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Abstrakty
The convective stability of a horizontal layer of viscoelastic conducting liquid (Walters' liquid B') heated from below and rotating about a vertical axis in the presence of a magnetic field and thermal relaxation has been investigated. Linear stability theory and normal mode analysis are used to derive an eigenvalue system of eighth order, and an exact eigenvalue equation for a neutral instability is obtained. Critical Rayleigh numbers and wave numbers for the onset of instability are presented graphically as functions of Taylor number for various values of the Chandrasekhar number and the relaxation time at a Prandtl number Pr = l.
Czasopismo
Rocznik
Tom
Strony
41--51
Opis fizyczny
Bibliogr. 22 poz.
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autor
- Faculty of Education, Department of Mathematics Salalah-211, P.O. Box 2801, Sultanate of Oman, m_i_othman@yahoo.com
Bibliografia
- [1] Chandrasekhar, S: Hydrodynamic and Hydromagnetic Stability, (1961), Oxford Univ., Press, London.
- [2] Green, T: III Phys. of Fluids, (1968), 11, 1410.
- [3] Oldroyd, JG: Proc. Roy. Soc., (1950), A200, 523.
- [4] Oldroyd, JG: Proc. Roy. Soc., (1958), A245, 278.
- [5] Vest, CM, Arpasi, VS: J. Fluid Mech., (1969), 36, 613.
- [6] Maxwell, JC: Phil. Trans. Roy. Sac., (1867), 157.
- [7] Fredrickson, AG: Principles and Applications of Rheology, (1964), Prentice-Hall, Inc.
- [8] Takashima, M: Phys. Letters 31A, (1970), 379.
- [9] Takashima, M: J. Phys. Soc. Japan, (1970), 29, 1061.
- [10] Walters, K: Second-order effects in elasticity, Plasticity and Fluid Dynamics, (1964), Pergamon, Oxford, 507.
- [11] Beard, DW, Walters, K: Elastico-viscous boundary-layer flows. I. Two- dimensional flow near a stagnation point, Proc. Gamb. Phil. Soc., (1964), 60, 667-671.
- [12] El-Dabe, NT, Sallam, NS: Magnetohydrodynamic flow and heat transfer in a viscoelastic incompressible fluid confined between a horizontal stretching sheet and a parallel porous wall, Gan. J. Phys., (1998), 76, 949-964.
- [13] Singh, A, Singh, J: Magnetohydrodynamic flow of a viscoelastic fluid past an accelerated plate, Nat. Acad. Sci. Lett., (1983), 6, 233-241.
- [14] Bahar, LY: Transfer matrix approach to elastodynamics of layered medium, J. Acoust. Soc. Am., (1975), 75, 606-609.
- [15] Ezzat, M: State space approach to unsteady two-dimensional free convection flow through a porous medium, Gan. J. Phys., (1994), 72, 311-317.
- [16] Ezzat, M, Abd-Elaal, M: Free convection effects on a viscoelastic boundary layer flow with one relaxation time through a porous medium, J. Franklin Inst., (1997), 334B, 685.
- [17] Ezzat, M, Othman, MI: Thermal instability in a rotating micropolar fluid layer subject to an electric field, Int. J. Engng. Sci., (2000), 38, 1851-1867.
- [18] Othman, MI, Ezzat, MA: Electromagneto-hydrodynamic instability in a horizontal viscoelastic fluid layer with one relaxation time, Acta Mechanica, (2001), 150, 1-9.
- [19] Othman, MI: Electromagneto-hydrodynamic stability in a horizontal visco-elastic fluid layer in the presence of a vertical temperature gradient, Int. J. Engng. Sci., (2001), 39, 1217-1232.
- [20] Takashima, M: Thermal instability in a viscoelastic fluid layer II. Effect of rotation, J. Phys. Soc. Japan., (1972), 33, 797-804.
- [21] Rama Rao, KV: Thermal instability in a micropolar fluid layer subjected to a magnetic field, Int. J. Engng. Sci., (1980), 18, 741-750.
- [22] Sharma, RC, Kumar, P: Effect of rotation on thermal convection in micro polar fluids, Int. J. Engng. Sci., (1994), 32, 545-551.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-LOD9-0022-0042