First slide

Conduction

Question

The temperature of the two outer surfaces of a composite slab consisting of two materials having coefficients of thermal conductivity K and 2K and thickness x and 4x, respectively are T₂ and T₁(T₂ >T₁). The rate of heat transfer through the slab, in steady state is
$[\frac{KA (T_{2} - T_{1})}{X}] f$ with f equal to

Difficult

A

1
B

$\frac{1}{2}$
C

$\frac{2}{3}$
D

$\frac{1}{3}$

Solution

The two plates arc connected in series. Their total thermal resistance is given by $R_{S} = R_{1} + R_{2} = \frac{X}{KA} + \frac{4 X}{2 KA} = \frac{3 X}{KA}$
The rate of flow of heat through the composite plate is given by
$\frac{Q}{t} = \frac{Δθ}{R_{S}} = \frac{(T_{2} - T_{1})}{(3 x / KA)} = \frac{KA (T_{2} - T_{1})}{3 x}$
$= [\frac{KA (T_{2} - T_{1})}{x}] \times \frac{1}{3}$
Comparing with given equation, we get $f = \frac{1}{3}$ .

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