Electrohydrodynamic stability in a horizontal viscoelastic fluid layer in the presence of a vertical temperature gradient

The problem of the onset of stability in a horizontal layer of viscoelastic dielectric liquid (Walters' liquid B ′) under the simultaneous action of a vertical ac electric field and a vertical temperature gradient is analyzed. Applying linear stability theory an equation of eight order is derived. 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. Critical Rayleigh electric numbers, wave number and frequencies for the onset of instability are presented graphically as function of Rayleigh heat number for various values of Prandtl number and the elastic parameters.