Analytical and numerical approaches for heat conduction in composite materials

A rectangular composite slab constituted by two different materials with linearly temperature-dependent thermal conductivity is selected as a test example. The analytical solution can be obtained by introducing the Kirchhoff transformation. Using the exact solution as a comparison base, it is found that the evaluation of the thermal conductivity at the control-volume surface using the harmonic mean operation is generally better than that using the arithmetic mean operation. However, if we intend to obtain the information right at some specific interfaces of abrupt change of thermal conductivity, the recommended grid layout is arranged so that each specific interface is placed with a grid node and more accurate predictions, particularly at these interesting interfaces, can be obtained.