Hall and ion-slip effects on MHD fluid flow in a rotating curved duct with aspect ratio 3

Abstract

This study numerically investigates the fully developed two-dimensional, steady, viscous, incompressible magnetohydrodynamic fluid flow that passes through a rotating curved duct with an aspect ratio of 3. The curvature of the duct has been taken over a wide range of 0.01 ≤ δ ≤ 0.5. The governing equations are derived from the Navier–Stokes equations, and these equations are transformed into their non-dimensional form by applying usual transformations. The velocity of the flow is influenced by a pressure gradient force (namely, Dean forces) along the axial direction of the curved duct. The flow is also accelerated due to the combined action of the centrifugal and Coriolis forces. The effects of the Dean number, rotation, magnetic, Hall, and ion-slip parameters are examined on that flow. The spectral method is used as the primary tool to calculate the numerical solution, while the Chebyshev polynomial, collocation, and Newton–Raphson methods are used as supporting tools. The arc length method has also been used to calculate the results at any point of the critical zone of the solution curve. The main focal point of this paper is to investigate the effect of the magnetic parameter, Hall parameter, and ion-slip parameter on the flow characteristics in the rotational curve duct with a comparatively large aspect ratio. There are symmetric 2-, 4-, up to 12-vortex solutions that have been found for the streamlines of the secondary flow. In contrast, 1-, 2-, up to uncountable contour plots have been found for the axial flow. Specifically, asymmetric flow structures have been found for a small curvature and large Dean number.