A Characterization Theorem in Magneto-Thermal Convection in Rivlin-Ericksen Viscoelastic Fluid

Abstract

A layer of Rivlin-Ericksen viscoelastic fluid heated from below is considered in the presence of uniform vertical magnetic field. Following the linearized stability theory and normal mode analysis, the paper mathematically established the condition for characterizing the oscillatory motions which may be neutral or unstable, for any combination of perfectly conducting, free and rigid boundaries at the top and bottom of the fluid. It is established that all non-decaying slow motions starting from rest, in a Rivlin-Ericksen viscoelastic fluid of infinite horizontal extension and finite vertical depth, which is acted upon by uniform vertical magnetic field opposite to gravity and a constant vertical adverse free and rigid boundaries and the exact solutions of the problem investigated in closed form, are not obtainable. temperature gradient, are necessarily non-oscillatory, in the regime