Transport in Porous Media

, Volume 80, Issue 1, pp 137–151 | Cite as

On the Convection in a Porous Medium with Inclined Temperature Gradient and Vertical Throughflow. Part I. Normal Modes

Article

Abstract

In this analysis, we apply the methods of the theory of linear absolute and convective instabilities to studying the destabilization of transverse modes in a model of convection in an extended horizontal layer of a saturated porous medium with inclined temperature gradient and vertical throughflow. In this first part of the analysis, normal modes are treated and neutral curves are obtained for a variety of values of the horizontal Rayleigh number, Rh, and the Péclet number, Qv. The computations are performed by using a high-precision pseudo-spectral Chebyshev-collocation method. Our results compare well with the results found in the literature for the critical values of the vertical Rayleigh number. It is shown that the horizontal temperature gradient effect, inducing a Hadley circulation, is stabilizing for any fixed value of the throughflow velocity. The throughflow effect is stabilizing, for each of the values of Rh = 0, 10, 20, 30. For higher values of Rh = 40, 50, 60 considered, the influence of increasing throughflow on the stability is mixed. For a vanishing horizontal temperature gradient the critical normal mode is non-oscillatory, for all the values of throughflow. In all the cases of a non-zero horizontal temperature gradient and a non-zero throughflow considered, the critical normal mode is oscillatory, and the oscillatory frequency is an increasing function of both Rh and Qv.

Keywords

Saturated porous layer Darcy flow Inclined temperature gradient Vertical throughflow Stability of transverse modes 

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© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Institut de Mécanique des Fluides et des Solides—UMR 7507 ULP—CNRSUniversité de StrasbourgStrasbourgFrance
  2. 2.Department of Applied MathematicsUniversity of SheffieldSheffieldUK

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