The effect of thermal relaxation time on a electrohydrodynamic viscoelastic fluid layer heated from below

Abstract

The problem of the onset of stability in a horizontal layer of a viscoelastic dielectric liquid with one relaxation time heated from below under the action of a vertical ac electric field is analyzed. Linear stability theory is used to derive an eigenvalue system of order eight 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 required eigenvalue relationship from which various critical values are determined in detail. The critical Rayleigh number and wave number for the onset of instability are presented graphically as functions of the Grashof number for various values of the Prandtl number and one relaxation time. A comparison is made with the results obtained in the absence of an electric field. PACS No.: 47.27.T