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# A cylinder of radius r and thermal conductivity ${\text{K}}_{1}$  is surrounded by a cylinder shell of internal radius r and outer radius 3r whose thermal conductivity is  ${\text{K}}_{2}$. There is no loss of heat from the surface of the cylinder when the ends of the combined system are maintained at temperatures  ${\text{T}}_{1}$ and  ${\text{T}}_{2}$. The effective thermal conductivity of the system under steady state is

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a
K1K2K1+K2
b
K1+K2
c
K1+8K29
d
8K1+K29
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detailed solution

Correct option is C

the cylinders are In parallel KParallel=K1A1+K2A2A1+A2---(1), here K is coefficient of thermal conductivity,                                                                A is area of cross section area of cross section inner cylinder is A1=πr2, here r = radius  area of cross section outer cylinder is A2=9πr2-πr2  A2=8πr2 substitute given values in eqn(1) KP=K1πr2+K2.8πr2πr2+8πr2 KParallel=K1+8K29

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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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