Measure and evaluate the hydrothermal flow of a Newtonian fluid in homogeneous permeable media equipped with a fin: A numerical approach

Abstract

This study envisions the hydrothermal characteristics of a viscous fluid in a homogenously permeable hexagonal enclosure. Permeability aspects in the flow domain are described by employing the Brinkman-extended Darcy law. A corrugated hexagonal enclosure along with the placement of a star-shaped fin is taken into account. Heated rectangular blocks at horizontal extremities are installed, and sliding sides of the enclosure are considered to be cold to provide convective potential to the flow. In addition, adjoining portions of the heated rectangular blocks are supposed to be adiabatic. The dimensionless governing equations of the resultant problem are derived initially and then solved numerically by implementing the Galerkin finite element approach, and COMSOL is obliged. For this purpose, first, domain discretization is demonstrated in view of 2D elements by performing hybridized meshing. Then, the system of non-linear equations is resolved by a non-linear solver (PARADISO). The grid convergence test is performed to confirm the credibility of the carried out simulations by calculating the average Nusselt number at different refinement levels. A change in associated distributions against the involved physical parameters (Darcy number (Da), Rayleigh number (Ra), and Prandtl number (Pr)) for a wide range is revealed through graphs and tables. Quantities like kinetic energy and heat flux (local and average) are also evaluated through concerned parameters. The results clearly demonstrate that the Darcy number tends to reduce the heat transfer rate. In particular, it is depicted that by increasing the Rayleigh number (Ra), strengthening in the temperature potential arises in the system, thereby magnifying the heat transfer rate. Moreover, it is disclosed that by reducing the Darcy number, kinetic energy shows a decreasing trend.