Overstable Convection in Viscoelastic Nanofluid Layer Saturated By a Darcy-Brinkman Porous Medium Embedded by Dust Particles

Abstract

he paper presents a linear stability analysis for the effect of dust particles on the onset of thermal convection in viscoelastic nanofluid
layer saturated by a Darcy-Brinkman porous medium embedded with dust particles. The rheology of viscoelasticity is described by constitutive relations purposed by Oldroyd-B model. The nanofluid layer incorporates the effect of Brownian motion along with thermophoresis. The set of partial differential equations using the normal mode technique is reduced to non- dimensional ordinary differential equations in different non – dimensional parameters. Using the appropriate stress free boundary conditions, exact solutions are obtained. Both stationary and oscillatory convection are investigated using normal mode technique. It is found that
instability sets in as oscillatory motions rather than stationary convection. For the stationary convection, the effects of the Lewis number ( ) e L , concentration Rayleigh number ( ) n R , modified diffusivity ratio (NA) and Darcy number (Da) the stability of the system has been investigated  numerically. The oscillatory modes are introduced by the stress-relaxation time and strain- retardation parameter. The sufficient condition for the non-exi stence over s tabi l i ty i s l2 > l1 . The effect of various parameters for on thermal Rayleigh number the overstability has been presented graphically. Nanofluid Viscoelastic, Thermal convection, dust particles,
Darcy-Brinkman porous medium.