A study of phase portraits, multistability and velocity profile of magneto-hydrodynamic Jeffery–Hamel flow nanofluid

Abstract

Bifurcation analysis is studied for the first time in magneto-hydrodynamic (MHD) Jeffery–Hamel flow nanofluids. The dimensionless ordinary differential equations is formulated by using the similarity transformations. The phase portraits of the travelling wave solutions are examined using bifurcation theory on the dynamical system of the considered equation. Moreover, multistability and sensitivity analysis is used to examine quasi-periodic and periodic behavior for various initial conditions. The (MHD) Jeffery–Hamel flow solutions are derived analytically by applying the extended direct algebraic approach and the influence of the different physical parameters for velocity profiles, have been examined. It is found that the physical parameter i.e, Reynolds number and channel angle rising in convergent flow results in an increase in the velocity profiles, signifying that backflow is excluded, while an inverse behavior can be attributed to a diverging flow. • Magneto-hydrodynamic Jeffery–Hamel flow has been observed by bifurcation analysis. • All possible phase portraits are drawn. • The influence of the magnetic field and nanoparticles on the magneto-hydrodynamic Jeffery–Hamel flow has been studied. • The influence of the different physical parameters on the velocity profiles have been examined.