Upper Limits to Growth Rate in Magneto-Thermosolutal Convection in Rivlin-Ericksen Viscoelastic Fluid in a Porous Medium

Thermosolutal convection in a layer of Rivlin-Ericksen viscoelastic fluid of Veronis (1965) type is considered in the presence of uniform vertical magnetic field in a porous medium. Following the linearized stability theory and normal mode analysis, the paper through mathematical analysis of the governing equations of Rivlin-Ericksen viscoelastic fluid convection in the presence of uniform vertical magnetic field, for any combination of free and rigid boundaries of infinite horizontal extension at the top and bottom of the fluid, established that the complex growth rate of oscillatory perturbations, neutral or unstable for all wave numbers, must lie inside right half of the a semi-circle, in the -plane, where is the thermosolutal Rayleigh number, Q is the Chandrasekhar number, F is the viscoelasticity parameter, is the magnetic Prandtl number, is the porosity and is the medium permeability. This prescribes the bounds to the complex growth rate of arbitrary oscillatory motions of growing amplitude in the Rivlin-Ericksen viscoelastic fluid in Veronis (1965) type configuration in the presence of uniform vertical magnetic field in a porous medium. A similar result is also proved for Stern (1960) type of configuration. The result is important since the result hold for any arbitrary combinations of dynamically free and rigid boundaries.