Nonlinear instability of an Oldroyd elastico–viscous magnetic nanofluid saturated in a porous medium

Abstract

Through viscoelastic potential theory, a Kelvin-Helmholtz instability of two semi-infinite fluid layers, of Oldroydian viscoelastic magnetic nanofluids (MNF), is investigated. The system is saturated by porous medium through two semi-infinite fluid layers. The Oldroyd B model is utilized to describe the rheological behavior of viscoelastic MNF. The system is influenced by uniform oblique magnetic field that acts at the surface of separation. The model is used for the MNF incorporated the effects of uniform basic streaming and viscoelasticity. Therefore, a mathematical simplification must be considered. A linear stability analysis, based upon the normal modes analysis, is utilized to find out the solutions of the equations of motion. The onset criterion of stability is derived; analytically and graphs have been plotted by giving numerical values to the various parameters. These graphs depict the stability characteristics. Regions of stability and instability are identified and discussed in some depth. Some previous studies are recovered upon appropriate data choices. The stability criterion in case of ignoring the relaxation stress times is also derived. To relax the mathematical manipulation of the nonlinear approach, the linearity of the equations of motion is taken into account in correspondence with the nonlinear boundary conditions. Taylor's theory is adopted to expand the governing nonlinear characteristic equation according to of the multiple time scales technique. This analysis leads to the well-known Ginzburg–Landau equation, which governs the stability criteria. The stability criteria are achieved theoretically. To simplify the mathematical manipulation, a special case is considered to achieve the numerical estimations. The influence of orientation of the magnetic fields on the stability configuration, in linear as well as nonlinear approaches, makes a dual role for the magnetic field strength in the stability graphs. Stability diagram is plotted for different sets of physical parameters. A new stability as well as instability region, in the parameter space, appears due to the nonlinear effects.

A review on the flow instability of nanofluids

“…Hossain and Khan [20] showed that the flow became unstable owing to the presence of nanoparticles in a wall-driven flow through a tube, and flow instability was dependent on the particle concentration, the particle density, and the Reynolds number. Moatimid et al [21] studied the flow stability in a porous medium for the Oldroyd elastico-viscous magnetic fluid. Rudyak et al [22] found that the degree of destabilization was enhanced by an increase in the particle concentration and a decrease in the particle diameter in the pipe.…”

Nonlinear EHD instability of two viscoelastic fluids under the influence of mass and heat transfer

“…Our upcoming study will address these forms non-Newtonian models in consideration due to the practical applications of the various structures of non-Newtonian prototyping as progress works. Furthermore, particular linear stability non-Newtonian standards were explored along with our earlier articles 10 , 46 , 50 – 52 . Therefore, away from the simplified formulation of Hsieh’s formula 38 and[39[, the future works will adopt the energy as well as the concentration equations.…”