Simulation of the onset of convection in a porous medium layer saturated by a couple-stress nanofluid

Umavathi, JC; Beg, OA

Abstract

Linear and nonlinear stability analyses for the onset of time-dependent convection in a
horizontal layer of a porous medium saturated by a couple-stress non-Newtonian nanofluid,
intercalated between two thermally insulated plates, are presented. Brinkman and MaxwellGarnett formulations are adopted for nanoscale effects. A modified Darcy formulation that
includes the time derivative term is used for the momentum equation. The nanofluid is
assumed to be dilute and this enables the porous medium to be treated as a weakly
heterogeneous medium with variation of thermal conductivity and viscosity, in the vertical
direction. The general transport equations are solved with a Galerkin-type weighted residuals
method. A perturbation method is deployed for the linear stability analysis and a Runge–
Kutta–Gill (RKG) quadrature scheme for the nonlinear analysis. The critical Rayleigh
number, wave numbers for the stationary and oscillatory modes and frequency of oscillations
are obtained analytically using linear theory and the non-linear analysis is executed with
minimal representation of the truncated Fourier series involving only two terms. The effect of
various parameters on the stationary and oscillatory convection behavior is visualized. The
effect of couple stress parameter on the stationary and oscillatory convections is also shown
graphically. It is found that the couple stress parameter has a stabilizing effect on both the
stationary and oscillatory convections. Transient Nusselt number and Sherwood number
exhibit an oscillatory nature when time is small. However, at very large values of time both
Nusselt number and Sherwood number values approach their steady state values. The study is
relevant to the dynamics of biopolymers in solution in microfluidic devices and rheological
nanoparticle methods in petroleum recovery.

Citation

Umavathi, J., & Beg, O. (2021). Simulation of the onset of convection in a porous medium layer saturated by a couple-stress nanofluid. Microfluidics and Nanofluidics, 25(6), 53. https://doi.org/10.1007/s10404-021-02448-5

• Journal Article Type: Article
• Acceptance Date: May 3, 2021
• Publication Date: Jun 5, 2021
• Deposit Date: May 4, 2021
• Publicly Available Date: Jun 5, 2022
• Journal: Microfluidics and Nanofluidics
• Print ISSN: 1613-4982
• Electronic ISSN: 1613-4990
• Publisher: Springer Verlag
• Volume: 25
• Issue: 6
• Pages: 53
• DOI: https://doi.org/10.1007/s10404-021-02448-5
• Publisher URL: https://doi.org/10.1007/s10404-021-02448-5
• Related Public URLs: http://link.springer.com/journal/10404
• Additional Information: Access Information : This is a post-peer-review, pre-copyedit version of an article published in Microfluidics and Nanofluidics. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10404-021-02448-5