SEM-based numerical framework for non-Darcy mixed convection in a porous cavity with three adiabatic thin baffles on the hot wall

Abstract

Purpose The purpose of this paper is to develop a numerical framework based on the accurate spectral element method (SEM) to simulate the mixed convective heat transfer within a porous enclosure with three adiabatic thin baffles of different lengths in nine cases and analyze the effects of several parameters. Design/methodology/approach The authors develop an improved time-splitting method to solve the Darcy–Brinkman–Forchheimer model. No extra assumptions are introduced for the intermediate velocity, and the final velocity field satisfies the incompressible constraint strictly compared with the classical method. The governing equations are split into a pure convection problem, a Stokes problem and a thermal diffusion problem. The least-squares variation is adopted for the Stokes problem, and the Galerkin variation is used for the other two problems, such that the pressure and velocity can be discretized with the same interpolation order, which benefits the numerical accuracy and program design. Findings Regarding the method, the excellent spectral accuracy, the capability of discretizing complex computational regions and the improved time-splitting methods make SEM an effective tool to accurately predict the non-Darcy convective heat transfer; as for the numerical tests, it is observed that weakened convection and heat transfer are induced by the increasing length of the baffles. The flow and heat transfer in channel 1 is only related to the length of baffle 1 because of the downward-driven right sidewall, and it is more difficult for baffle 3 to form the secondary flow on its tip. Originality/value A novel numerical framework for Darcy–Brinkman–Forchheimer model is developed, expanding the application of SEM for simulating non-Darcy convective heat transfer to improve the numerical accuracy. Numerical results and analysis for flow and heat fields could help designers understand the control of heat transfer using adiabatic baffles better.