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Linear stability of a developing thermal front induced by a constant heat flux

Citation

Noghrehabadi, A and Rees, DAS and Bassom, AP, Linear stability of a developing thermal front induced by a constant heat flux, Transport in Porous Media, 99, (3) pp. 493-513. ISSN 0169-3913 (2013) [Refereed Article]

Copyright Statement

Copyright 2013 Springer Science+Business Media Dordrecht

DOI: doi:10.1007/s11242-013-0197-z

Abstract

A developing thermal front is set up by suddenly imposing a constant heat flux on the lower horizontal boundary of a semi-infinite fluid-saturated porous domain. The critical time for the onset of convection is determined using two main forms of analysis. The first of these is an approximate method which is effectively a frozen-time model while the second implements a set of parabolic simulations of monochromatic disturbances placed in the boundary layer at an early time. Results from the two approaches are compared and it is found that instability only occurs when the nondimensional disturbance wavenumber, k, is less than unity. The neutral curve for the primary mode possesses a vertical asymptote at k = 1 in wavenumber/time parameter space which is in contrast to the more usual teardrop shape which occurs when the surface is subject to a constant temperature. Asymptotic analyses are performed for the frozen-time model which yield excellent predictions for both branches of the neutral curve and the locus of the maximum growth rate curve at late times.

Item Details

Item Type:Refereed Article
Keywords:convective instabilities, linear theory, porous medium, boundary layer, thermal front, constant heat flux
Research Division:Mathematical Sciences
Research Group:Applied Mathematics
Research Field:Theoretical and Applied Mechanics
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Bassom, AP (Professor Andrew Bassom)
ID Code:105718
Year Published:2013
Web of Science® Times Cited:5
Deposited By:Mathematics and Physics
Deposited On:2016-01-13
Last Modified:2017-11-01
Downloads:0

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