Stability of static conjugate heat transfer coupling approaches using Robin interface conditions

The combined solution of fluid convective and solid conductive heat transfer, known as conjugate heat transfer, is becoming increasingly important for engineering design applications, because it allows for more accurate and reliable predictions compared to single-domain simulations. However, predicting conjugate heat transfer requires a coupled simulation approach, where interactions between both domains are accounted for. A prevalent method uses a partitioned thermal fluid-solid coupling approach; this method, however, invokes stability complications. Recent research has focused on establishing efficient algorithms for predicting conjugate heat transfer, while in previous studies [1, 2] the authors revealed that the stability of partitioned coupling methods depends mainly on the Biot number of the problem. This work extends the stability prediction to the more general Robin-Robin interface conditions. For the fluid domain, Robin conditions are an uncommon, however, promising boundary condition, which essentially leads to three new coupling methods. Applying a perturbation method for the stability analysis, this work derives a new stability criterion for the considered interface conditions, again, solely depending on the Biot number of the problem. The obtained stability criterion is the most general criterion applicable to static partitioned coupling approach and includes the previously found results. As proof of concept, the validity of the derived criterion is demonstrated with numerical experiments on a flat plate test case.