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Nonlinear Stability for Thermal Convection in a Brinkman Porous Material with Viscous Dissipation

Straughan, Brian

Nonlinear Stability for Thermal Convection in a Brinkman Porous Material with Viscous Dissipation Thumbnail


Authors

Brian Straughan



Abstract

We investigate nonlinear stability in a model for thermal convection in a saturated porous material using Brinkman theory, taking into account viscous dissipation effects. There are (at least) two models for viscous dissipation available, and we include a derivation of one of these by assuming that the flow in the porous medium may be described by a theory for a mixture of an elastic solid and a linearly viscous fluid. A fully nonlinear stability result is provided when either of the viscous dissipation functions is taken into account, and it is shown that from the nonlinear energy stability viewpoint both models are, in a sense, equivalent.

Citation

Straughan, B. (2020). Nonlinear Stability for Thermal Convection in a Brinkman Porous Material with Viscous Dissipation. Transport in Porous Media, 134(2), 303-314. https://doi.org/10.1007/s11242-020-01446-5

Journal Article Type Article
Acceptance Date Jul 2, 2020
Online Publication Date Jul 17, 2020
Publication Date 2020-09
Deposit Date Jul 31, 2020
Publicly Available Date Jul 31, 2020
Journal Transport in Porous Media
Print ISSN 0169-3913
Electronic ISSN 1573-1634
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 134
Issue 2
Pages 303-314
DOI https://doi.org/10.1007/s11242-020-01446-5

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

Copyright Statement
Advance online version This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.





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