Stability analysis of water-alumina nanofluid film at the spherical interface

Abstract

The interface of a viscous fluid and [Formula: see text]-water nanofluid is analyzed through linear instability analysis in a spherical configuration. The viscous fluid lies inside the sphere while the outside region contains nanofluid. In this model, the viscosity of the nanofluid is considered a function of the base fluid viscosity, nanoparticles volume fraction, fractal aggregates, and nanoparticles shape. The perturbed flow is taken as irrotational, and the linear perturbation equations are solved through viscous irrotational theory. The perturbations growth rate can be computed through a 2-degree polynomial and the coefficients of this polynomial are the functions of the Atwood number, Richardson number, Weber number, Reynolds number, etc. The nanofluid interface is found more stable than the viscous fluid interface. The density of nanofluids raises the amplitude of disturbances while the nanofluid's viscosity has a reverse effect.

Irrotational flow analysis of Rayleigh-Taylor instability in nanofluid layer with tangential magnetic field

“…The study specifically investigated the influence of a constant tangential electric field on two dielectric fluids in the presence of steady relative velocities. Agarwal et al [1] investigated a spherical nanofluid interface and observed that the viscosity of the nanofluid contributes to interface stabilization, while the fractal index of the nanoparticles exhibits a destabilizing nature.…”

“…where p n and p v stand for the pressures of the nanofluid and viscous incompressible fluid phases, respectively, J denotes the current density, while H is the magnetic field vector defined as H = H êx . The density ρ n and viscosity µ n may be represented using the subsequent expressions [1]…”

“…where µ ef stands for the viscosity of the pristine fluid, ϕ m represents the uppermost volume fraction achievable for spheroidal nanoparticles, and the shape parameter of the nanoparticles is labeled as δ. The aggregate volume fraction of the nanoparticles, denoted as ϕ ag , can be expressed using the equivalent volume fractions of the nanoparticles, denoted as ϕ mod , and the fractal index d, as detailed by Agarwal et al in [1],…”