IJPAM: Volume 67, No. 4 (2011)

EFFECT OF HEAT GENERATION ON THE ONSET OF
MARANGONI CONVECTION IN SUPERPOSED LAYERS
OF FLUID AND SATURATED POROUS MEDIUM

N.F.M. Mokhtar$^1$, N.M. Arifin$^2$, R. Nazar$^3$
F. Ismail$^4$, M. Suleiman$^5$
$^{1,2,4,5}$Department of Mathematics
Institute for Mathematical Research
Faculty of Science
University Putra Malaysia
Serdang, Selangor Darul Ehsan, 43400, MALAYSIA
$^1$e-mail: norihan@math.upm.edu.my
$^3$School of Mathematical Sciences
Faculty of Science and Technology
University Kebangsaan Malaysia
Bangi, Selangor Darul Ehsan, 43600, MALAYSIA


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 lower rigid surface and the upper non-deformable surface are assumed to be perfectly insulating. The critical eigenvalues are solved exactly and the asymptotic solution of the long wavelength is also obtained using regular perturbation technique. The effect of variation of different physical parameters on the onset of Marangoni convection in the presence of heat generation is investigated in details. The internal heating in the fluid layer and the porous layer are found to decrease the critical conditions.

Received: December 16, 2010

AMS Subject Classification: 76E06, 76E25

Key Words and Phrases: Marangoni convection, heat generation, porous medium

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 67
Issue: 4