Marangoni convection in a relatively hotter or cooler liquid layer with free boundaries

• Autorzy: Gupta A. K. , Shandil R. G.

Identyfikatory

DOI

10.2478/ijame-2013-0035

• Języki publikacji: EN

Abstrakty

EN

In this paper, we study the onset of cellular convection in a horizontal fluid layer heated from below, with a free-slip boundary condition at the bottom when the driving mechanism is surface tension at the upper free surface, in the light of the modified analysis of Banerjee et al. (Jour. Math. & Phys. Sci., 1983, 17, 603). This leads to a formulation of the problem which depends upon whether the liquid layer is relatively hotter or cooler. It is found that the phenomenon of surface tension driven instability problems should not only depend upon the Marangoni number which is proportional to the maintained temperature differences across the layer but also upon another parameter that arises due to variation in the specific heat at constant volume on account of the variations in temperature. Numerical results are obtained for the problem wherein the lower free boundary is perfectly thermally conducting.

Słowa kluczowe

EN

surface tension; convection; conducting; linear stability

PL

napięcie powierzchniowe; konwekcja; przewodzenie; stabilność liniowa

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2013
• Tom: Vol. 18, no. 2
• Strony: 581--588
• Opis fizyczny: Bibliogr. 12 poz., tab., wykr.

Twórcy

autor

Gupta A. K.

• Himachal Pradesh University, Centre for Evening Studies Shimla-171001, India

autor

Shandil R. G.

• Department of Mathematics, Himachal Pradesh University Shimla-171005, India

Bibliografia

• Banerjee M.B., Gupta J.R., Shandil R.G., Sharma K.C. and Katoch D.C. (1983): A modified analysis of thermal andthermohaline instability of a liquid layer heated underside. - Jour. Math. and Phys. Sci., vol.17, pp.603-629.
• Bénard H. (1901): Les tourbillons cellulaires dans une napple liquide transportant de la chaleur par cinvection enrégime permanent. - Ann. Chimie (Paris)., vol.23, pp.62-144.
• Boeck T. and Thess A. (1997): Inertial Bénard-Marangoni convection. - J. Fluid Mech., vol.350, pp.149-175.
• Chandrashekhar S. (1961): Hydrodynamic and Hydromagnetic Stability. - London: Oxford University Press.
• Gupta A.K. and Shandil R.G. (2011a): Nature of neutral state in Marangoni convection in relatively hotter or coolerliquid layer with free boundaries, In: Recent Advances in Continuum Mechanics and Algebra (M.G. Gorla, 2011). - New Delhi: Regal publications.
• Gupta A.K. and Shandil R.G. (2011b): Marangoni convection in a relatively hotter or cooler liquid layer. - Nat. Acad. Sci. India, Accepted for publication..
• Nield D.A. (1964): Surface tension and buoyancy effects in cellular convection. - J. Fluid Mech., vol.19, pp.341-352.
• Pearson J.R.A. (1958): On convection cells induced by surface tension. - J. Fluid Mech., vol.4, pp.489-500.
• Rayleigh L. (1916): On convection currents in a horizontal layer of fluid, when the higher temperature is on theunderside. - Phil. Mag., vol.32, No.6, pp.529-546.
• Takashima M. (1970): Nature of the neutral state in convective instability induced by surface tension and buoyancy. - J. Phys. Soc. Jpn., vol.28, pp.810.
• Takashima M. (1981): Surface tension driven instability in a horizontal liquid layer with deformable free surface: I.Stationary convection. - J. Phys. Soc. Jpn., vol.50, pp.2745-2750.
• Vidal A. and Acrivos A. (1966): Nature of the neutral state in surface tension driven convection. - Phys. Fluids., vol.9, No.3, pp.615-616.