Numerical Investigation into Effect of Sidewall Thermal Conductance in Darcy-Bénard Convection

Coarse-grained porous-media thermal convection is crucial to the understanding of numerous natural and engineering applications. A survey of the literature reveals that most existing studies either disregard the effect of sidewall thermal conductance or apply a conduction-based model that assumes a linear temperature profile within the sidewalls when estimating the net convective heat transport. However, whether these approaches yield accurate results depends on several factors such as thermal conductivities of sidewalls and porous material and Rayleigh number. Therefore, the present study aims to conduct a three-dimensional numerical study to understand the effect of sidewall thermal conductance heat loss on heat transport for thermal convection of air in coarse-grained porous media. This effect is assessed by performing simulations using sidewalls of three different materials (styrofoam, acrylic, and high-density polyethylene) for a limited range of fluid-based Rayleigh numbers \(({10}^{6}\le {Ra_{f}}\le {10}^{8}\) ) and a fixed Darcy number ( \(Da=2.91\times {10}^{-4}\) ). These simulations are repeated for four different porous materials to understand the effect of thermal conductivity of porous material on sidewall thermal conductance. Results show that sidewall thermal conductance can be modeled using a linear temperature profile with reasonable accuracy when Rayleigh numbers are smaller ( \({Ra_{f}}\le {10}^{7}\) ) and the thermal conductivity of sidewalls is of the same order of magnitude as the stagnant fluid. A linear temperature profile assumption is also found to yield accurate results even at extremely high Rayleigh numbers, given that the porous matrix is highly conducting.