Q.

A cylinder of radius R made of material of conductivity K1  is surrounded by a cylindrical shell of internal radius R and outer radius 2R made of material of conductivity  K2, the two ends of the system are kept at two different temperatures. If there is no loss of heat from the surface, the effective 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

Both are parallelthe effective coefficient of thermal conductivity for a parallel combination of conductors is KParallel=K1A1+K2A2A1+A2 base area of inner cylinder isA1=πR2area of outer cylinder is A2=π(2R)2-πR2A2=3πR2 KP=K1.πR2+K2.3πR2πR2+3πR2 Keffective=KParallel=K1+3K24
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A cylinder of radius R made of material of conductivity K1  is surrounded by a cylindrical shell of internal radius R and outer radius 2R made of material of conductivity  K2, the two ends of the system are kept at two different temperatures. If there is no loss of heat from the surface, the effective conductivity of the system is