Effect of a Magnetic Field on the Onset of Marangoni Convection in a Micropolar Fluid

Authors: Mohd Nasir Mahmud, Ruwaidiah Idris, Ishak Hashim

Abstract:

With the presence of a uniform vertical magnetic field and suspended particles, thermocapillary instability in a horizontal liquid layer is investigated. The resulting eigenvalue is solved by the Galerkin technique for various basic temperature gradients. It is found that the presence of magnetic field always has a stability effect of increasing the critical Marangoni number.

Keywords: Marangoni convection, Magnetic field, Micropolar fluid, Non-uniform thermal gradient, Thermocapillary.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1062544

References:

[1] D.A. Nield, "Surface tension and buoyancy effects in the cellular convection of an electrically conducting liquid in a magnetic field", Zeitschrift f¨ur Angewandte Mathematik und Physik (ZAMP) 17 (1966) 131-139.
[2] M. Takashima, "Nature of the neutral state in convective instability induced by surface tension and buoyancy", Journal of Physical Society of Japan 28 (1970) 810.
[3] S.H. Davis, G.M. Homsy, "Energy stability theory for free surface problems: Buoyancy-thermocapillary layers", Journal of Fluid Mechanics 98 (1980) 527-553.
[4] D.A. Nield, "Surface tension and buoyancy effect in cellular convection", Journal of Fluid Mechanics 19 (1964) 341-352.
[5] N. Rudraiah, V. Ramachandramurthy, O.P. Chandna, "Effects of magnetic field and non-uniform temperature gradient on Marangoni convection", International Journal of Heat and Mass Transfer 28 (1985) 1621-1624.
[6] N. Rudraiah, P.G. Siddheshwar, "Effect of non-uniform basic temperature gradient on the onset of Marangoni convection in a fluid with suspended particles", Aerospace Science and Technology 4 (2000) 517-523.
[7] P.G. Siddheshwar, S. Pranesh, "Magnetoconvection in fluids with suspended particles under lg and ╬╝g", Aerospace Science and Technology 6 (2002) 105-114.
[8] M.I. Char, C.C. Chen, "Effect of a non-uniform temperature gradient on the onset of oscillatory B'enard-Marangoni convection of an electrically conducting liquid in a magnetic field", Int. J. Engrg. Sci. 41 (2003) 1711- 1727.
[9] I. Hashim, Z. Siri, "Stabilization of steady and oscillatory Marangoni instability in rotating fluid layer by feedback control strategy, Numerical Heat Transfer", Part A: Applications 54(6) (2008) 647-663.
[10] S. Awang Kechil, I. Hashim, "Control of Marangoni instability in a layer of variable-viscosity fluid", International Communication in Heat and Mass Transfer doi:10.1016/j.icheatmasstransfer.2008.06.006
[11] Z. Siri, I. Hashim, "Control of oscillatory Marangoni convection in a rotating fluid layer", International Communication in Heat and Mass Transfer doi:10.1016/j.icheatmasstransfer.2008.06.008
[12] S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Oxford University Press, Oxford, 1961.
[13] K.-T. Chiang, "Effect of a non-uniform basic temperature gradient on the onset of Benard-Marangoni convection: Stationary and oscillatory analyses", International Communication in Heat and Mass Transfer 32 (2005) 192-203.
[14] M.H.O. Dupont, M. Hennenberg, J.C. Legros, "Marangoni-B'enard instabilities under non-steady conditions: Experimental and theoretical results", International Journal of Heat and Mass Transfer 35 (1992) 3237- 3244.