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The thermal instability of a rotating Rivlin-Ericksen viscoelastic fluid in the presence of uniform vertical magnetic field is considered. For the case of stationary convection, Rivlin-Ericksen viscoelastic fluid behaves like a Newtonian fluid. It is found that rotation has a stabilizing effect, whereas the magnetic field has both stabilizing and destabilizing effects. Graphs have been plotted by giving numerical values to the parameters, to depict the stability characteristics. The rotation and magnetic field are found to introduce oscillatory modes in the system which were nonexistent in their absence.

Results of investigation on the transport of vorticity in Rivlin-Ericksen viscoelastic fluid in the presence of suspended magnetic particles is presented here. Equations governing the transport of vorticity in Rivlin-Ericksen viscoelastic fluid in the presence of suspended magnetic particles are obtained from the equations of magnetic fluid flow. From these equations it follows that the transport of solid vorticity is coupled with the transport of fluid vorticity. Further, we find that because of thermokinetic process, fluid vorticity may exist in the absence of solid vorticity, but when fluid vorticity is zero, then solid vorticity is necessarily zero. A two-dimensional case is also studied and found that the fluid vorticity is indirectly influenced by the temperature and the magnetic field gradient.

The stability of the plane interface separating two viscoelastic (Walters B′) superposed fluids of uniform densities in the presence of suspended particles is considered. The stability analysis has been carried out, for mathematical simplicity, for two highly viscoelastic fluids of equal kinematic viscosities and equal kinematic visco‐elasticities. For the (density wise) stable configuration, the system is found to be stable or unstable for the wave number range k ≤ or > \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$ {{1} \over {{\sqrt{2\nu \prime}}}} $\end{document} depending on the kinematic viscoelasticity ν′. However, the system is found to be unstable for the unstable configuration.

The present paper mollifies the nastily behaving governing equations of Dufourdriven thermosolutal convection of the Veronis type by the construction of an appropriate linear transformation and extends the results of M. B. Banerjee et al.

The double-diffusive convection in an Oldroydian viscoelastic fluid is mathematical investigated under the simultaneous effects of magnetic field and suspended particles through porous medium. A sufficient condition for the invalidity of the `principle of exchange of stabilities' is derived, in the context, which states that the exchange principle is not valid provided the thermal Rayleigh number $R$, solutal Rayleigh number$R_S$, the medium permeability $P_1$ and the suspended particles parameter $B$ are restricted by the inequality $\frac{BP_1}{\pi^2}(R+R_S)<1$.

The effect of uniform magnetic field on the Dufour-driven thermosolutal convection of an electrically conducting fluid completely confined in an arbitrary region bounded by rigid walls is considered. Some general qualitative results concerning the character of marginal state, stability of oscillatory motions and limitations on the oscillatory motions of growing amplitude, are derived. The results for the horizontal layer geometry in the present case follow as a consequence.

The thermal instability of a rotating Rivlin-Ericksen viscoelastic fluid in the presence of uniform vertical magnetic field is considered. For the case of stationary convection, Rivlin-Ericksen viscoelastic fluid behaves like a Newtonian fluid. It is found that rotation has a stabilizing effect, whereas the magnetic field has both stabilizing and destabilizing effects. Graphs have been plotted by giving numerical values to the parameters, to depict the stability characteristics. The rotation and magnetic field are found to introduce oscillatory modes in the system which were nonexistent in their absence.