Cookies

We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.


Durham Research Online
You are in:

Nonlinear stability for thermal convection in a Brinkman porous material with viscous dissipation.

Straughan, Brian (2020) 'Nonlinear stability for thermal convection in a Brinkman porous material with viscous dissipation.', Transport in porous media., 134 (2). pp. 303-314.

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.

Item Type:Article
Full text:(VoR) Version of Record
Available under License - Creative Commons Attribution.
Download PDF (Advance online version)
(959Kb)
Full text:(VoR) Version of Record
Available under License - Creative Commons Attribution.
Download PDF
(1246Kb)
Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1007/s11242-020-01446-5
Publisher statement: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/.
Date accepted:02 July 2020
Date deposited:31 July 2020
Date of first online publication:17 July 2020
Date first made open access:31 July 2020

Save or Share this output

Export:
Export
Look up in GoogleScholar