A coupling numerical methodology for weakly transient conjugate heat transfer problems

This study deals with the development of a partitioned coupling strategy at the fluid–solid interface for weakly transient heat transfer problems. The thermal coupling is carried out by an iterative procedure (strong coupling) between a transient solid and a sequence of steady states in the fluid. Continuity of temperature and heat flux is ensured at each coupling time step.Emphasis is put on the choice of interface conditions at the fluid–solid interface. Two fluid–solid transmission procedures are considered in this paper: Dirichlet–Robin and Neumann–Robin conditions. These conditions are theoretically examined and it is shown that the Biot number is a key parameter for determining relevant interface conditions. Stability diagrams are provided in each case and the most effective coupling coefficients are highlighted and expressed. Numerical thermal computations are then performed for two different Biot numbers. They confirm the efficiency of the interface conditions in terms of accuracy, stability and convergence. At the end of this paper a comparison between a partitioned and a monolithic approach is presented.