Model for classical and ultimate regimes of radiatively driven turbulent convection

Abstract

Abstract

Model for thermal convection with uniform volumetric energy sources

“…As the GL theory is based on Prandtl-Blasius-Pohlhausen laminar boundary layers (Grossmann & Lohse 2000), the mean temperature can be written as (Creyssels 2020)…”

“…To predict the variations of Nusselt numbers with and for internal heating and cooling convection experiments, Creyssels (2020) proposed the assumption that, for high numbers, the dynamical structure of the convective flow be considered to be the same as that in standard RB experiments. Notably, he assumed that the 5 dimensionless parameters (, –) defined within the framework of the GL theory do not depend on the way the heat is injected and extracted in the experiment.…”

“…Notably, he assumed that the 5 dimensionless parameters (, –) defined within the framework of the GL theory do not depend on the way the heat is injected and extracted in the experiment. Besides, the thickness of each thermal boundary layer is assumed to be only controlled by the difference of temperature between the bulk flow and the corresponding plate using the following equation ((2.1) in Creyssels 2020): Then, the central idea of the GL theory is to split both mean kinetic energy and thermal dissipation rates into two contributions each, one from the bulk (Bu) and one from the boundary layers (BLs) as and each contribution is modelled as follows: In (2.4)–(2.6), represents the characteristic velocity of the bulk flow. Grossmann & Lohse (2001) introduced the function because the relevant velocity at the edge between the thermal BL and the thermal bulk can be less than , depending on the ratio .…”

“…Natural convection induced by internal heat production is a phenomenon that occurs very often in geophysical, astrophysical and engineering systems (Goluskin 2015). By following the analysis recently given by Creyssels (2020), the purpose of this paper is to extend the many theoretical, numerical and experimental results of Rayleigh–Bénard (RB) convection to two internally heated (IH) convection systems shown in figures 1( a ) and 1( b ). In RB convection, convective flow is produced by thermal boundary conditions that cause heat to enter through the lower hot plate and exit through the upper cold plate.…”

“…Up to now, no theory has been able to predict these exponents whereas, for RB convection, the theory developed by Grossmann & Lohse (2000, 2001) (henceforth the GL theory, (2.18) and (2.19)) describes well the behaviour of and . Creyssels (2020) has recently developed a simple theoretical model to predict the and -dependent Nusselt number for a modified RB experiment in which heat is injected by volume but only in the lower thermal boundary layer. At the same time, the upper boundary layer is cooled with the same rate in order to have a constant energy in the convection cell, as in a standard RB cell.…”