Thermal Instability in a Viscoelastic Fluid Layer. III. Effect of a Magnetic Field

Abstract

The stability of a horizontal layer of an electrically conducting, viscoelastic fluid (Oldroyd fluid) heated from below in the presence of a magnetic field is considered, on the assumption that both bounding surfaces are free. Linear stability theory is used to derive an eigenvalue system of sixth order, and an exact eigenvalue equation for a neutral instability is obtained. Critical Rayleigh numbers, wave numbers, and frequencies for the onset of instability are presented graphically as functions of the Chandrasekhar number for various values of the Prandtl number and the elastic parameters. It is shown that the effects which arise in consequence of the coupling between the magnetic field and the viscoelastic behaviour of a fluid are exceedingly complicated.