Aspect-ratio effect on Natural Convection subject to horizontal temperature gradient

Direct numerical simulations of natural convection in low aspect-ratio (AR) cavities with heated and cooled side walls and adiabatic top and bottom are performed. Three cavities with $AR=0.5$, 1, and 2 are simulated in the range of Rayleigh number ($Ra$) from 1 to $10^8$ and Prandtl number $Pr=0.71$. Mean velocity magnitude, Nusselt number ($Nu$), and boundary layer thicknesses are computed as functions of $Ra$. In the laminar flow regime with $Ra$ approximately from $10^3$ to $10^7$, power-law scalings $\sim Ra^\beta$ of velocity magnitude, $Nu$, and boundary layer thicknesses are found in three cavities. Threshold Ra values are examined at the onset of the power-law growth in each cavity. Aspect-ratio effect on flow structure and heat transfer are demonstrated.