Questions

# A cylinder of radius R made of material of conductivity ${\text{K}}_{\text{1}}$  is surrounded by a cylindrical shell of internal radius R and outer radius 2R made of material of conductivity  ${\text{K}}_{2}$, 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
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detailed solution

Correct option is C

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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Two rods of length ${\mathrm{d}}_{1}$ and ${\mathrm{d}}_{2}$ and coefficients of thermal conductivities ${\mathrm{K}}_{1}$ and ${\mathrm{K}}_{2}$ are kept touching each other. Both have the same area of cross-section. The equivalent of thermal conductivity is

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