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

Aminreza Noghrehabadi, D. Andrew S. Rees, Andrew P. Bassom

Research output: Contribution to journalArticle

8 Citations (Scopus)

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, {Mathematical expression}, is less than unity. The neutral curve for the primary mode possesses a vertical asymptote at {Mathematical expression} 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.
Original languageEnglish
Pages (from-to)493-513
JournalTransport in Porous Media
Volume99
Issue number3
Early online date17 Jul 2013
DOIs
Publication statusPublished - Sep 2013

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