## Convective instability in a horizontal porous channel with permeable and conducting side boundaries

##### Journal article, Peer reviewed

##### Permanent lenke

http://hdl.handle.net/11250/138205##### Utgivelsesdato

2013##### Metadata

Vis full innførsel##### Originalversjon

Barletta, A., Rossi di Schio, E., & Storesletten, L. (2013). Convective instability in a horizontal porous channel with permeable and conducting side boundaries. Transport in Porous Media. doi: 10.1007/s11242-013-0198-y 10.1007/s11242-013-0198-y##### Sammendrag

The stability analysis of the motionless state of a horizontal porous channel with
rectangular cross-section and saturated by a fluid is developed. The heating from below
is modelled by a uniform flux, while the top wall is assumed to be isothermal. The side
boundaries are considered as permeable and perfectly conducting. The linear stability of
the basic state is studied for the normal mode perturbations. The principle of exchange of
stabilities is proved, so that only stationary normalmodes need to be considered in the stability
analysis.The eigenvalue problem for the neutral stability condition is solved analytically, and
a closed-form dispersion relation is obtained for the neutral stability. The Darcy–Rayleigh
number is expressed as an implicit function of the longitudinalwave number and of the aspect
ratio. The critical wave number and the critical Darcy–Rayleigh number are evaluated for
different aspect ratios. The preferredmodes under critical conditions are detected. It is found
that the selected patterns of instability at the critical Rayleigh number are two-dimensional,
for slender or square cross-sections of the channel. On the other hand, instability is three
dimensional when the critical width-to-height ratio, 1.350517, is exceeded. Eventually, the
effects of a finite longitudinal length of the channel are discussed.

##### Beskrivelse

Published version of an article in the journal: Transport in Porous Media. Also available on Science Direct: http://dx.doi.org/10.1007/s11242-013-0198-y