Consider a composite slab consisting of two different materials having equal thickness and thermal conductivities $K$ and $2 K$ respectively. The equivalent thermal conductivity of the slab is

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$\frac{2}{3} K$

$\sqrt{2} K$

$3 K$

$\frac{4}{3} K$

answer is D.

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Detailed Solution

The equivalent thermal conductivity when the slabs are connected in series is:

$K_{eq} = \frac{\sum x_{n}}{\frac{\sum x_{n}}{\sum K_{n}}} = \frac{x + x}{\frac{x}{K} + \frac{x}{2 K}} = \frac{2 x (2 K^{2})}{(2 Kx + Kx)} = \frac{4}{3} K$

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