Electromagneto-hydrodynamic instability in a horizontal viscoelastic fluid layer with one relaxation time

The stability of viscoelastic conducting liquid (Walters's liquid B′) heated from below in the presence of a magnetic field is considered. Linear stability theory is used to derive an eigenvalue system of sixth 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 required eigenvalue relationship from which various critical values are determined in detail. Critical Rayleigh number and wavenumber for the onset of instability are presented graphically as functions of the Chandrasekhar number at a Prandtl numberPr=100 and for various values of the one relaxation time and the elastic parameters.