On the conjugate interface conditions and Galilean invariance

TL;DR

This paper critiques a proposed heat flux continuity condition for conjugate heat transfer with moving interfaces, demonstrating it violates Galilean invariance and advocating for the original diffusion heat flux condition.

Contribution

It identifies the violation of Galilean invariance in a previously proposed heat flux condition and defends the original diffusion-based condition as more physically consistent.

Findings

The total heat flux continuity condition violates Galilean invariance.

The original diffusion heat flux condition remains valid for stationary and moving interfaces.

The critique clarifies the physical consistency of heat flux conditions in conjugate heat transfer.

Abstract

In the referred paper("H. Karani, C. Huber, Physical Review E, 91(2)(2015) 023304"), a total heat flux continuity condition for conjugate heat transfer problems with moving interfaces was proposed. The authors asserted both conductive and advective heat fluxes are conserved simultaneously in their formulation. This condition had been cited by many subsequent studies. However, it is found that the total heat flux continuity condition violates Galilean invariance. The original diffusion heat flux continuity condition is reasonable for both stationary and moving interfaces.