## Effect of a finite external heat transfer coefficient on the Darcy-Benard instability in a vertical porous cylinder

##### Journal article, Peer reviewed

##### Permanent lenke

http://hdl.handle.net/11250/138203##### Utgivelsesdato

2013##### Metadata

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##### Originalversjon

Barletta, A., & Storesletten, L. (2013). Effect of a finite external heat transfer coefficient on the Darcy-Benard instability in a vertical porous cylinder. Physics of Fluids, 25(4), 14 p. doi: 10.1063/1.4799253 10.1063/1.4799253##### Sammendrag

The onset of thermal convection in a vertical porous cylinder is studied by considering the heating from below and the cooling from above as caused by external forced convection processes. These processes are parametrised through a finite Biot number, and hence through third-kind, or Robin, temperature conditions imposed on the lower and upper boundaries of the cylinder. Both the horizontal plane boundaries and the cylindrical sidewall are assumed to be impermeable; the sidewall is modelled as a thermally insulated boundary. The linear stability analysis is carried out by studying separable normal modes, and the principle of exchange of stabilities is proved. It is shown that the Biot number does not affect the ordering of the instability modes that, when the radius-to-height aspect ratio increases, are displayed in sequence at the onset of convection. On the other hand, the Biot number plays a central role in determining the transition aspect ratios from one mode to its follower. In the limit of a vanishingly small Biot number, just the first (non-axisymmetric) mode is displayed at the onset of convection, for every value of the aspect ratio. (C) 2013 American Institute of Physics

##### Beskrivelse

Publised version of an article from the journal: Physics of Fluids. Copyright (2013) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. Article appears in Volume 25 issue 4 of the journal: http://dx.doi.org/10.1063/1.4799253