Validity of Principle of Exchange of Stabilities of Rivilin- Ericksen Fluid Permeated with Suspended Particles in Porous Medium Under the effect of Rotation with Variable Gravity Field by using Operator Method

The Thermosolutal Convection in Riviliin-Ericksen elastico-viscous fluid in porous medium is considered to include the effect of suspended particles and rotation under variable gravity. In the present, to establish the Principle of Exchange of Stabilities (PES) by using a method of a Positive Operator, a generalization of a positive matrix Where in, the resol vent of the linearized stability operator is analyzed which is in the form m of a composition of certain integral operators. Motivated by the analysis of Weinberger and the works of Herron, our objective here is to extend this analysis of positive operator to establish the PES. It is established by the method of positive operator of W Weinberger that PES is valid for this problem under sufficient conditions and g (z) is nonnegative throughout the fluid layer.