Analytical Investigation of Stability and Chaos in Magnetohydrodynamic Jeffery-Hamel Nanofluid Flows

This study presents an analytical investigation of the nonlinear dynamics of magnetohydrodynamic (MHD) Jeffery–Hamel nanofluid flow in converging–diverging channels, with emphasis on stability transitions and chaotic behavior. Kerosene-based nanofluids containing AlO, CuO, and FeO nanoparticles are examined under a transverse magnetic field. The Navier–Stokes equations are reduced to a nonlinear ordinary differential system using similarity transformations, and closed-form solutions are obtained via the Extended Hyperbolic Function method. A Hamiltonian formulation is derived to characterize the energy structure of the system, while a range of chaos diagnostics is employed to identify transitions between steady, quasi-periodic, and chaotic flow regimes. The results show that magnetic field strength significantly enhances flow stability by introducing Lorentz-force damping, which suppresses velocity fluctuations and delays the onset of chaos. Channel geometry also plays a key role: stronger convergence accelerates the flow and promotes instability, whereas larger divergence reduces peak velocity and supports stable behavior. Among the considered nanofluids, FeO exhibits the strongest stabilizing effect due to its enhanced magnetic interaction. These findings demonstrate that magnetic field intensity, nanoparticle type, and channel angle can serve as effective control parameters for regulating nonlinear flow behavior in MHD nanofluid systems, which is important for the reliable design of microfluidic and thermal management devices.