Conjugate heat transfer (CHT) occurs when two media at different temperatures are in contact. At the contact surface between the two media, heat is transferred from the hotter to colder medium. The physics of how the transfer takes place is governed by Fourier’s law:

where q is the heat flux, VT the temperature gradient, and k a proportionality constant known as thermal conductivity.

In the case of two coupled solvers, heat transfer occurs at the surface interface of the two domains. To understand why this is a two-way coupling, consider the situation where Solver A sends q to Solver B, which is calculated based on the temperature gradient at the interface. When Solver B applies this heat flux as a boundary condition, the temperature at the interface changes. So, according to Fourier’s law, the heat flux which was sent across originally was incorrect. So, you now have to go back to Solver A, apply the new temperature, update the solution, and send the updated heat flux to Solver B. This process can be repeated until convergence.

A variety of Ansys (part of Synopsys) products can perform CHT independently. For example, Fluent, CFX, and Thermal Desktop have intrinsic CHT capabilities. This type of approach should be used wherever possible as it can be done more efficiently and tends to avoid numerical stability limitations.

In cases where two different solvers need to be coupled, this can be achieved using System Coupling, which couples the two physics using an iterative process. This iterative process can sometimes be numerically unstable, depending on the interface conditions, system properties, and mesh resolution. Fortunately, most CHT problems can be stabilized in System Coupling by appropriate selection of interface conditions and applying additional stabilization algorithms as needed.