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Fluids 2017, 2(2), 27; doi:10.3390/fluids2020027

Hexagonal Cell Formation in Darcy–Bénard Convection with Viscous Dissipation and Form Drag

1
Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, UK
2
Departement Physik, Theoretische Physik, Universität Basel, Klingelbergstr. 82, CH 4056 Basel, Switzerland
*
Author to whom correspondence should be addressed.
Academic Editor: Asterios Pantokratoras
Received: 22 March 2017 / Revised: 17 May 2017 / Accepted: 18 May 2017 / Published: 20 May 2017
(This article belongs to the Special Issue Convective Instability in Porous Media)
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Abstract

Recent interest in the effects of viscous dissipation on convective flows in porous media has centred almost exclusively on forced convection flows. In this paper, we investigate the manner in which it affects the onset and early stages of convection in Darcy–Bénard convection. A weakly nonlinear theory is described briefly, and it is shown that hexagonal cells are preferred over rolls when the Rayleigh number is sufficiently close to 4 π 2 . At higher Rayleigh numbers, two-dimensional rolls are preferred. When weak form drag is included, then subcritical convection eventually disappears as the Forchheimer parameter increases, yielding a highly novel situation wherein hexagonal convection arises supercritically. The range of stability of hexagons is found to increase. View Full-Text
Keywords: convection; porous, instability, weakly nonlinear, viscous dissipation, form drag convection; porous, instability, weakly nonlinear, viscous dissipation, form drag
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Rees, D.A.S.; Magyari, E. Hexagonal Cell Formation in Darcy–Bénard Convection with Viscous Dissipation and Form Drag. Fluids 2017, 2, 27.

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