Effect of internal heat generation on Marangoni convection in a superposed fluid-porous layer with deformable free surface

N. M. Mokhtar, N. M. Arifin, Roslinda Mohd. Nazar, F. Ismail, M. Suleiman

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Linear stability analysis is applied to investigate the effect of internal heat generation on Marangoni convection in a two-layer system comprising an incompressible fluid-saturated porous layer over which lies a layer of the same fluid. The upper free surface is deformable and is subject to a general thermal condition, while the lower boundary is rigid and is fixed at a constant temperature (isothermal) or a constant heat flux. The Beavers-Joseph condition is employed at the interface and the Forchheimerextended- Darcy equation is employed to describe the flow regime in the porous medium. The linear stability theory and the normal mode analysis are applied and the resulting eigenvalue problem is solved exactly. For both the upper and lower boundaries fixed at a constant heat flux, the analytical asymptotic solution of long wavelength is obtained using regular perturbation technique. It is observed that the critical Marangoni number decreases with an increase in the dimensionless heat source strength. However, an increase of the Bond number and the decrease of the Darcy number will help to slow the process of destabilizing the system.

Original languageEnglish
Pages (from-to)5550-5563
Number of pages14
JournalInternational Journal of Physical Sciences
Volume6
Issue number23
Publication statusPublished - 9 Oct 2011

Fingerprint

Marangoni convection
heat generation
Heat generation
Heat flux
Linear stability analysis
Perturbation techniques
Fluids
heat flux
fluids
Bond number
Porous materials
incompressible fluids
heat sources
Wavelength
eigenvalues
perturbation
wavelengths
Temperature
Hot Temperature
Convection

Keywords

  • Heat generation
  • Marangoni convection
  • Porous layer

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Electronic, Optical and Magnetic Materials

Cite this

Effect of internal heat generation on Marangoni convection in a superposed fluid-porous layer with deformable free surface. / Mokhtar, N. M.; Arifin, N. M.; Mohd. Nazar, Roslinda; Ismail, F.; Suleiman, M.

In: International Journal of Physical Sciences, Vol. 6, No. 23, 09.10.2011, p. 5550-5563.

Research output: Contribution to journalArticle

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