Effect of Finite Thermal Conductivity Bounding Walls on Darcy–Bénard Convection

Abstract

Natural convection in fluid-saturated, horizontal porous-media is quintessential to many applications like geothermal reservoirs and solar thermal storage systems. Researchers have dedicated substantial effort over the years in pursuit of altering natural convection within a horizontal porous-media (Darcy–Bénard) system. Although significant research efforts have been directed toward understanding the effects of bounding walls in horizontal (Rayleigh–Bénard) convection systems, similar investigations for Darcy–Bénard convection systems are still lacking. Therefore, this study examines the effect of thermal properties of horizontal bounding plates on porous-media Nusselt number at high Rayleigh–Darcy numbers (105−107). Numerical simulations are performed by employing Darcy–Forchheimer model within a three-dimensional cylindrical computational domain to emulate Darcy–Bénard systems for two aspect ratios (1 and 2) and six different plate materials having nondimensional plate thicknesses of 0.02, 0.08, and 0.16. Polypropylene and compressed CO2 gas are chosen as solid and fluid phases for the porous media, respectively, that encompass a range of Darcy numbers (10−6−10−3). Findings reveal that when the ratio of thermal resistances of porous layer and plates falls below 4.61, the corrected Nusselt number deviates by more than 10% from the corresponding ideal Nusselt number with infinitely conducting bounding plates. The study also proposes a correction factor to estimate this deviation, which shows a good agreement with numerical results.