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 $K_{1}$ and that of the outer cylinder is $K_{2}$ . Assuming no loss of heat, the effective thermal conductivity if the system for heat flowing along the length of the cylinder is:

K_{1} + K_{2}

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\frac{K_{1} + K_{2}}{2}

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\frac{2 K_{1} + 3 K_{2}}{5}

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\frac{K_{1} + 3 K_{2}}{4}

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Solution

The correct option is C $\frac{K_{1} + 3 K_{2}}{4}$
$K_{e q} = \frac{K_{1} A_{1} + K_{2} A_{2}}{A_{1} + A_{2}}$

$K_{e q} = \frac{K_{1} (π R^{2}) + K_{2} (3 π R^{2})}{4 π R^{2}}$

$K_{e q} = \frac{K_{1} + 3 K_{2}}{4}$

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The correct option is C K1+3K24Keq=K1A1+K2A2A1+A2Keq=K1(πR2)+K2(3πR2)4πR2Keq=K1+3K24

The correct option is C $\frac{K_{1} + 3 K_{2}}{4}$
$K_{e q} = \frac{K_{1} A_{1} + K_{2} A_{2}}{A_{1} + A_{2}}$

$K_{e q} = \frac{K_{1} (π R^{2}) + K_{2} (3 π R^{2})}{4 π R^{2}}$

$K_{e q} = \frac{K_{1} + 3 K_{2}}{4}$