Onset of surface-tension-driven convection in superposed layers of fluid and saturated porous medium

• Autorzy: Shivakumara I. S. , Suma S. P. , Chavaraddi K. B.
• Języki publikacji: EN

Abstrakty

EN

The onset of surface-tension-driven convection is studied 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 of the porous layer is either perfectly heat conducting or insulating, while the upper heat insulating fluid boundary is free and at which the surface tension effects are allowed for. At the contact surface between the fluid-saturated porous medium and the adjacent bulk fluid, both Beavers-Joseph and the Jones conditions are employed. The resulting eigenvalue problem is solved exactly. Besides, analytical expression for the critical Marangoni number is obtained for insulating boundaries by using regular perturbation technique. The effect of variation of different physical parameters on the onset of Marangoni convection is investigated in detail. It is found that the parameter ..., the ratio of the thickness of the fluid layer to that of the porous layer, has a profound effect on the stability of the system.

Słowa kluczowe

EN

critical Marangoni number; fluid; saturated porous medium; Marangoni convection; perturbation technique

PL

krytyczna liczba Marangoniego; płyn; nasycony ośrodek porowaty; konwekcja Marangoniego; technika zakłóceń

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Archives of Mechanics
• Rocznik: 2006
• Tom: Vol. 58, nr 2
• Strony: 71--92
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

Shivakumara I. S.

autor

Suma S. P.

autor

Chavaraddi K. B.

• UGC-CAS in Fluid Mechanics Department of Mathematics, Bangalore University, Bangalore-560 001, India,

Bibliografia

• 1. J.R.A. PEARSON, On convection cell induced by surface tension, J. Fluid Mech., 4, 489-500, 1958.
• 2. D.A. NIELD, Surface tension and buoyancy effect in cellular convection, J. Fluid Mech., 19,341-352, 1965.
• 3. N. RUDRAIAH, V. RAMACHANDRAMURTHY, O.P. CHANDNA, Effects ofmagnetic field and non-uniform temperature gradient on Marangoni convection, Int. J. Heat Mass Transfer, 28,1621-1624,1985.
• 4. M.I. CHAR, C.C. CHEN, Effect of non-uniform temperature gradient on the onset of oscillatory Benard-Marangoni convection of an electrically conducting liquid in a magnetic field, Int. J. Engg. Sci., 41, 1711-1727, 2003.
• 5. D.A. NIELD, A. BEJAN, Convection in porous media, 2nd Edition, Springer-Verlag, New York 1999.
• 6. K. VAFAI, Handbook of porous media, Marcel Dekker, New York 2000.
• 7. M. HENNENBERG, M.Z. SAGHIR, A. REDNIKOV, J.C. LEGROS, Porous media and the Benard-Marangoni problem, Transp. Porous Media, 27, 327-355, 1997.
• 8. N. RUDRAIAH, V. PRASAD, Effect of Brinkman boundary layer on the onset of Marangoni convection in a fluid saturated porous layer, Acta Mechanica, 127, 235-246, 1998.
• 9. D.A. NIELD, Onset of convection in a fluid layer overlying a layer of a porous medium, J. Fluid Mech., 81, 513-522, 1977.
• 10. M.E. TASLIM, V. NARUSAWA, Thermal stability of horizontally superposed porous and fluid layers, ASME J. Heat Transfer, 111, 357-362, 1989.
• 11. G. McKAY, Onset of buoyancy-driven convection in superposed reacting fluid and porous layers, J. Engg. Math., 33, 31-46, 1998.
• 12. B. STRAUGHAN, Surface-tension-driven convection in a fluid overlying a porous layer, Comput. Phys., 170, 320-337, 2001.
• 13. B. STRAUGHAN, Effect of property variation and modelling on convection in a fluid overlying a porous layer, J. Numer. Analyt. Meth. Geomech., 26, 75-97, 2002.
• 14. F. CHEN, Throughflow effects on convective instability in superposed fluid and porous j layers, J. Fluid Mech., 23, 113-133, 1990.
• 15. A. KHALILI, I.S. SHIVAKUMARA, S.P. SUMA, Convective instability in superposed fluid and porous layers with vertical throughflow, Transp. Porous Media, 51, 1-18, 2001.
• 16. T.H. DESAIVE, G. LEBON, M.H. HENNENBERG, Coupled capillary and gravity driven instability in a liquid film overlying a porous layer, Physical Review E, 64, 66304-66308, 2001.
• 17. M. CARR, Penetrative convection in a superposed porous-medium-fluid layer via internal heating, J. Fuid Mech, 509, 305-329, 2004.
• 18. D.A. NIELD, Modelling the effect of surface tension on the onset of natural convection in * a saturated porous medium, Transp. Porous Media, 31, 365-368, 1998.
• 19. G.S. BEAVERS, D.D. JOSEPH, Boundary conditions at a naturally permeable wall, g J. Fluid Mech. 30, 197-207, 1967.
• 20. M. CIESZKO, J. KUBIK, Derivation of matching conditions at the surface between fluid-satuarated porous solid and bulk fluid, Transp. Porous Media, 34, 319-336, 1999.
• 21. I.P. JONES, Low Reynolds number flow past a porous spherical shell, Proc. Camb. Phil. Soc., 73, 231-238, 1973.
• 22. A. VIDAL, A. ACRIVOS, Nature of the neutral state in surface tension driven convection, Phys. Fluids, 9, 615-616, 1966.