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

Moderate

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a

K1K2K1+K2

b

K1+K2

c

K1+8K29

d

8K1+K29

answer is 3.

(Detailed Solution Below)

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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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