The exact solution of nonlinear stress-free convection under the influence of magnetic fields

• Autorzy: El-Kholy S. A.
• Języki publikacji: EN

Abstrakty

EN

This paper aims at transforming nonlinear equations (Navier-Stokes, energy and magnetic induction) in steady state into ordinary high order differential equations. The exact solution for it has been found using a suitable transformation. The second goal is studying the state conditions of heating from below in a horizontal layer and studying the influence of the magnetic field on the phenomenon of convection itself. This model paper has uncovered the properties of electricity-conducting fluid elements. These properties have been disclosed neither in theory nor in practice. This study has been applied on the stress-free boundaries. All of which have realistic manifestation, in nature. They study convection in geophysics and astrophysics. Results have been illustrated in three dimensions to generalize the study and use it practically.

Słowa kluczowe

EN

convection; solar; magnetic field; stress-free; exact solution; nonlinear

PL

konwekcja; pole magnetyczne; dokładne rozwiązanie; nieliniowość

• Wydawca: Wydawnictwo Politechniki Łódzkiej
• Czasopismo: Mechanics and Mechanical Engineering
• Rocznik: 2004
• Tom: Vol. 7, nr 2
• Strony: 13--22
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

El-Kholy S. A.

• Mathematical Department, Faculty of Science, Menoufia University, Shebin, El-Kom, Egypt

Bibliografia

• [1] Busse, FH: Non-linear interaction of magnetic field and convection, J. Fluid Mech., (1995), 71, pp. 193-206.
• [2] Busse, FH and Clever, RM: Three-dimensional convection in the presence of strong vertical magnetic fields, Eur. J. Mech. B/Fluids., (1996), 15, pp. 1-15.
• [3] Chandrasekhar, S: Hydrodynamic and Hydromagnetic Stability, (1961), Oxford, Clarendon Press.
• [4] Chossat, P, Krupa, M, Melbourna, I and Scheel, A: Magnetic dynamos in rotating convection, a dynamical systems approach, Dynamics of Continuous, (1999), 5, pp. 527-540.
• [5] Christensen, U: Effects of phase transitions on mantle convection, Ann. Rev. Earth Planet. Sci, (1995), 23, pp. 65-67.
• [6] Clever, R and Busse, FH: Non-linear oscillatory convection in the presence of a vertical magnetic field, J. Fluid Mech., (1989), 201, pp. 507-523.
• [7] Derrick. S and Grossman, A: Introduction to Differential Equations with boundary value problem, (1987), Third Edition, by University of Montana, New York, Los Angeles, San Francisco.
• [8] Doin, MP, Fleitout, L, Christiensen, U: Mantle convection and stability of depleted and undepleted continental lithosphere, J. Geophys., Res., (1997), 10, pp. 2771-2787.
• [9] Hudid, H, Henry, D and Kaddech, S: Numerical study of convection in the horizontal Bridgman configuration under the action of a constant magnetic field - Part 1, J. Fluid Mech., (1997), 333, pp. 23-30.
• [10] Manglik, A, Christensen, U: Mantle plumes, convection and decompression melting, Current Science, (1997), 73, pp. 1078-1083.
• [11] Ponty, Y, Passot, T and Sulem, IL: A new instability for finite Prandtl number rotating convection with free-slip boundary conditions, Phys. Fluids, (1997), 9, pp. 67-75.
• [12] Vasseur, P and Roillard, L: The Brinkman model for natural convection in a porous layer, effect of non-uniform thermal quarclient, Int. J. Heat Mass Transfer, (1993), 36, pp. 4199-4206.
• [13] Wolfram, S: Mathematica: a System for Doing Mathematics by Computer, (1996), Bonn, New York.
• [14] Zhang, K: On coupling between the Poincare equation and heat equation, J. Fluid Mech., (1994), 268, pp. 211-229.
• [15] Zhang, K: On coupling between the Poincare equation and heat equation: non-slip boundary condition, J. Fluid Mech., (1995), 284, pp. 239-256.