Consider a two-layer system where one layer has twice the thickness and six times the thermal conductivity as the other layer, but the layers have the same area. One edge of the system is at temperature T₁ = 24° C and the other is at T₂ = 0° C. In the steady state, what is the temperature at the interface?

In the steady state, the rate of heat flow through each layer is the same.

Setting the heat flow rates through each layer to be equal gives:

6 Κ A

T1 - T 2 L

= Κ A

T - T2 L

Cancelling all the common factors, and plugging in T₁ = 24° C and T₂ = 0° C gives:

3 (T₁ - T) = T   →   T = 18° C