Magneto-hydrodynamic Flow through a Rotating Rectangular Straight and Curve Duct with Magnetic Field

Abstract

This research involves a numerical exploration of the characteristics of fully developed, steady, viscous, incompressible flow within a curved duct with square and rectangular cross-sections. The study considers both isothermal and non-isothermal conditions, while also accounting for the influence of magnetic fields, Hall currents, and Ion-slip currents. In this investigation, the dimensions of the cross-section are defined as having a height of 2h and a width of 2d. The analysis covers curved ducts with both square and rectangular cross sections for both isothermal and non-isothermal flow scenarios. In both cases, the aspect ratio is taken as l = 1 or 2 or 3, whereas the curvature of the duct ranges from 0.01 to 5. Also, the behaviour of the flow characteristic is investigated for non-isothermal flow through the straight duct in the presence of Hall and Ion-slip currents. A pressure gradient force, known as Dean Forces, is applied in the direction of the curved duct's centreline. This flow is further influenced by a combination of forces, including gravitational force, Lorentz force, centrifugal force, and Coriolis force. The gravitational force exerts its effect on the fluid. Additionally, the Lorentz force results from the interaction of electric and magnetic forces, while centrifugal and Coriolis forces stem from the duct's rotation and curvature. To model this complex system, governing equations are derived from the Navier–Stokes and Energy equations using cylindrical coordinates. These equations are then converted into their non-dimensional forms through the customary non-dimensional analysis. The spectral approach is used as the main instrument to perform the calculations. Additionally, as auxiliary tools, the Newton-Raphson, Collocation, Chebyshev polynomial, and arc-length procedures are employed. The arc-length method has been used to avoid the difficulties near the point of inflection and calculate the results at this point. The flow depends on the Taylor number υ δ δ d Tr 0 2 2 2 Ω = (Rotation parameter), Magnetic parameter ρυ B σ d M e 2 0 2 = , Grashof Number 2 3 υ β T g d Gr ∆ = ammeter Hall parameter ) (m , and Ion-slip parameter ) (α . The study examines the impact of Tr, Grand Dnon flow characteristics to compare and validate the findings with prior research. The primary objective of this investigation is to elucidate how M, m, and α influence flow characteristics within both rotational square and rectangular curved ducts, as well as in straight square ducts. Both co-rotating and counter rotating flow patterns are investigated here. Finally, a general discussion and conclusions on the solutions to the problems considered in the research study for different values of the magnetic, Hall, and Ion-slip parameters on the flow properties in some particular cases of Dean Number and different duct curvature are described.