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.

Explanation:

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

it may be wrong but i think its a