×

zbMATH — the first resource for mathematics

Magnetohydrodynamic stability of streaming jet pervaded internally by varying transverse magnetic field. (English) Zbl 1264.76119
Summary: The Magnetohydrodynamic stability of a streaming cylindrical model penetrated by varying transverse magnetic field has been discussed. The problem is formulated, the basic equations are solved, upon appropriate boundary conditions the eigenvalue relation is derived and discussed analytically, and the results are verified numerically. The capillary force is destabilizing in a small axisymmetric domain \(0 < x < 1\) and stabilizing otherwise. The streaming has a strong destabilizing effect in all kinds of perturbation. The toroidal varying magnetic field interior the fluid has no direct effect at all on the stability of the fluid column. The axial exterior field has strong stabilizing effect on the model. The effect of all acting forces altogether could be identified via the numerical analysis of the stability theory of the present model.

MSC:
76W05 Magnetohydrodynamics and electrohydrodynamics
35B35 Stability in context of PDEs
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] B. J. W. S. Rayleigh, The Theory of Sound, Dover, New York, NY, USA, 2nd edition, 1945. · Zbl 0061.45904
[2] S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Dover, New York, NY, USA, 1981. · Zbl 0142.44103
[3] P. H. Robert, An Introduction to MHD, Longman, London, UK, 1967.
[4] L. Chenng, “Instability of a gas jet in liquid,” Physics of Fluids, vol. 28, article 2614, 3 pages, 1985.
[5] J. M. Kendall, “Experiments on annular liquid jet instability and on the formation of liquid shells,” Physics of Fluids, vol. 29, no. 7, pp. 2086-2094, 1986.
[6] P. G. Drazin and W. H. Reid, Hydrodynamic Stability, Cambridge Mathematical Library, Cambridge University Press, Cambridge, Mass, USA, 2nd edition, 2004. · Zbl 1057.76015
[7] A. E. Radwan, “Effect of magnetic fields on the capillary instability of an annular liquid jet,” Journal of Magnetism and Magnetic Materials, vol. 72, no. 2, pp. 219-232, 1988.
[8] A. E. Radwan, M. A. Elogail, and N. E. Elazab, “Large hydromagnetic axisymmetric instability of a streaming gas cylinder surrounded by bounded fluid with non uniform field,” Kyungpook Mathematical Journal, vol. 47, no. 4, pp. 455-471, 2007. · Zbl 1280.76009
[9] A. E. Radwan and A. A. Hasan, “Axisymmetric electrogravitational stability of fluid cylinder ambient with transverse varying oscillating field,” IAENG International Journal of Applied Mathematics, vol. 38, no. 3, pp. 113-120, 2008. · Zbl 1229.76040
[10] A. E. Radwan and A. A. Hasan, “Magneto hydrodynamic stability of self-gravitational fluid cylinder,” Applied Mathematical Modelling, vol. 33, no. 4, pp. 2121-2131, 2009. · Zbl 1205.76304
[11] A. A. Hasan, “Electrogravitational stability of oscillating streaming fluid cylinder,” Physica B, vol. 406, no. 2, pp. 234-240, 2011. · Zbl 1273.35269
[12] M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, Dover, New York, NY, USA, 1970. · Zbl 0171.38503
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.