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Q.

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

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a

1

b

1/3

c

2/3

d

1/2

answer is D.

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Detailed Solution

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$K_{eff} = \frac{\sum l_{i}}{\sum \frac{l_{i}}{K_{i}}} = \frac{x + 4 x}{\frac{x}{K} + \frac{4 x}{2 K}} = \frac{5}{3} K$
$\frac{dQ}{dt} = \frac{(5 / 3 K) A (T_{1} - T_{2})}{5 x} = [\frac{KA (T_{1} - T_{2})}{x}] (\frac{1}{3}) \Rightarrow f = \frac{1}{3}$

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