A Bayesian Approach to Interfacial Heat Transfer Coefficient Model Selection in Al–Si Alloy Solidification

Abstract Accurate thermal analysis in permanent mold casting depends on a proper representation of the Interfacial Heat Transfer Coefficient (IHTC), which governs temperature prediction and, consequently, metallurgical and mechanical outcomes. However, the literature offers many IHTC models, making the choice of an adequate formulation non-trivial and often unjustified. This work adopts a Bayesian framework to identify the most suitable IHTC description. Nine models, with one to four parameters, were tested. The forward problem, involving the thermal field along the solidifying alloy, was solved with the finite volume method, while the inverse problem was addressed by Sequential Monte Carlo within Approximate Bayesian Computation (SMC-ABC). To enhance prior information and narrow the parameter search space, the Moth-Flame Optimization algorithm was integrated into the procedure. The methodology was applied to three Al–Si alloys: Al-3wt.%Si, Al-7wt.%Si, and Al-9wt.%Si. Among the options, the two-parameter time-dependent exponential formulation showed the best agreement with observed thermal behavior. To the best of the authors’ knowledge, this is the first study to systematically evaluate, compare, and select IHTC models, establishing the exponential law as the most reliable choice for immediate application in microstructural control and thermal design of directional casting.