A composite plane wall consists of a Li = 50 mm thick layer of insulation (ki = 0.05 W/m·K) and a Ls = 25 mm thick layer of siding (ks = 0.10 W/m·K). The inner temperature of the insulation is 25oC. The outer temperature of the siding is - 10oC. Steady state conditions apply. Determine the temperature at the interface between the two layers, in oC, and the rate of heat transfer through the wall, in W per m2 of surface area.

Question

Mohammad Porter

Physics

4 April, 11:08

A composite plane wall consists of a Li = 50 mm thick layer of insulation (ki = 0.05 W/m·K) and a Ls = 25 mm thick layer of siding (ks = 0.10 W/m·K). The inner temperature of the insulation is 25oC. The outer temperature of the siding is - 10oC. Steady state conditions apply. Determine the temperature at the interface between the two layers, in oC, and the rate of heat transfer through the wall, in W per m2 of surface area.

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Ducky · Answer 1

Let the temperature of interface be θ

In steady state, rate of heat flow in the two mediums will be equal.

Rate of heat flow in thick layer

=.05 A (25 - θ) / 50 x 10⁻³

Rate of heat flow in thin layer

.1 x A (θ + 10) / 25 X 10⁻³

.05 A (25 - θ) / 50 x 10⁻³ =.1 x A (θ + 10) / 25 X 10⁻³

.05 X (25 - θ) / 2 = 0.1 (θ + 10)

05 X (25 - θ) =.2 (θ + 10)

1.25 -.05 θ =.2 θ + 2

- 0.75 =.25 θ

θ = - 3 degree only