A wall consists of alternating blocks of length 'd' and coefficient of thermal conductivity $k_{1} a n d k_{2}$ respectively as shown in figure. The cross sectional area of the blocks are the same. The equivalent coefficient of thermal conductivity of the wall between left and right is :

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$\frac{k_{1} + k_{2}}{2}$

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

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

$\frac{3 k_{1} k_{2}}{k_{1} + k_{2}}$

answer is D.

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Detailed Solution

$\begin{array}{l} R_{t h} = \frac{l}{k A} \\ \frac{1}{R_{e q}} = 3 (\frac{1}{R_{1}} + \frac{1}{R_{2}}) \\ \frac{k_{e q} 6 A}{d} = 3 (\frac{k_{1} A}{d} + \frac{k_{2} A}{d}) \\ k_{e q} = \frac{k_{1} + k_{2}}{2} \end{array}$

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