Comparison between Dirichlet-Robin and Neumann-Robin Interface Conditions in CHT Problems

Abstract

± This paper presents and compares the stability and the performance of two different boundary conditions in steady conjugate heat transfer (CHT) problems. The Dirichlet-Robin interface and the Neumann-Robin interface condition have been implemented. The choice between the two interface conditions depends on the numerical Biot number that is a local representation of the thermal fluid-structure interaction and plays a key role in the stability of the coupling process. The coupling coefficient of the Robin condition is determined by the transition of the amplification factor derived from a normal mode stability analysis based on the Godunov-Ryabenkii theory. A study of an academic 2D test case illustrates that, although the Dirichlet-Robin interface condition is optimal for low and moderate thermal fluid-structure interaction, the Neumann-Robin condition is a relevant choice at higher thermal fluid-structure interaction.