First slide

Conduction

Question

Two conductors having thicknesses d₁ and d₂ , thermal conductivities K₁ and K₂ are placed one above the other. The equivalent thermal conductance is:

Moderate

A

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

$\frac{(d_{1} - d_{2}) (K_{1} d_{2} + K_{2} d_{1})}{1 (K_{1} + K_{2})}$
C

$\frac{K_{1} K_{2} (d_{1} + d_{2})}{d_{1} K_{2} + d_{2} K_{1}}$
D

none of the above

Solution

$Here, \frac{d_{1} + d_{2}}{kA} = \frac{d_{1}}{K_{1} A} + \frac{d_{2}}{K_{2} A} So, K = \frac{K_{1} K_{2} (d_{1} + d_{2})}{d_{1} K_{2} + d_{2} K_{1}}$

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