# Free convection beneath a heated horizontal plate in a rapidly rotating system

Whittaker, RJ ORCID: https://orcid.org/0000-0001-9598-5938 and Lister, JR (2007) Free convection beneath a heated horizontal plate in a rapidly rotating system. Journal of Fluid Mechanics, 586. pp. 491-506. ISSN 0022-1120

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## Abstract

Laminar flow beneath a finite heated horizontal plate in a rapidly rotating system is considered in both axisymmetric and planar geometries. In particular, we examine the case where the Ekman layer is confined well within a much deeper (yet still thin) thermal boundary layer. This situation corresponds to the regime E-3/2 xs226A Ra xs226A E-5/2, where E and Ra are the natural Ekman and Rayleigh numbers for the system (equation (2.6)). The outward flux of buoyant fluid from beneath the plate occurs primarily in the Ekman layer, while outward flow in the thicker thermal boundary layer is inhibited by a dominant thermal-wind balance. The O(Ra-1/2 E-3/4 thickness of the thermal boundary layer is determined by a balance between Ekman suction and diffusion. There are several possible asymptotic regimes near the outer edge of the plate, differing only by logarithmic factors, but in all cases the edge corresponds to a simple boundary condition on the interior flow. With a uniform plate temperature, the dimensionless heat transfer (equation (7.6)) is given by a Nusselt number $\Nu\,{\sim} \tfrac{1}{2}\Ra^{1/2}\Ek^{3/4}[\ln (\Ra^{-1} \Ek ^{-5/2})]^{1/2}$. The solution for a uniform plate heat flux is also presented.

Item Type: Article Faculty of Science > School of Mathematics http://dx.doi.org/10.1017/S0022112007007... Robert Whittaker 10 Mar 2011 12:48 24 Oct 2022 01:35 https://ueaeprints.uea.ac.uk/id/eprint/20895 10.1017/S0022112007007252