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JEE Main 2019 (12 Jan, Shift 1) · Heat Conduction

Heat Conduction question from JEE Main 2019 (12 Jan, Shift 1)

Q48JEE Main 2019 · 12 JAN · SHIFT 1Difficult

Heat Conduction

A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The thermal conductivity of the material of the inner cylinder is K1 and the of the outer cylinder is K2. Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is:

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Answer: (b)

Heat flows along the length: the two parts are in parallel, $K_{eq}A_{total} = K_1A_1 + K_2A_2$
$A_1 = \pi R^2$ , $A_2 = \pi(4R^2 - R^2) = 3\pi R^2$ , $A_{total} = 4\pi R^2$
$K_{eq}(4\pi R^2) = K_1\pi R^2 + 3K_2\pi R^2$
So the answer is (b) $\dfrac{K_1+3K_2}{4}$ .

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