Although most surfaces seem flat, on a microscopic level all of them are found to possess micro asperities. This effectively reduces the contact area, and a temperature drop is observed at the interface between the two surfaces in contact Holman, 1997, Hasselström and Nilsson, 2012.

One way to solve this problem is to resolve the microscopic zig-zag interfaces (the right picture in the following) with very small voxels and result in a large computational domain. The more attractive way, however, is to introduce contact resistance to the simulation. The rough surface of two different materials in contacts does not need to be resolved, but a contact resistance is assigned to it.

The heat flow at the interface is expressed as

where is contact conductance, in W/(m²∙K), is the temperature difference across the interface. And the specific contact resistivity is defined as

From considerations of energy conservation, the heat flow between the two bodies in contact, bodies A and B, is found as: