Q.
A cylinder of radius r and thermal conductivity K1 is surrounded by a cylinder shell of internal radius r and outer radius 3r whose thermal conductivity is K2. There is no loss of heat from the surface of the cylinder when the ends of the combined system are maintained at temperatures T1 and T2. 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
answer is C.
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Detailed Solution
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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