Double-Diffusive Convection in Presence of Compressible Rivlin-Ericksen Fluid with Fine Dust

An investigation is made on the effect of suspended particles (fine dust) on double-diffusive convection of a compressible Rivlin-Ericksen elastico-viscous fluid. The perturbation equations are analyzed in terms of normal modes after linearizing the relevant set of equations. A dispersion relation governing the effects of viscoelasticity, compressibility, stable solute gradient, and suspended particles is derived. For stationary convection, Rivlin-Ericksen fluid behaves like an ordinary Newtonian fluid due to the vanishing of the viscoelastic parameter. The stable solute gradient compressibility has a stabilizing effect on the system whereas suspended particles hasten the onset of thermosolutal instability. The Rayleigh numbers and the wave numbers of the associated disturbances for the onset of instability as stationary convection are obtained and the behaviour of various parameters on Rayleigh numbers has been depicted graphically. It has been observed that oscillatory modes are introduced due to the presence of viscoelasticity, suspended particles, and stable solute gradient which were not existing in the absence of these parameters.