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Adiabatic eigenflows in a vertical porous channel

Published online by Cambridge University Press:  22 May 2014

A. Barletta  and
L. Storesletten
A. Barletta*
Affiliation:
Department of Industrial Engineering, Alma Mater Studiorum Università di Bologna, Viale Risorgimento 2, 40136 Bologna, Italy
L. Storesletten
Affiliation:
Department of Mathematics, University of Agder, Postboks 422, 4604 Kristiansand, Norway
*
†Email address for correspondence: [email protected]
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Abstract

The existence of an infinite class of buoyant flows in a vertical porous channel with adiabatic and impermeable boundary walls, called adiabatic eigenflows, is discussed. A uniform heat source within the saturated medium is assumed, so that a stationary state is possible with a net vertical through-flow convecting away the excess heat. The simple isothermal flow with uniform velocity profile is a special adiabatic eigenflow if the power supplied by the heat source is zero. The linear stability analysis of the adiabatic eigenflows is carried out analytically. It is shown that these basic flows are unstable. The only exception, when the power supplied by the heat source is zero, is the uniform isothermal flow, which is stable. The existence of adiabatic eigenflows and their stability analysis is extended to the case of spanwise lateral confinement, viz. in the case of a vertical rectangular channel. A generalisation of this study to a vertical channel with an arbitrary cross-sectional shape is also presented.

JFM classification

Convection: Buoyancy-driven instability Convection: Convection in porous media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 749 , 25 June 2014 , pp. 778 - 793
Copyright
© 2014 Cambridge University Press 

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