A cylinder of radius R made of a material of thermal conductivity $K_{1}$ is surrounded by a cylindrical shell of inner radius R and outer radius 2R made of material of thermal conductivity $K_{2}$ . The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is

K_{1} + K_{2}

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

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

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

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Solution

The correct option is C $\frac{K_{1} + 3 K_{2}}{4}$
We can consider this arrangement as a parallel combination of two materials having different thermal conductivities $K_{1} a n d K_{2}$
For parallel combination $K = \frac{K_{1} A_{1} + K_{2} A_{2}}{A_{1} + A_{2}}$

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Similar questions

Q. A cylinder of radius

R

made of a material of thermal conductivity

K_{1}

is surrounded by a cylindrical shell of inner radius

R

and outer radius

2 R

made of a material of thermal conductivity

K_{2}

. The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in the steady state. The effective thermal conductivity of the system is

A cylinder of radius R made of a material of thermal conductivity $K_{1}$ is surrounded by a cylindrical shell of inner radiusRand outer radius 2Rmade of material of thermal conductivity $K_{2}$ . The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is