Advice needed: Electro-thermal modeling and natural convection – Robin BC vs. OpenFOAM/preCICE coupling?

General
1

Hello everyone,

I am currently working on a 3D electro-thermal simulation of a bimetallic strip using FEniCS.

So far, I have successfully implemented a one-way coupled solver:

  1. I solve the electrical Poisson equation to compute the electric potential.
  2. I calculate the Joule heating source term (\sigma \nabla V \cdot \nabla V).
  3. I solve the steady-state heat equation using this generated source term.

My current issue:

To make the thermal variational problem well-posed, I am currently forcing a Dirichlet boundary condition (fixed temperature) on one of the boundaries. However, in reality, my physical system does not have any fixed-temperature boundaries. The heating of the bimetallic strip is entirely balanced by natural convection with the surrounding air.

I am looking for advice on the best workflow to properly account for this natural convection. I am considering two main options:

  • Option 1: Robin Boundary Condition (Newton’s Law of Cooling) could modify my thermal variational formulation to replace the Dirichlet BC with a Robin BC on the external boundaries, adding a surface integral term like \int_{\partial \Omega} h (T - T_{\text{air}}) v \, ds. This keeps the entire workflow inside FEniCS and is computationally cheap. However, it requires estimating the convective heat transfer coefficient (h) for natural convection, which is notoriously difficult and non-uniform for complex 3D geometries.
  • *Option 2: FEniCS-OpenFOAM coupling via preCICE could set up a full Conjugate Heat Transfer (CHT) simulation. FEniCS would handle the solid domain (electro-thermal physics) and OpenFOAM would handle the surrounding fluid domain (buoyancy-driven airflow), using preCICE to couple the interfacial temperatures and heat fluxes.

My questions for the community:

  1. For those who have modeled small electrical components in the open air, is the Robin BC approach (Option 1) generally considered “good enough,” or is the error in assuming an empirical h too large for natural convection?
  2. If Option 1 is viable, are there recommended practices in FEniCS for defining h when it depends on the temperature difference itself (requiring a non-linear solver for the heat equation)?
  3. If Option 2 is the better route, are there any known pitfalls or specific tutorials when coupling FEniCS and OpenFOAM for this specific type of low-speed natural convection?

Any insights, workflow recommendations, or examples would be greatly appreciated.

Thank you in advance for your time and help!