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Conditional and unconditional nonlinear stability for convection induced by absorption of radiation in a porous medium

Hill, Antony A.

Authors

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Antony Hill Antony.Hill@uwe.ac.uk
College Dean of Learning and Teaching



Abstract

Convection induced by the selective absorption of radiation is investigated, for the case of an internal heat source that is modelled quadratically with respect to concentration. The growth rate for the linearised system is shown to be real, and a linear instability analysis is performed. To establish conditional and unconditional nonlinear stability results, both the Darcy and Forchheimer models are employed to describe fluid flow. Due to the presence of significant regions of potential subcritical instabilities, the results indicate that linear theory may only be accurate enough to predict the onset of convective motion when the model for the internal heat source is predominantly linear.

Citation

Hill, A. A. (2004). Conditional and unconditional nonlinear stability for convection induced by absorption of radiation in a porous medium. Continuum Mechanics and Thermodynamics, 16(4), 305-318. https://doi.org/10.1007/s00161-003-0151-3

Journal Article Type Article
Publication Date May 1, 2004
Journal Continuum Mechanics and Thermodynamics
Print ISSN 0935-1175
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 16
Issue 4
Pages 305-318
DOI https://doi.org/10.1007/s00161-003-0151-3
Keywords conditional nonlinear stability, unconditional nonlinear stability, compound matrix method
Public URL https://uwe-repository.worktribe.com/output/1065010
Publisher URL http://dx.doi.org/10.1007/s00161-003-0151-3