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

• 作者: Md. Mahmud Alam Md. Mainul Hoque
• 来源期刊: 流体动力学(英文)
• 学科: 数学
• 关键词: CURVATURE Spectral Method TAYLOR NUMBER Dean NUMBER and Magnetic Parameter
• 年，卷（期）: 2015,（2）
• 页码范围: 121-127
• 页数: 7页
• 分类号: O1

摘要

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 −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.