Stability analysis and unsteady nature of MHD flow through a rotating curved rectangular duct with Hall and ion-slip currents

This paper investigates a computational study on magnetohydrodynamic (MHD) flow, exploring solution structure and unsteady nature of thermal flows, in a rotating curved rectangular duct (CRD) incorporating the effects of Hall and ion-slip currents, motivated by the board range of engineering applications involving magnetic flow control, thermomagnetic devices, filtration systems and thermal transport in a rotating system. The spectral method serves as the main computational approach, supported by Chebyshev polynomials, Collocation tech- niques, and Fourier series expansions, to study non-isothermal flow behavior across varying magnetic field strengths (M). Steady curves are obtained and linear stability of the flows is examined. The findings indicate that the asymmetry in the flow structure becomes weaker, eventually transitioning to a symmetrical state as M in- creases. The flux decreases, the intensity of the axial velocity reduces and moves to the middle of the duct as M is increased, while the linearly stable zone gradually expands. Furthermore, the linearly stable flow regime expands significantly with the increase of the magnetic field strength. The results further identify a magnetic parameter Mc = 10.15 as a critical value beyond which the flow transitions to a fully stable state. In the unsteady regime, oscillatory and chaotic flow behaviors are progressively weakened, and the steady-state region becomes domi- nant for higher values of M. The Hall parameter (m) is found to enhance both flux and axial velocity intensity, whereas the ion-slip parameter (α) shows minimal impact on secondary and axial flows. Heat transfer effects remain relatively unchanged within the curved channel under MHD influence. Overall, the findings provide valuable findings on MHD flow dynamics, with potential relevance to various industrial and engineering applications.