Hexagonal Cell Formation in Darcy–Bénard Convection with Viscous Dissipation and Form Drag
Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, UK
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
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
. 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.
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).
Scifeed alert for new publications
Never miss any articles
matching your research from any publisher
- Get alerts for new papers matching your research
- Find out the new papers from selected authors
- Updated daily for 49'000+ journals and 6000+ publishers
Define your Scifeed now
Share & Cite This Article
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.
Rees DAS, Magyari E. Hexagonal Cell Formation in Darcy–Bénard Convection with Viscous Dissipation and Form Drag. Fluids. 2017; 2(2):27.
Rees, D. A.S.; Magyari, Eugen. 2017. "Hexagonal Cell Formation in Darcy–Bénard Convection with Viscous Dissipation and Form Drag." Fluids 2, no. 2: 27.
Show more citation formats
Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
[Return to top]
Multiple requests from the same IP address are counted as one view.