| Sains Malaysiana 34(1): 133-138 (2005)   Kesan Medan Magnet Menegak ke atas Lengkung Sut Olakan Benard-Marangoni Mantapdalam Lapisan Mengufuk Bendalir
 (The Effect of a Vertical Magnetic Field on the Onset  of Study Bernard-Marangoni Convection in a Horizontal Layer of Electrically  Conducting Fluid)     Ruwaidiah Idris  Jabatan Matematik Fakulti Sains dan Teknologi Kolej Universiti Sains Dan  Teknologi Malaysia  Mengabang Telipot 21030 Kuala Terengganu Terengganu D. I, Malaysia   Ishak Hashim Pusat Pengajian Sains  Matematik Fakulti Sains dan Teknologi Universiti Kebangsaan  Malaysia  43600 UKM Bangi, Selangor  D.E., Malaysia     ABSTRAK   Dalam  makalah ini kesan medan magnet menegak seragam ke atas lengkung sut permulaan  olakan mantap Benard-Marangoni dalam lapisan bendalir mengufuk berpengalir  elektrik dikaji tertakluk kepada kecerunan suhu yang seragam dalam had asimptot  gelombang pendek. Kami dapati medan magnet tidak memberi kesan kepada sebutan  utama lengkung sut dalam had gelombang pendek.     ABSTRACT   In this work we use an  analytical technique to analyse the effect of a vertical uniform magnetic field  on the onset of steady Benard-Marangoni convection in a horizontal layer of  electrically conducting fluid subject to a uniform vertical temperature gradient  in the asymptotic limit short waves.  We  found that in the limit of short waves, the leading order expression for the  marginal curve is not affected by the magnetic field.     RUJUKAN/REFERENCES   Chandrasekhar, S. 1961. Hydrodynamics  and Hydromagnetic Stability. UK: Oxford University Press.  Hashim, I. 2000. The effect of a  uniform vertical magnetic field on the onset of steady Marangoni convection in  semi-infinitely deep layer of conducting fluid. Matematika 16 (1):  1-10.  Hashim, I. & Wilson, S. K. 1999a. The effect of a uniform vertical  magnetic field on the onset of steady Marangoni convection in a horizontal  layer of conducting fluid. Int. J. Heat and Mass Transfer 42: 525-533.  Hashim, I. & Wilson, S. K. 1999b. The effect of a uniform vertical  magnetic field on the onset of oscillatory Marangoni convection in a horizontal  layer of conducting fluid. Acta Mechanica 132: 129-146.  Hashim, I. & Wilson, S. K. 1999c. The onset of oscillatory  Marangoni convection in a semi-infinitely deep layer of fluid. Z. Angew.  Math. Phys. 50: 1-14.  Hurle, D. T. J. 1981. Surface aspects  of crystal growth from melt. Adv. In Colloid Interface Sci. 15: 101-130.  Mills, K. C. & Keene, B. J. 1990. Factor affecting variable weld  penetration. Int. Material Rev. 35(4): 185-216.  Ostrach, S. 1988. Fluid mechanics in  crystal growth melts. Crystal 11: 72-122.  Pearson, J. R. A. 1958. On convection  cells induce by surface tension. J. Fluid Mech. 4: 489-500.  Regnier,  V. C. & Lebon, G. 1995. Time growth on convection length of fluctuation in  thermocapillary convection with surface deformation. Q. J. Mech. appl. Math. 48: 57-75.  Schwabe, D. 1988. Surface  tension-driven flow in crystal growth melts. Crystal 11: 75-112.  Scriven, L. E. & Sternling, C. V. 1964. On cellular convection driven by  surface tension gradients: Effect of mean surface tension and surface  viscosity. J. Fluid Mech. 19: 321-340.  Smith, K. A. 1996. On convective  instability induced by surface tension gradients. 1. Fluid Mech. 24:  401-414.  Takashima, M. 1981a. Surface tension  driven instability in horizontal liquid layer with deformable free surface. 1.  Stationary convection. J. Phys. Soc. Japan 50(8): 2745-2750.  Takashima, M. 1981b. Surface tension  driven instability in horizontal liquid layer with deformable free surface. II.  Overstability. J. Phys. Soc. Japan 50(8): 2751-2756.  Wilson, S. K. 1993a. The effect of a  uniform magnetic field on the onset of Marangoni convection in a layer of  conducting fluid. Q. J. Mech. Appl.  Math. 46(2): 211-248.  Wilson, S. K. 1993b. The effect of a  uniform magnetic field on the onset of steady Benard-Marangoni convection in a  layer of conducting fluid. J. Eng. Math. 27: 161-188.  Wilson, S. K. & Thess, A. 1997. On the linear growth rates of the long-wave  modes in Benard-Marangoni convection. Phys. Fluids 9(8): 2455-2457.    |