Effect of internal heat generation on the onset of Brinkman-Benard convection in a ferrofluid saturated porous layer

C. E. Nanjundappa, I. S. Shivakumara, Jinho Lee, M. Ravisha

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

The effect of internal heat generation on the criterion for the onset of convection in a horizontal ferrofluid saturated porous layer in the presence of a uniform magnetic field is studied using the Brinkman-Lapwood extended Darcy flow model with fluid viscosity different from effective viscosity. The lower boundary is taken to be rigid - isothermal and the upper surface is free and subject to the general thermal condition. The resulting eigenvalue problem is solved numerically using the Galerkin method with the Rayleigh number as the eigenvalue. The stability of the system is found to be dependent on the dimensionless internal heat source strength Ns, Darcy number Da, viscosity ratio Λ, Biot number Bi, magnetic Rayleigh number, R m and the nonlinearity of fluid magnetization parameter M 3. The effect of increase in the value of Rm, N s and M3 is to hasten, while increase in the value of Bi, Λ and Da-1 is to delay the onset of thermomagnetic convection in a ferrofluid saturated porous layer. Further, increase in the value of Bi, Da-1 and Ns as well as decrease in Λ, Rm and M3 is to diminish the dimension of convection cells.

Original languageEnglish
Pages (from-to)160-168
Number of pages9
JournalInternational Journal of Thermal Sciences
Volume50
Issue number2
DOIs
Publication statusPublished - 2011 Feb 1

Fingerprint

Magnetic fluids
ferrofluids
heat generation
Heat generation
convection
Viscosity
Rayleigh number
viscosity
eigenvalues
Biot number
convection cells
Fluids
fluids
Galerkin method
Galerkin methods
heat sources
Magnetization
nonlinearity
Magnetic fields
magnetization

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Engineering(all)

Cite this

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abstract = "The effect of internal heat generation on the criterion for the onset of convection in a horizontal ferrofluid saturated porous layer in the presence of a uniform magnetic field is studied using the Brinkman-Lapwood extended Darcy flow model with fluid viscosity different from effective viscosity. The lower boundary is taken to be rigid - isothermal and the upper surface is free and subject to the general thermal condition. The resulting eigenvalue problem is solved numerically using the Galerkin method with the Rayleigh number as the eigenvalue. The stability of the system is found to be dependent on the dimensionless internal heat source strength Ns, Darcy number Da, viscosity ratio Λ, Biot number Bi, magnetic Rayleigh number, R m and the nonlinearity of fluid magnetization parameter M 3. The effect of increase in the value of Rm, N s and M3 is to hasten, while increase in the value of Bi, Λ and Da-1 is to delay the onset of thermomagnetic convection in a ferrofluid saturated porous layer. Further, increase in the value of Bi, Da-1 and Ns as well as decrease in Λ, Rm and M3 is to diminish the dimension of convection cells.",
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Effect of internal heat generation on the onset of Brinkman-Benard convection in a ferrofluid saturated porous layer. / Nanjundappa, C. E.; Shivakumara, I. S.; Lee, Jinho; Ravisha, M.

In: International Journal of Thermal Sciences, Vol. 50, No. 2, 01.02.2011, p. 160-168.

Research output: Contribution to journalArticle

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