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The stability of a developing thermal front in a porous medium. I linear theory


Reference:

Selim, A. and Rees, D. A. S., 2007. The stability of a developing thermal front in a porous medium. I linear theory. Journal of Porous Media, 10 (1), pp. 1-15.

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Abstract

In this paper, we analyze the stability of the developing thermal boundary layer that is induced by suddenly raising the temperature of the lower horizontal boundary of a uniformly cold semi-infinite porous domain. A full linear stability analysis is developed, and it is shown that disturbances are governed by a parabolic system of equations. Numerical solutions of this system are compared with the neutral stability curve obtained by approximating the system as an ordinary differential eigenvalue problem. Different criteria are used to mark the onset of convection of an evolving disturbance, namely, the maximum disturbance temperature, the surface rate of heat transfer, and the disturbance energy. It is found that these different measures yield different neutral curves. We also show that the disturbances have a favoured evolutionary path in the sense that disturbances introduced at different times or with different initial profiles eventually tend toward that common path. Copyright © 2006 Begell House, Inc.

Details

Item Type Articles
CreatorsSelim, A.and Rees, D. A. S.
DOI10.1615/JPorMedia.v10.i1.10
Uncontrolled Keywordsthermodynamic stability, eigenvalues and eigenfunctions, boundary layers, approximation theory, porous materials, heat transfer, differential equations
DepartmentsFaculty of Engineering & Design > Mechanical Engineering
Research CentresAerospace Engineering Research Centre
RefereedYes
StatusPublished
ID Code1501

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