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.