Effects of conjugate heat transfer on large-scale flow structures in convection

Abstract

The constant temperature and constant heat flux thermal boundary conditions, both developing distinct flow patterns, represent limiting cases of ideally conducting and insulating plates in Rayleigh-B\'enard convection (RBC) flows, respectively. This study bridges the gap in between, using a conjugate heat transfer (CHT) set-up and studying finite thermal diffusivity ratios $\kapparatioIL$ to better represent real-life conditions in experiments. A three-dimensional RBC configuration including two fluid-confining plates is studied via direct numerical simulations given a Prandtl number $\Pr=1$. The fluid layer of height $H$ and horizontal extension $L$ obeys no-slip boundary conditions at the two solid-fluid interfaces and an aspect ratio of $\Gamma=L/H=30$ while the relative thickness of each plate is $\Gs=H_s/H=15$. The entire domain is laterally periodic. Here, different $\kapparatioIL$ are investigated for moderate Rayleigh numbers $\Ra=\left\{ 10^4, 10^5 \right\}$. We observe a gradual shift of the size of the characteristic flow patterns and their induced heat and mass transfer as $\kapparatioIL$ is varied, suggesting a relation between the recently studied turbulent superstructures and supergranules for constant temperature and constant heat flux boundary conditions, respectively. Performing a linear stability analysis for this CHT configuration confirms these observations theoretically while extending previous studies by investigating the impact of a varying solid plate thickness $\Gs$. Moreover, we study the impact of $\kapparatioIL$ on both the thermal and viscous boundary layers. Given the prevalence of finite $\kapparatioIL$ in nature, this work is a starting point to extend our understanding of pattern formation in geo- and astrophysical convection flows.