Abstract
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.
Highlights
The term conjugate heat transfer is used when the two modes of heat transfer – convection and conduction – are considered simultaneously
One of the goals of this paper is to extend the validity of this approach to weakly transient CHT problems
Verstraete [29] developed a stability theory for stationary CHT problems based on a 1D model, in which the Biot number determines the optimal choice of interface quantities
Summary
The term conjugate heat transfer is used when the two modes of heat transfer – convection and conduction – are considered simultaneously. Appropriate methods must be investigated to ensure flux and temperature continuity at the interface and the choice of interface conditions play a crucial role in stability and convergence speed. In this study, both approaches will be exploited and compared. Superscripts m iteration step in coupling period n temporal index in the solid domain ðÞ spatial mean quantity ð^Þ unknown quantity ensures temperatures and flux continuity at the interface, and does not require the use of interface conditions and interpolations that may result in stability issues. The behavior (well-posedness, stability, convergence) of interface conditions in a CHT procedure in partitioned techniques has been studied in different ways. One of the goals of this paper is to extend the validity of this approach to weakly transient CHT problems
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