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Q.

A metallic rod of radius R and thermal conductivity K is tightly filled into another hollow cylinder of inner radius R and outer radius 2R as shown in the figure. Material of the hollow cylinder has a thermal conductivity 2K. Then equivalent thermal conductivity of the composite rod is

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a

5K4

b

7K4

c

3K4

d

9K4

answer is B.

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Detailed Solution

R1 = Thermal resistance of solid rod = lK.πR2R2 = thermal resistance of hollow cylinder = =l2K.π2R2-R2=l6KπR2For the composite rod, Re=lKe.π2R2=l4KeπR2In the composite rod, the solid rod and the cylinder are joined in parallel combination.∴1Re=1R1+1R2⇒4KeπR2l=6K.πR2l+KπR2l⇒Ke=7K4

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