First slide

Conduction

Question

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

Easy

A

$\frac{2}{3} K$
B

$\sqrt{2 K}$
C

3K
D

$\frac{4}{3} K$

Solution

$K_{eq} = \frac{\sum l_{i}}{\sum \frac{l_{i}}{k_{i}}} = \frac{l + l}{\frac{l}{k} + \frac{l}{2 k}} = \frac{4 K}{3}$
$K_{e f f} = \frac{2 k_{1} k_{2}}{k_{1} + k_{2}} = \frac{2 \times k \times 2 k}{k + 2 k} = \frac{4 k}{3}$

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