Heat flux and wall shear stress in large-aspect-ratio turbulent vertical convection

Abstract

Thermally driven flows are ubiquitous in nature. An important and longstanding question is how heat transfer depends on the control parameters of the flow. In this Letter, the author presents a theoretical analysis that answers such question for large aspect-ratio turbulent thermal convection in a fluid between two vertical walls maintained at different temperatures. This analysis yields the dependence of heat flux and wall shear stress on the Rayleigh and Prandtl numbers in the high Rayleigh-number limit.