Effect of a Magnetic Field on the Onset of Marangoni Convection in a Micropolar Fluid
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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:55329", author = "Mohd Nasir Mahmud and Ruwaidiah Idris and Ishak Hashim", title = "Effect of a Magnetic Field on the Onset of Marangoni Convection in a Micropolar Fluid", 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.", volume = "3", number = "2", pages = "113-3", }
