Abstract
We study penetrative convection of a fluid confined between two horizontal plates, the temperatures of which are such that a temperature of maximum density lies between them. The range of Rayleigh numbers studied is and the Prandtl numbers are and 11.6. An evolution equation for the growth of the convecting region is obtained through an integral energy balance. We identify a new nondimensional parameter, , which is the ratio of temperature difference between the stable and unstable regions of the flow; larger values of denote increased stability of the upper stable layer. We study the effects of on the flow field using well-resolved lattice Boltzmann simulations and show that the characteristics of the flow depend sensitively upon it. For the range , we find that for a fixed the Nusselt number, , increases with decreasing . We also investigate the effects of on the vertical variation of convective heat flux and the Brunt-Väisälä frequency. Our results clearly indicate that in the limit the problem reduces to that of the classical Rayleigh-Bénard convection.
12 More- Received 2 June 2017
DOI:https://doi.org/10.1103/PhysRevFluids.3.043501
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