A bifurcation study of natural convection in porous media with internal heat sources: The non-Darcy effects

Eungsoo Choi; A. Chakma; K. Nandakumar

doi:10.1016/S0017-9310(97)00127-0

A bifurcation study of natural convection in porous media with internal heat sources: The non-Darcy effects

Eungsoo Choi, A. Chakma, K. Nandakumar^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

Abstract

Multiplicity features of natural convection flow in porous media, generated and sustained by a uniform internal heat source are investigated. The flow, in a two-dimensional enclosure, is described by the Brinkman's extension of the Darcy equation. No-slip boundary conditions are used. The focus is on the role of the Brinkman viscous term in influencing the location of singular points. The behavior of the system is regulated by two control parameters, the Rayleigh number (the dynamic parameter) and the Darcy number. The singular solutions are constructed using algorithms from bifurcation theory. Multiple solutions consisting of symmetric and nonsymmetric solution branches, are revealed as the control parameters change. The range of the Rayleigh number for which a unique solution exists is enlarged when the Darcy number is increased.

Original language	English
Pages (from-to)	383-392
Number of pages	10
Journal	International Journal of Heat and Mass Transfer
Volume	41
Issue number	2
DOIs	https://doi.org/10.1016/S0017-9310(97)00127-0
State	Published - Jan 1998
Externally published	Yes

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title = "A bifurcation study of natural convection in porous media with internal heat sources: The non-Darcy effects",

abstract = "Multiplicity features of natural convection flow in porous media, generated and sustained by a uniform internal heat source are investigated. The flow, in a two-dimensional enclosure, is described by the Brinkman's extension of the Darcy equation. No-slip boundary conditions are used. The focus is on the role of the Brinkman viscous term in influencing the location of singular points. The behavior of the system is regulated by two control parameters, the Rayleigh number (the dynamic parameter) and the Darcy number. The singular solutions are constructed using algorithms from bifurcation theory. Multiple solutions consisting of symmetric and nonsymmetric solution branches, are revealed as the control parameters change. The range of the Rayleigh number for which a unique solution exists is enlarged when the Darcy number is increased.",

author = "Eungsoo Choi and A. Chakma and K. Nandakumar",

note = "Funding Information: Acknowledgement-The financial support provided National Sciences and Engineering Research Council ada is gratefully acknowledged.",

year = "1998",

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T1 - A bifurcation study of natural convection in porous media with internal heat sources

T2 - The non-Darcy effects

AU - Choi, Eungsoo

AU - Chakma, A.

AU - Nandakumar, K.

N1 - Funding Information: Acknowledgement-The financial support provided National Sciences and Engineering Research Council ada is gratefully acknowledged.

PY - 1998/1

Y1 - 1998/1

N2 - Multiplicity features of natural convection flow in porous media, generated and sustained by a uniform internal heat source are investigated. The flow, in a two-dimensional enclosure, is described by the Brinkman's extension of the Darcy equation. No-slip boundary conditions are used. The focus is on the role of the Brinkman viscous term in influencing the location of singular points. The behavior of the system is regulated by two control parameters, the Rayleigh number (the dynamic parameter) and the Darcy number. The singular solutions are constructed using algorithms from bifurcation theory. Multiple solutions consisting of symmetric and nonsymmetric solution branches, are revealed as the control parameters change. The range of the Rayleigh number for which a unique solution exists is enlarged when the Darcy number is increased.

AB - Multiplicity features of natural convection flow in porous media, generated and sustained by a uniform internal heat source are investigated. The flow, in a two-dimensional enclosure, is described by the Brinkman's extension of the Darcy equation. No-slip boundary conditions are used. The focus is on the role of the Brinkman viscous term in influencing the location of singular points. The behavior of the system is regulated by two control parameters, the Rayleigh number (the dynamic parameter) and the Darcy number. The singular solutions are constructed using algorithms from bifurcation theory. Multiple solutions consisting of symmetric and nonsymmetric solution branches, are revealed as the control parameters change. The range of the Rayleigh number for which a unique solution exists is enlarged when the Darcy number is increased.

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A bifurcation study of natural convection in porous media with internal heat sources: The non-Darcy effects

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