A Characterization of Thermosolutal Convection in Rivlin-Ericksen Fluid in the Presence of Magnetic Field in a Porous Medium

Thermosolutal instability of Veronis type in Rivlin-Ericksen viscoelastic fluid in the presence of uniform magnetic field in a porous medium is considered. 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 arbitrary combination of free and rigid boundaries at the top and bottom of the fluid. It is established that all nondecaying slow motions starting from rest, magneto-thermosolutal instability of Veronis type in a Rivlin-Ericksen viscoelastic fluid of infinite horizontal extension and finite vertical depth in a porous medium, are necessarily nonoscillatory, in the regime where R_s is the Thermosolutal Rayliegh number, Q is the Chandrasekhar number, p₂ is the magnetic Prandtl number, p₃ is the thermosolutal Prandtl number, P₁ is the medium permeability, ε is the porosity and F is the viscoelasticity parameter. The result is important since it hold for all wave numbers and for any arbitrary combination of free and rigid boundaries at the top and bottom of the fluid. A similar characterization theorem is also proved for Stern type of configuration.