First slide

Conduction

Question

Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are K₁ and K₂. The thermal conductivity of the composite rod will be

Moderate

A

$\frac{3 (K_{1} + K_{2})}{2}$
B

$K_{1} + K_{2}$
C

$2 (K_{1} + K_{2})$
D

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

Solution

$In parallel \frac{1}{R_{eq}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} \frac{K_{eq} (2 A)}{l} = \frac{K_{1} A}{l} + \frac{K_{2} A}{l} K_{eq} = \frac{K_{1} + K_{2}}{2}$

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