A Nonlinear Stability Analysis of Convection in a Porous Vertical Channel Including Local Thermal Nonequilibrium

The problem is considered of thermal convection in a saturated porous medium contained in an infinite vertical channel with differentially heated sidewalls. The theory employed allows for different solid and fluid temperatures in the matrix. Nonlinear energy stability theory is used to derive a Rayl...

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Published inJournal of mathematical fluid mechanics Vol. 15; no. 1; pp. 171 - 178
Main Authors Scott, Nicola L., Straughan, B.
Format Journal Article
LanguageEnglish
Published Basel SP Birkhäuser Verlag Basel 01.03.2013
Springer Nature B.V
Subjects
Classical and Continuum Physics
Fluid- and Aerodynamics
Free convection
Mathematical Methods in Physics
Nonlinear analysis
Physics
Physics and Astronomy
Porous media
Rayleigh number
Stability analysis
76R10
Local thermal nonequilibrium
Porous vertical channel
Energy stability
76S05
80A20
Convection
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ISSN1422-6928
1422-6952
DOI10.1007/s00021-012-0109-y

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Summary:The problem is considered of thermal convection in a saturated porous medium contained in an infinite vertical channel with differentially heated sidewalls. The theory employed allows for different solid and fluid temperatures in the matrix. Nonlinear energy stability theory is used to derive a Rayleigh number threshold below which convection will not occur no matter how large the initial data. A generalized nonlinear analysis is also given which shows convection cannot occur for any Rayleigh number provided the initial data is suitably restricted.
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ISSN:1422-6928
1422-6952
DOI:10.1007/s00021-012-0109-y