Boundaries matter: Impact of sidewall conductance on porous-media thermal convection

Abstract

Thermal convection in a fluid-saturated horizontal porous medium is a ubiquitous problem in many real-world applications. To investigate this phenomenon in a laboratory setting, the porous medium must be bounded between bottom-hot and top-cold horizontal plates and laterally confined by low-conductivity sidewalls. Thermal coupling of sidewalls with hot and cold plates can create an additional heat transfer path, causing heat leakage from hot to cold plates. Previous studies have estimated this leakage using 1-D conduction model based on a Linear Temperature Profile (LTP) assumption, which completely overlooks convection in the porous layer. However, this assumption is yet to investigated which may lead to inaccurate estimation of experimental porous-media Nusselt numbers $\left(N{u}_{\text{pm}}\right)$. To address this issue, the present study evaluates the applicability of an LTP assumption and quantifies the influence of sidewall thermal conductivity on convection. This investigation is conducted using three-dimensional, pore-scale numerical simulations, wherein three sidewall materials of identical thicknesses are studied. These sidewalls are examined for two Darcy numbers $\left(Da\right)$ and four distinct porous media, with argon gas as a working fluid, over Rayleigh–Darcy numbers $\left(R{a}_K\right)$ ranging from $0.036-2.3\times 10^6$. Results reveal that increasing sidewall conductivity ($k_{sw}=0$–1.2 W/m$\cdot$ K) reduces $N{u}_{\text{pm}}$ values by 60% at $R{a}_K=207$. This influence weakens with decreasing $Da$ and increasing $R{a}_K$ and porous-media thermal conductivity $\left(k_{\text{pm}}\right)$. Moreover, the LTP assumption is found to be valid only for low $Da$, low $k_{sw}$, and high $k_{\text{pm}}$ values. Finally, an analytical model is proposed to estimate sidewall heat loss wherever LTP approach not applicable.