Consider thermal conduction through a composite material made of two layers, A a

Question

Consider thermal conduction through a composite material made of two layers, A and B. Layer A is 2.0 times as thick as layer B, and the thermal conductivity of material A is 3.0 times that of material B. If the temperature on the outside surface of A is 75 degree C and the temperature on the outside surface of B is 5 degree C, find the temperature at the interface of the two materials when a steady state of heat flow has been established. A) 40 degree C B) 33 degree C C) 61 degree C D) 26 degree C E) 47 degree C

Explanation / Answer

heat flow rate=k*A*temperature difference/thickness

where k=thermal conductivity

A=area

let thickness of B=x

thickness of A=2*x

conductivity of B=k

conductivity of A=3*k

let temperature of the interface be T degree celcius.

then equating heat flow rate of both the materials:

k*A*(75-T)/x=3*k*A*(T-5)/(2*x)

==>2*(75-T)=3*(T-5)

==>150-2*T=3*T-15

==>5*T=165

==>T=33 degree celcius

hence option B is correct.

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