Summary
The effect of throughflow on the onset of Marangoni convection in a horizontal layer of micropolar fluid flow bounded below by a rigid isothermal surface and above by a nondeformable free adiabatic surface, for marginal state, is studied. The determination of the critical Marangoni number entails solving the eigenvalue problem numerically for which the Single-term Galerkin method is employed.
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References
Napolitano, L. G.: Marangoni convection in space. Micrograv. Environ. Sci.225, 197–198 (1984).
Zierep, J., Oertel, Jr.: Convective transport and instability phenomena. Karlsruhe: G. Braun 1982.
Ostrach, S.: The influence of convection in continuous flow electrophoresis. ESA Special Publication114, 141–147 (1979).
Scriven, L. E., Sternling, C. V.: On cellular convection driven by surface tension gradients: effects of mean surface tension and surface viscosity. J. Fluid Mech.19, 321–340 (1964).
Smith, K. A.: On convective instability induced by surface tension gradients. J. Fluid Mech.24, 401–414 (1966).
Nield, D. A.: The onset of transient convective instability. J. Fluid Mech.71, 441–454 (1975).
Friedrich, R., Rudraiah, N.: Marangoni convection in a rotating fluid layer with non-uniform temperature gradient. Int. J. Heat Mass Transfer27, 443–449 (1984).
Vidal, A., Acrivos, A.: Nature of the neutral state in surface tension driven convection. Phys. Fluids9, 615–616 (1966).
Debler, W. R., Wolf, L. F.: The effects of gravity and surface tension gradients on cellular convection in fluid layers with parabolic temperature profiles. Trans. ASME, Series C, J. Heat Transfer92, 351–358 (1970).
McConaghy, G. A., Finlayson, B. A.: Surface tension driven oscillatory instability in a rotating fluid layer. J. Fluid Mech.39, 49–55 (1969).
Rudraiah, N., Ramachandramurthy, V., Chandana, O. P.: Effect of magnetic field and non-uniform temperature gradient on Marangoni convection. Int. J. Heat Mass Transfer28, 1621–1624 (1985).
Rudraiah, N.: Surface tension driven convection subjected to rotation and nonuniform temperature gradient. Mausam37, 39–44 (1986).
Rudraiah, N.: The onset of transient Marangoni convection in a liquid layer subjected to rotation about a vertical axis. Mater. Sci. Bull. Ind. Acad. Sci.4, 297–309 (1982).
Rudraiah, N., Veerappa, B., Balachandra Rao, S.: Effects of non-uniform thermal gradient and adiabatic boundaries on convection in porous media. Trans. ASME, Series C. J. Heat Transfer102, 254–260 (1980).
Wooding, R. A.: Rayleigh instability of a thermal boundary layer in flow through porous medium. J. Fluid Mech.9, 183–192 (1960).
Sutton, F. M.: Onset of convection in a porous channel with net throughflow. Phys. Fluids13, 1931–1934 (1970).
Homsy, G. M., Sherwood, A. E.: Connective instabilities in porous media with throughflow. AICh.E. J.22, 168–174 (1976).
Nield, D. A.: Convective instability in porous media with throughflow. AICh.E. J.33, 1222–1224 (1987).
Nield, D. A.: Throughflow effects in the Rayleigh-Bénard convective instability problem. J. Fluid Mech.185, 353–360 (1987).
Jones, M. C., Persichetti, J. M.: Connective instability in packed beds with throughflow. AICh.E. J.32, 1555–1557 (1986).
Eringen, A. C.: Theory of micropolar fluids. J. Math. Mech.16, 1–16 (1966).
Siddheswar, P. G., Pranesh, S.: Effect of non-uniform basic temperature gradient on Rayleigh-Bénard convection in a micropolar fluid. Int. J. Eng. Sci.36, 1183–1196 (1998).
Pearson, J. R. A.: On convective cells induced by surface tension. J. Fluid Mech.4, 489–500 (1958).
Datta, A. B., Sastry, V. U. K.: Thermal instability of a horizontal layer of micropolar fluid heated from below. Int. J. Eng. Sci.14, 631–637 (1976).
Chandrasekhar, S.: Hydrodynamic and hydromagnetic stability. Oxford: Clarendon press 1962.
Finlayson, B. A.: The method of weighted residual and variational principles. New York: Academic Press 1972.
Krishna, M. V., Rudraiah, N., Shivakumara, I. S.: Effect of throughflow on Marangoni convection. Int. Comm. Heat Mass Transfer (In press).
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Murty, Y.N., Ramana Rao, V.V. Effect of throughflow on Marangoni convection in micropolar fluids. Acta Mechanica 138, 211–217 (1999). https://doi.org/10.1007/BF01291845
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DOI: https://doi.org/10.1007/BF01291845