Marangoni Convection in a Relatively Hotter or Cooler Liquid Layer
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences - Tập 82 - Trang 103-106 - 2012
Tóm tắt
The onset of cellular convection induced by surface tension gradients on a thin layer of liquid as developed by Pearson (J Fluid Mech 4: 489–500, 1958[6]) is examined in the extended framework of Banerjee et al. (J Math Phys Sci 17: 603–629, 1983[11]). Numerical results are obtained for both the thermally conducting and insulating cases of the lower boundary surface. It is found that irrespective of the nature (conducting or insulating) of the lower boundary surface the critical Marangoni number does significantly depend upon whether the liquid layer is relatively hotter or cooler.
Tài liệu tham khảo
Bénard H (1900) Les tourbillons cellulaires dans une nappe liquide. Revue générale des Sciences pures et appliqués 11:1261–1271
Bénard H (1901) Les tourbillons cellulaires dans une nappe liquide transportant de la chaleur par convection en régime permanent. Annales de Chimie et de Physique 23:62–144
Rayleigh L (1916) On convection currents in a horizontal layer of fluid, when the higher temperature is on the underside. Phil Mag 32:529–546
Chandrasekhar S (1961) Hydrodynamic and hydromagnetic Stability. Clarendon Press, Oxford
Block MJ (1956) Surface tension as the cause of Bénard cells and surface deformation in a liquid film. Nature 178:650–651
Pearson JRA (1958) On convection cells induced by surface tension. J Fluid Mech 4:489–500
Nield DA (1964) Surface tension and buoyancy effects in cellular convection. J Fluid Mech 19:341–352
Koschmieder EL (1993) Bénard cells and taylor vortices. Cambridge University Press, Cambridge
Normand C, Pomeau Y, Velarde M (1977) Convective instability: a physicists approach. Rev Mod Phys 49:581–624
Schatz MF, VanHook SJ, McCormick WD, Swift JB, Swinney HL (1995) Onset of surface- tension- driven Bénard convection. Phys Rev Lett 75:1938–1941
Banerjee MB, Gupta JR, Shandil RG, Sharma KC, Katoch DC (1983) A modified analysis of thermal and thermohaline instability of a liquid layer heated underside. J Math Phys Sci 17:603–629
Banerjee MB, Gupta JR (1991) Studies in hydrodynamic and hydromagnetic stability. Silver Line Publications, Shimla