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

被引：0
作者：
Brian Straughan
机构：
[1] University of Durham,Department of Mathematics
来源：
Transport in Porous Media | 2020年 / 134卷
关键词：
Nonlinear stability; Viscous dissipation; Thermal convection; Brinkman porous media;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
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页码：303 / 314
页数：11
相关论文
共 55 条
[1]  
Al-Hadrami AK(2003)A new model for viscous dissipation in porous media across a range of permeability values Trans. Por. Med. 53 117-122
[2]  
Elliott L(2008)Comments on a paradox of viscous dissipation and its relation to the Oberbeck—Boussinesq approach Int. J. Heat Mass Transf. 51 6312-6316
[3]  
Ingham DB(2020)The energy method analysis of the Darcy - Bénard problem with viscous dissipation Contin. Mech. Thermodyn. 40 1-492
[4]  
Barletta A(2010)Convection—dissipation instability in the horizontal plane Couette flow of a highly viscous fluid J. Fluid Mech. 662 475-1648
[5]  
Barletta A(2011)Thermosolutal convective instability and viscous dissipation effect in a fluid-saturated porous medium Int. J. Heat Mass Transf. 54 1641-344
[6]  
Mulone G(2009)The onset of convection in a porous layer induced by viscous dissipation: a linear stability analysis Int. J. Heat Mass Transf. 52 337-1627
[7]  
Barletta A(2009)Darcy - Forchheimer flow with viscous dissipation in a horizontal porous layer: onset of convective instabilities ASME J. Heat Transf. 131 072602-344-514
[8]  
Nield DA(2010)Unstably stratified Darcy flow with impressed horizontal temperature gradient, viscous dissipation and asymmetric thermal boundary conditions Int. J. Heat Mass Transf. 53 1621-119
[9]  
Barletta A(2011)On the onset of dissipation thermal instability for the Poiseuille flow of a highly viscous fluid in a horizontal channel J. Fluid Mech. 681 499-12
[10]  
Nield DA(2011)Instability and viscous dissipation in the horizontal Brinkman flow through a porous medium Trans. Por. Med. 85 105-1349
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