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Resonant Penetrative Convection with an Internal Heat Source/Sink

Straughan, Brian

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Brian Straughan


We develop a detailed linear instability and nonlinear stability analysis for the situation of convection in a horizontal plane layer of fluid when there is a heat sink/source which is linear in the vertical coordinate which is in the opposite direction to gravity. This can give rise to a scenario where the layer effectively splits into three sublayers. In the lowest one the fluid has a tendency to be convectively unstable while in the intermediate layer it will be gravitationally stable. In the top layer there is again the possibility for the layer to be unstable. This results in a problem where convection may initiate in either the lowest layer, the upmost layer, or perhaps in both sublayers simultaneously. In the last case there is the possibility of resonance between the upmost and lowest layers. In all cases penetrative convection may occur where convective movement in one layer induces motion in an adjacent sublayer. In certain cases the critical Rayleigh number for thermal convection may display a very rapid increase which is much greater than normal. Such behaviour may have application in energy research such as in thermal insulation.


Straughan, B. (2014). Resonant Penetrative Convection with an Internal Heat Source/Sink. Acta Applicandae Mathematicae, 132(1), 561-581.

Journal Article Type Article
Acceptance Date Jan 14, 2014
Online Publication Date Jun 4, 2014
Publication Date Jun 4, 2014
Deposit Date Dec 6, 2018
Publicly Available Date Dec 6, 2018
Journal Acta Applicandae Mathematicae
Print ISSN 0167-8019
Electronic ISSN 1572-9036
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 132
Issue 1
Pages 561-581


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