Numerical analysis of flow and temperature fields in porous-partitioned cavities using non-linear Darcy-Brinkman-Forchheimer model

Abstract

In this study, the effects of partitioning a square cavity with both vertical and horizontal porous walls on conjugate natural convection heat transfer are investigated numerically using a non-linear Darcy-Brinkman-Forchheimer model. The primary objective is to establish benchmark solutions and a dataset for validating Computational Fluid Dynamics (CFD) simulations. The governing equations, including mass, Navier-Stokes, and energy, are discretized using a staggered grid system based on the control volume method. To handle porous media, a FORTRAN code is developed based on the non-linear Darcy-Brinkman-Forchheimer model and initially validated against three challenging benchmark cases. These cases involve mixed and natural convection heat transfer in a square porous cavity, with and without a magnetic field. Through comparative analysis with existing data, the accuracy and robustness of the numerical model in capturing complex flow and heat transport phenomena in porous media are confirmed. Subsequently, the validated numerical model is applied to examine conjugate natural convection heat transfer in a square cavity partitioned with both vertical and horizontal porous matrices. In the final stage of the investigation, the influence of a magnetic field on the heat transfer rate within the partitioned enclosure is also explored. The results reveal significant impacts of the Darcy number and porous region orientation on the thermal and hydrodynamic characteristics of the system. Moreover, substantial variations in heat transfer rate and flow intensity within the computational domain are observed with decreasing the Darcy number and increasing Hartman numbers.