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Q.

A cylinder of radius R made of a material of thermal conductivity & is surrounded by a cylindrical shell of inner radius .E and outer radius 2 .R made of a material  of thermal conductivity K2. The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the systems in steady state. The effective thermal conductivity of the system is

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a

K1+K2

b

K1K2K1+K2

c

K1+3K24

d

3K1+K24

answer is C.

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Detailed Solution

Heat flowing per second through cylinder of radius R Q1=K1πR2T1−T2lHeat flowing per second through outer shell of radius 2 RQ2=K2π(2R)2−π(R)2T1−T2lTotal Q=Q1+Q2          =K1+3K2πR2T1−T2l              ....(1)Let K be the equivalent thermal conductivity of the system. Then           Q=Kπ(2R)2T1−T2l                  ....(2)From eqs. (1) and (2), we have     K1+3K2=4K     K=K1+3K24
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A cylinder of radius R made of a material of thermal conductivity & is surrounded by a cylindrical shell of inner radius .E and outer radius 2 .R made of a material  of thermal conductivity K2. The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the systems in steady state. The effective thermal conductivity of the system is