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 towards understanding the effects of bounding walls in horizontal (Rayleigh-Bénard) convection systems, similar investigations for Darcy-Bénard convection systems are still lacking. Therefore, the present 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 non-dimensional 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.