Thermal Instability in a Porous Medium Layer Saturated with a Viscoelastic Nanofluid

Abstract

The onset of convection in a horizontal layer of a porous medium saturated with a viscoelastic nanofluid was studied in this article. The modified Darcy model was applied to simulate the momentum equation in porous media. An Oldroyd-B type constitutive equation was used to describe the rheological behavior of viscoelastic nanofluids. The model used for the viscoelastic nanofluid incorporates the effects of Brownian motion and thermophoresis. The onset criterion for stationary and oscillatory convection was analytically derived. The effects of the concentration Rayleigh number, Prandtl number, Lewis number, capacity ratio, relaxation, and retardation parameters on the stability of the system were investigated. Oscillatory instability is possible in both bottom-and top-heavy nanoparticle distributions. Results indicated that there is competition among the processes of thermophoresis, Brownian diffusion, and viscoelasticity that causes the convection to set in through oscillatory rather than stationary modes. Regimes of stationary and oscillatory convection for various parameters were derived and are discussed in detail.

Group analysis and numerical computation of magneto-convective non-Newtonian nanofluid slip flow from a permeable stretching sheet

“…6a, b, namely, that pseudoplastic fluids achieve greater concentration magnitudes relative to Newtonian nanofluids. As indicated in many studies including Kuznetsov and Nield (2010) for Newtonian nanofluids, Sheu (2011) for viscoelastic nanofluids and Uddin et al (2013a) for power-law nanofluids, an increase in Brownian motion parameter effectively depresses nanoparticle concentrations in the nanofluid regime. This is attributable to the enhanced mass transfer to the sheet wall from the main body of the nanofluid (boundary layer) with increasing Brownian motion.…”

“…These studies have revealed many interesting features of nonNewtonian nanofluids. Sheu (2011) employed an Oldroyd-B viscoelastic model to study nanofluid convection in a horizontal layer of a saturated porous medium. Goyal and Bhargava (2013) used the Reiner-Rivlin second order rheological model to simulate the effect of velocity slip boundary condition on the flow and heat transfer of nonNewtonian nanofluid over a stretching sheet.…”

Rayleigh-Bénard convection in an elastico-viscous Walters’ (model B’) nanofluid layer

“…However, we assumed these conditions, which have also been previously adopted by several authors (Tzou [6], Nield and Kuznetsov [12], Sheu [29]), because they allow the linear stability analysis to be analytically performed.…”

“…Using the scales defined above and using Boussinesq approximation, temperature gradients in the dilute suspension of nanoparticles are small enough to linearize Eq. (5) by neglecting the term involving the product of ϕ and T (Tzou [6], Sheu [29]), Eqs. (1), (5), (6) and (7) in non-dimensional form can be written as…”

“…Nield [27] discussed the thermal instability problem in a porous medium saturated by non-Newtonian fluids which were modeled by using a power law fluid. Recently, Shivkumara et al [28] studied the effect of thermal modulation on the onset of thermal convection in Walters' B viscoelastic fluid in a porous medium while Sheu [29] used the Oldroyd-B fluid model to describe the rheological behavior of the nanofluid. More recently, Rana et al [30] studied the thermosolutal convection in compressible Walters' (model B') fluid permeated with suspended particles in a Brinkman porous medium.…”