A Numerical Study of MHD Laminar Flow in a Rotating Curved Pipe with Circular Cross Section

Md. Mainul Hoque, Md. Mahmud Alam

Discipline of Mathematics, School of Engineering and Technology, Khulna University, Khulna, Bangladesh.

DOI: 10.4236/ojfd.2015.52014                

Abstract

The incompressible viscous steady flow through a rotating curved pipe of circular cross-section with magnetic field is investigated numerically to examine the combined effects of rotation (Coriolis force), magnetic field and curvature (centrifugal force) on the flow. The curvature of the pipe has been assumed to be small, that is, the radius of the circle in which the central line of the pipe is coiled is large in comparison with the radius of the cross section. Spectral method is applied as a main tool for the numerical technique, where Fourier series, Chebyshev polynomials, Collocation methods, and Iteration method are used as secondary tools. The flow depends on the Taylor number (Tr), Dean Number (Dn), Magnetic Parameter (M) and the dimensionless curvature of the pipe δ. When Tr > 0, the rotation is in the direction so that the Coriolis force enforces the curvature effect. When Tr < 0, the rotation is in the direction so that the Coriolis force exhibits an opposite effect to that of the curvature. The calculations are carried out for −1500 ≤ Tr ≤ 1500, Dn ≥ 1000 (large Dean number), M ≥ 0 and δ = 0.01. Due to high magnetic field four-vortex solution is observed in a rotating curved pipe system. Visualization is attained with MAPLE software.

Keywords

Curvature, Spectral Method, Taylor Number, Dean Number and Magnetic Parameter

Conflicts of Interest

The authors declare no conflicts of interest.

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