Non-isothermal magnetohydrodynamic fluid flow along the centerline in a rotating curved square duct with Hall and ion-slip current

Abstract

This study is considered a fully developed non-isothermal, viscous, incompressible fluid flow that passes through the centerline of a rotating square curved duct in the presence of the magnetic field with Hall and ion-slip current. This non-isothermal duct is generated by keeping the heat on the outer wall and cool on the inner wall; the upper and lower walls are taken as adiabatic. The aspect ratio of the duct is taken l = 1 so that the duct cross section is viewed as square. The gravitational force acts on the flow as an external force, and a pressure gradient force (namely, Dean number effects) has been applied along the centerline of the duct. Due to the rotation of the system and the duct curvature, the flow is influenced by the centrifugal and Coriolis forces. The calculations are carried out by the spectral method as the primary tool, while the Chebyshev polynomial, collocation method, Newton–Raphson method, and arc-length method are used as secondary tools. The focus is to show the effects of the magnetic parameter (M), Hall parameter (m), and ion-slip parameter (α) on the flow characteristics of this rotationally curved square duct. The new findings have been shown in various values of M, m, and α for the three cases of Dean numbers, such as case I: Dn = 1000, case II: Dn = 3000, and case III: Dn = 5000, with different curvatures, while the rotational parameter is fixed at Tr = 20. Here, it is considered that Dn, Gr, Tr, M, m, and α are varied, while the curvature of the duct δ ranges from 0.01 to 0.5.