Guidelines for modeling perfect contact behavior using Thermal Coupling

This topic describes a recommended approach for defining thermal coupling coefficients based on material properties and mesh size.

Introduction

When creating thermal models, you often need thermal coupling interfaces to transfer heat between non-conformal meshes or between different modeling representations. Choosing an appropriate thermal coupling coefficient is critical for obtaining physically realistic results.

Physics-based HTC estimation

Avoid selecting an arbitrary thermal coupling coefficient, such as 1000 W/(m2·K). The purpose of a thermal coupling heat transfer coefficient (HTC) is not to model convection, but to reproduce the conductive heat transfer across a near-perfect contact interface. An HTC that is too low introduces artificial thermal resistance, while an HTC that is too high can lead to excessive numerical diffusion. A more physically consistent approach is to estimate the HTC from the material thermal conductivity and the local mesh size.

For a conductive interface, the heat flux can be approximated using Fourier's law:

Where:

  • k is the material thermal conductivity.
  • Tprimary is the temperature on the primary side.
  • Tsecondary is the temperature on the secondary side.
  • L is the distance between the centroids of the elements adjacent to the interface. For a uniform mesh, L is approximately equal to the element size.

Equating this conductive heat transfer to the thermal coupling formulation leads to the following estimate for the thermal coupling coefficient:

Where:

  • h is the thermal coupling coefficient.
  • k is the material thermal conductivity.
  • L is the characteristic element size normal to the interface.

This formulation provides a physically meaningful HTC that scales automatically with both material properties and mesh density.

Interfaces between different materials

When the two sides of the thermal coupling have different materials or different mesh sizes, use the following generalized expression:

Where:

  • k1 and k2 are the thermal conductivity of the primary and secondary side, respectively.
  • Δx1 and Δx2 are the element height normal to the interface on the primary and secondary side, respectively.