## THERMAL SCIENCE

International Scientific Journal

### THERMAL CONVECTION OF DUSTY COMPRESSIBLE RIVLIN-ERICKSEN VISCOELASTIC FLUID WITH HALL CURRENTS

**ABSTRACT**

An investigation is made on the effect of Hall currents and suspended particles on the hydromagnetic stability of a compressible, electrically conducting Rivlin-Ericksen elastico-viscous fluid. The perturbation equations are analyzed in terms of normal modes after linearizing the relevant set of hydromagnetic equations. A dispersion relation governing the effects of viscoelasticity, magnetic field, Hall currents, compressibility and suspended particles is derived. For the stationary convection Rivlin-Ericksen fluid behaves like an ordinary Newtonian fluid due to the vanishing of the viscoelastic parameter. Compressibility and magnetic field are found to have a stabilizing effect on the system whereas Hall currents and suspended particles hasten the onset of thermal instability. These analytic results are confirmed numerically and the effects of various parameters on the stability parameter are depicted graphically. The critical Rayleigh numbers and the wavenumbers of the associated disturbances for the onset of instability as stationary convection are obtained and the behavior of various parameters on critical thermal Rayleigh numbers has been depicted graphically. It has been observed that oscillatory modes are introduced due to the presence of viscoelasticity, suspended particles and Hall currents which were not existing in the absence of these parameters.

**KEYWORDS**

PAPER SUBMITTED: 2011-01-28

PAPER REVISED: 2011-10-10

PAPER ACCEPTED: 2011-10-11

**THERMAL SCIENCE** YEAR

**2012**, VOLUME

**16**, ISSUE

**Issue 1**, PAGES [177 - 191]

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