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  • Stuck here, help me understand: 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 that of the outer cylinder is K2. Assuming no loss

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 that 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 :

  • Option 1) (K1+3K2)/4

     

  • Option 2)  (K1+K2)/2

     

  • Option 3)  K1+K2

     

  • Option 4)  (2K1+3K2)/5

     

Answers (1)

best_answer

 

Equivalent Thermal Conductivity in Parallel -

\frac{K_{1}A_{1}+K_{2}A_{2}+..........K_{n}A_{n}}{A_{1}+A_{2}+..............A_{n}}

-

Both are in parallel combination

k_{ea}=\frac{k_{1}A_{1}+k_{2}A_{2}}{A_{1}+A_{2}}

A_{1}=\pi R^{2}

A_{2}=\pi \left (4 R^{2} \right )-\pi R^{2}=3\pi R^{2}

k_{ea}=\frac{k_{1}\times \pi R^{2}+k_{2}\left ( 3\pi R^{2} \right )}{4\pi R^{2}}

k_{ea}=\frac{k_{1}+3k_{2}}{4}


Option 1)

 \frac{K_{1} + 3 K_{2}}{4}

Option 2)

 \frac{K_{1} + K_{2}}{2}

Option 3)

 K_{1} + K_{2}

Option 4)

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

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