b) Heat transfer coefficient (c) Temperature gradient 22. Page 6 of 16

Answer 1

Since, the heat transfer is along the length of the Cylinder from higher Temperature (Tu) to the lower Temperature (TL), thermal resistances will be parallel. Consider L as the length of the composite cylinder, Constider Ri as the thermal resistance of the inner cylinder and R2 as the thermal resistance of the ater cylinder. Since the thermal resistances are in parallel, there fare the equivalent resistance will be given as :- I. I+1 - 0 Rey R. R2 Heat transfer is across length, there fare thermal resistance is given as: - R = L K, A ki Trz R2 = L R₂ A2 K₂ TT [(22) ²-a K₂ 3 Tr Substitute in eg.

Tr24 кер чты", К, ТА“ Е ЗА kea = k +3ka There fare, option (o is carrect.