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The Effect of Conducting Boundaries on the Onset of Convection in a Porous LayerWhich is Heated from Below by Internal Heating

Mohammad, Afiqah Nadzirah and Rees, D. Andrew and Mojtabi, Abdelkader The Effect of Conducting Boundaries on the Onset of Convection in a Porous LayerWhich is Heated from Below by Internal Heating. (2017) Transport in Porous Media, 117 (2). 189-206. ISSN 0169-3913

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Official URL: https://doi.org/10.1007/s11242-017-0828-x

Abstract

The onset of convection in a porous layer heated from below is considered, and we determine how the presence of two solid but heat-conducting bounding plates of finite thickness alters the manner in which convection ensues. Heat is generated by the lower plate (with an insulating lower boundary), but the upper one is passive with a fixed upper boundary temperature. It is shown that this composite layer may mimic in turn one of the three different types of classical single-layer onset problems which are well-known in the literature. The type which is selected (or indeed whether it corresponds to a transitional case) depends quite critically on the precise values of the relative thickness of the solid layers and their conductivity ratio. It is also shown that care needs to be taken over declaring that the solid plates are thin: extreme values of the conductivity ratio can yield a stability criterion which appears to be different from that suggested by the imposed boundary conditions.

Item Type:Article
Additional Information:Thanks to Spinger editor. The definitive version is available at https://link.springer.com/ The original PDF of the article can be found at https://link.springer.com/article/10.1007%2Fs11242-017-0828-x
HAL Id:hal-01542773
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Other partners > University of Bath (UNITED KINGDOM)
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Deposited On:20 Jun 2017 08:19

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