We often encounter plane walls that consist of several layers of different materials. The thermal resistance concept can still be used to determine the rate of steady heat transfer through such composite walls. As you may have already guessed, this is done by simply noting that the conduction resistance of each wall is L/kA connected in series, and using the electrical analogy. That is, by dividing the temperature difference between two surfaces at known temperatures by the total thermal resistance between them.

Consider a plane wall that consists of two layers (such as a brick wall with a layer of insulation). The rate of steady heat transfer through this two-layer composite wall can be expressed as (Fig. 3.1)

Fig. 3.1: The thermal resistance network for heat transfer through a two-layer plane wall subjected to convection on both sides.

Q ̇=$\frac{(T_∞1-T_∞2)}{R_total}$

Where $R_total$ is the total thermal resistance, expressed as

$R_total$=$R_(conv,1)$+$R_(wall,1)$+$R_(wall,2)$+$R_(conv,2)$

= $\frac{1}{(h_1 A)}$+$\frac{L_1}{(k_1 A)}$+$\frac{L_1}{(k_2 A)}$+$\frac{1}{(h_2 A)}$

The subscripts 1 and 2 in the Rwall relations above indicate the first and the second layers, respectively. We could also obtain this result by following the approach used above for the single-layer case by noting that the rate of steady heat transfer Q through a multilayer medium is constant, and thus it must be the same through each layer. Note from the thermal resistance network that the resistances are in series, and thus the total thermal resistance is simply the arithmetic sum of the individual thermal resistances in the path of heat flow