Non-Isothermal Steady Flow through a Rotating Square Straight Duct with Hall and Ion-Slip Currents

This research delved into examining the behavior of fully developed, viscous, non-isothermal, steady, laminar, incompressible fluid flow along the centerline of a straight square duct, considering the influence of magnetic fields as well as Hall and Ion-slip currents. To make the non-isothermal state of the flow, the right hand wall of the duct is considered as heated whereas left hand wall is cooled; the lower and upper walls are considered as adiabatic. A constant pressure gradient force, known as the Dean Force, is exerted along the centerline of the duct. Additionally, external forces, including gravitational force, Lorentz force, pressure gradient force, centrifugal force, and Coriolis force, influence the flow. The Lorentz force is also modified by applying the Hall and Ion-slip currents. The governing equations are derived from the continuity equation, the Navier-Stokes equation, and the energy equation. The spectral method is employed as the primary tool to obtain numerical solutions, complemented by secondary tools such as Chebyshev polynomials, Newton-Raphson method, collocation method, and arc-length method. The study examines the impact of various parameters, including the Grashof number (Gr), Taylor number (Tr), Dean number (Dn), magnetic parameter (M), Hall parameter (m), and Ion-slip parameter (а), on the velocity and temperature distributions within the flow. This investigation is conducted by analyzing solution curves of flux against the mentioned parameters. Furthermore, the corresponding flow patterns are analyzed at different points along the straight duct. As the new findings, the results are shown under the various distinct values of M, m and а at Dean Number Dn=500, 5000, 10000 with Taylor number is fixed at Tr=20.