Marangoni Convection in a Fluid Saturated Porous Layer with a Deformable Free Surface

Authors: Nor Fadzillah Mohd Mokhtar, Norihan Md Arifin, Roslinda Nazar, Fudziah Ismail, MohamedSuleiman

Abstract:

The stability analysis of Marangoni convection in porous media with a deformable upper free surface is investigated. The linear stability theory and the normal mode analysis are applied and the resulting eigenvalue problem is solved exactly. The Darcy law and the Brinkman model are used to describe the flow in the porous medium heated from below. The effect of the Crispation number, Bond number and the Biot number are analyzed for the stability of the system. It is found that a decrease in the Crispation number and an increase in the Bond number delay the onset of convection in porous media. In addition, the system becomes more stable when the Biot number is increases and the Daeff number is decreases.

Keywords: Deformable, Marangoni, Porous, Stability.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1061830

References:

[1] Horton,C.W, & Rogers, F.T., Jr., "Convective Currents in a Porous Medium". J. App. Phys., 1945, pp. 367 - 370.
[2] Lapwood, E.R., "Convective of a Fluid in a Porous Medium". Proc. Camb. Phl. Soc. 1948, pp. 508 - 521.
[3] Pearson, J.R.A., "On Convection Cells induced by surface Tension", J. Fluid Mech., 1958, pp. 489-500.
[4] Sparrow,E.M, Goldstein,R.J, & Jonsson,V.K., "Thermal Instability in a Horizontal Fluid layer : Effect of Boundary Conditions and Non Linear Temperature Profile", J. Fluid Mech., 1964, pp. 513 - 528.
[5] Scriven,L. & Sternling,C., "On Cellular Convection Driven by Surface Tension Gradients : Effect of Mean Surface Viscosity", J. Fluid Mech, 1964, pp. 321-340.
[6] Nield D.A., "Surface Tension and Buoyancy Effect in Cellular Convection", J. Fluid Mech., 1965, pp. 341-352
[7] Katto,Y., and Masuoka,T., "Criterion for the Onset of Convective Flow in a Fluid in a Porous Medium", International Journal of Heat and Mass Transfer, 1967, pp. 297 - 309.
[8] Gupta V. P, & Joseph D. H, "Bounds for Heat Transport in a Porous layer", J. Fluid Mech.,1973, pp.491 - 514
[9] Gasser, R. D. and Kazimi, M. S. "Onset of Convection in a Porous Medium with Internal Heat Generation". Fast Reactor Safety Division, Department of Applied Science, Brookhaven National Laboratory, Upto, New York. Journal of Heat Transfer, 1976, pp. 49 - 54.
[10] Nield, D.A., " Onset of Convection in a Fluid Layer overlying a layer of porous layer". J. Fluid Mech.1977, pp. 513-522 .
[11] 11Davis S.H & Homsy G.M.," Energy Stability Theory for free-surface Problem: Buoyancy-thermocapillary layers". J. Fluid Mech., 1980, pp. 527-530.
[12] Pillatsis, G., Talim, M. E. and Narusawa, U. "Thermal instability of a Fluid-Saturated Porous Medium Bounded by Thin Fluid Layer". ASME J. Heat Transfer, 1987, pp. 677-682.
[13] Taslim, M. E. and Narusawa,V., "Thermal stability of horizontally superposed porous and fluid layers" , ASME J. Heat Transfer, 1989, pp. 357-362.
[14] Perez-Garcia C. & Carneiro G., "Linear Stability Analysis of Benard- Marangoni convection in Fluids with a Deformable Free Surface", Phys Fluids A, 1991, pp. 292-298.
[15] Ming-I Charand Ko-Ta Chiang. "Stability Analysis of Benard- Marangoni Convection in Fluids with Internal Heat Generation", J. Phys. D: Appl. Phys., 1994, pp. 748 - 755.
[16] M. Hennenberg, M. Ziad Saghir, A. Rednikov and J.C. Legros., "Porous Media and the Benard-Marangoni Problem". Transport in Porous Media. 1997, pp. 327 - 355.
[17] Shivakumara, I. S., and Chavaraddi, K. B., " Marangoni convection in a composite Porous layer and a fluid layer with a Deformable Free Surface", International Journal of Fluid Mechanics Research,, 2007, pp. 352 - 373.