Bifurcation analysis for thermal convection in a rotating porous layer

I. S. Shivakumara, M. N. Savitha, Krishna B. Chavaraddi, N. Devaraju

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

The linear and weakly nonlinear thermal convection in a rotating porous layer is investigated by constructing a simplified model involving a system of fifth-order nonlinear ordinary differential equations. The flow in the porous medium is described by Lap wood-Brinkman-extended Darcy model with fluid viscosity different from effective viscosity. Conditions for the occurrence of possible bifurcations are obtained. It is established that Hopf bifurcation is possible only at a lower value of the Rayleigh number than that of simple bifurcation. In contrast to the non-rotating case, it is found that the ratio of viscosities as well as the Darcy number plays a dual role on the steady onset and some important observations are made on the stability characteristics of the system. The results obtained from weakly nonlinear theory reveal that, the steady bifurcating solution may be either sub-critical or supercritical depending on the choice of physical parameters. Heat transfer is calculated in terms of Nusselt number.

Original languageEnglish
Pages (from-to)225-238
Number of pages14
JournalMeccanica
Volume44
Issue number3
DOIs
Publication statusPublished - 01-06-2009
Externally publishedYes

Fingerprint

free convection
Viscosity
viscosity
Hopf bifurcation
Bifurcation (mathematics)
Rayleigh number
Nusselt number
Ordinary differential equations
Porous materials
Wood
differential equations
heat transfer
occurrences
Heat transfer
Fluids
fluids
Convection
Hot Temperature

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Shivakumara, I. S., Savitha, M. N., Chavaraddi, K. B., & Devaraju, N. (2009). Bifurcation analysis for thermal convection in a rotating porous layer. Meccanica, 44(3), 225-238. https://doi.org/10.1007/s11012-008-9163-1
Shivakumara, I. S. ; Savitha, M. N. ; Chavaraddi, Krishna B. ; Devaraju, N. / Bifurcation analysis for thermal convection in a rotating porous layer. In: Meccanica. 2009 ; Vol. 44, No. 3. pp. 225-238.
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Shivakumara, IS, Savitha, MN, Chavaraddi, KB & Devaraju, N 2009, 'Bifurcation analysis for thermal convection in a rotating porous layer', Meccanica, vol. 44, no. 3, pp. 225-238. https://doi.org/10.1007/s11012-008-9163-1

Bifurcation analysis for thermal convection in a rotating porous layer. / Shivakumara, I. S.; Savitha, M. N.; Chavaraddi, Krishna B.; Devaraju, N.

In: Meccanica, Vol. 44, No. 3, 01.06.2009, p. 225-238.

Research output: Contribution to journalArticle

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Shivakumara IS, Savitha MN, Chavaraddi KB, Devaraju N. Bifurcation analysis for thermal convection in a rotating porous layer. Meccanica. 2009 Jun 1;44(3):225-238. https://doi.org/10.1007/s11012-008-9163-1