• THERMAL INSTABILITY IN A ROTATING MICROPOLAR VISCOELASTIC FLUID LAYER UNDER EFFECT OF ELECTRIC FLIED

Sayed A. Zaki*, Mohamed I. Othman, Adel Y. Elmekawy

Abstract


The problem of onset of convective instability in a dielectric micropolar viscoelastic fluid (Walters’ liquid  heated from below confined between two horizontal plates under the simultaneous action of the rotation of the system, vertical temperature gradient, one relaxation time and vertical electric field is considered. Linear stability theory is used to derive an eigenvalue of twelve order, and an exact eigenvalue equation for a neutral instability is obtained. Under somewhat artificial boundary conditions, this equation can be solved exactly to yield the eigenvalue relationship from which various critical values are determined in detail. Critical Rayleigh heat numbers and wave number for the onset of instability are presented graphically as a function of rotation at a certain value of the Prandtl number, for various values of the relaxation time, the Rayleigh electric number, the elastic parameter and micropolar parameters.


Keywords


Instability, Viscoelastic, Rotation, micropolar, The power series method.

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