Cross-flow heat exchangers as shown in figure 1 are built for efficient heat transfer between two fluid streams without mixing them. In order to achieve this objective it is paramount to increase the surface area active for heat transfer. This usually results in designs which are comprised of channels which are much smaller than the distribution ducts. Hence meshing the whole domain of the equipment would yield very big meshes. However, in many situations the flow and heat transfer in individual channels can be described adequately using engineering correlations. In this case, the heat exchanger can be modelled as a pseudo three phase system composed of fluid 1, fluid 2 and solid where the volume fraction of each component is determined by the channel geometry and does not change in time. The motion of each fluid is then governed by the momentum equation for the fluid flow in an anisotropic porous medium.
