Question

Derive an expression for the rate of heat flow through a composite slab consisting of two materials with different thermal conductivities and thicknesses. Assume that the temperatures at the outer surfaces of the slab are T₁ and T₂, and that the interface between the two materials is at temperature T.

A composite wall consists of two layers: a 10 cm thick layer of brick (thermal conductivity = 0.7 W/m·K) and a 5 cm thick layer of insulation (thermal conductivity = 0.2 W/m·K). The inner surface of the brick layer is at 20°C, and the outer surface of the insulation layer is at 0°C. Calculate the heat flux through the composite wall and the temperature at the interface between the two layers.