2. Introduction to Composite Wall Heat Conduction and Thermal Conductivity

Recall that the steady-state heat equation takes the form:

This equation dictates the shape of the temperature profile over the material for a given temperature difference. This differential equation will always produce a linear (or, if dT/dx = 0, a homogenous) relationship between temperature, T and distance away from the heat source, x in a plane wall. Therefore, if one can determine the temperature at two values of x (i.e. have 2 sets of boundary conditions), then one can fully determine the temperature profile across the wall if the wall is made of one material.

If the plane wall is made of multiple materials, as in a composite wall, then the temperature profile across the wall is likely to consist of many sections with different linear temperature gradients, as can be seen below:

These temperature gradients depend upon the each of the materials' thermal conductivity, k. To understand the temperature profile across a composite wall one needs knowledge of all the boundary conditions. For example, in the composite wall above, knowing Ts1, T2, T3 and Ts4 and using the steady-state conduction equation gives a full understanding of the wall's temperature profile. 

But what if the question in an exam isn't that simple? What if you were expected to design a system which resists heat flow, rather than to just provide a simple conduction steady-state analysis for a number of given boundary conditions? In these circumstances, it is useful to represent the heat flux-temperature system as an electrical system, where thermal resistance is represented by electrical resistance, heat rate is represented by current and temperature difference is represented by potential difference.

Before attempting to tackle a thermal resistance analysis, it is important to define heat flow, heat flux and the difference between the two terms.