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Non-linear stability bounds for a horizontal layer of a porous medium with an exothermic reaction on the lower boundary

Scott, Nicola L.

Non-linear stability bounds for a horizontal layer of a porous medium with an exothermic reaction on the lower boundary Thumbnail


Authors

Nicola L. Scott



Abstract

We use the energy method to find regions of stability for a horizontal layer of a Darcy porous medium with an exothermic reaction on the lower layer. The results are compared to the linear instability results for this model found by Scott and Straughan [16]. It is shown that there is a region in which sub-critical instabilities may occur, but for small Lewis numbers, 0<Le<100<Le<10, the non-linear stability boundary is reasonably close to the linear instability boundary. The effect of varying the parameters of the reaction on the stability curve is discussed.

Citation

Scott, N. L. (2013). Non-linear stability bounds for a horizontal layer of a porous medium with an exothermic reaction on the lower boundary. International Journal of Non-Linear Mechanics, 57, 163-167. https://doi.org/10.1016/j.ijnonlinmec.2013.07.004

Journal Article Type Article
Publication Date Dec 1, 2013
Deposit Date Jun 24, 2013
Publicly Available Date Aug 30, 2013
Journal International Journal of Non-Linear Mechanics
Print ISSN 0020-7462
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 57
Pages 163-167
DOI https://doi.org/10.1016/j.ijnonlinmec.2013.07.004
Keywords Porous media, Convection, Non-linear, Energy method, Exothermic reaction, Stability.

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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/

Copyright Statement
This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and
reproduction in any medium, provided the original author and source are credited.




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