Numerical Simulation of Rotating MHD Flow with Heat Transfer (original) (raw)
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Acta Mechanica, 2006
This paper is devoted to the numerical study of axisymmetric rotating flow in enclosed cylinders with aspect ratios R (diameter divided by height) equal to 0.25, 0.33, 0.5, 1, 2, 3 and 4. The steady motion of the liquid is caused by the action of a low-frequency, low-induction rotating magnetic field with magnetic Taylor numbers lying in the range from 0.0025 AE Ta cr to 0.9 AE Ta cr , where Ta cr refers to the critical magnetic Taylor number. We found that the ratio between global meridional to global azimuthal flow velocity passes a distinct maximum which depends on the aspect ratio. It marks the transition from the viscous to the inertial regime. Their characteristic features are examined by analysis of the angular velocity and the torques exerted by the boundaries, in dependence on Ta and the aspect ratio.
International Journal of Heat and Mass Transfer, 2009
Forced convection heat transfer across a circular cylinder rotating with a constant non-dimensional rotation rate ðaÞ varying from 0 to 6 are investigated for Reynolds numbers of 20-160 and a Prandtl number of 0.7. Flow transitions is reported here for a wider range of Reynolds number and rotation rates. Heat transfer visualization technique using heatlines is implemented here, probably for the first time, in finite volume framework for the unsteady heat transfer problem in complex domain and used for heat flow analysis. Rotation can be used as a drag reduction and heat transfer suppression technique.
On the Stability of Rotating MHD Flows
Fluid Mechanics and Its Applications, 1999
We present a numerical study of the flow induced by a rotating magnetic field on a liquid metal which fills a cylindrical container. Using a low frequency approximation and assuming axisymmetry, a finite difference technique is employed for the calculation of the flow field. Two different cases are considered in order to show that using a rotating magnetic field requires a detailed knowledge of its interaction with the flow. In the first situation, which is isothermal, it is shown that increasing the field intensity leads to the occurrence of Taylor-Couette type centrifugal instabilities depending upon the aspect ratio of the cavity. In the second case, which includes a heat transfer problem, it is shown that applying a very moderate rotating field to an initially unstable thermally driven convection is able to restore the flow stability.
2020
Several technological applications involve the flow of liquid metals in ducts under a magnetic field, for instance, the coolants of fusion reactors. In this paper, using a magnetohydrodynamic MHD formulation based on the electric potential, we obtain an analytical solution for the flow of a liquid metal in a rectangular duct with two insulating walls and two perfectly conducting walls perpendicular to the applied uniform magnetic field. As the Hartmann number increases, the flow displays high velocities in the boundary layers attached to the insulating walls and a quasi-stagnant flow at the core. The effect of this flow pattern on the forced convection heat transfer is then explored numerically considering a uniform heat flux on either the conducting or insulating walls. Compared to the hydrodynamic case, the MHD flow enhances the heat transfer as the Hartmann number increases only in the case when the heat flux is applied at the insulating walls where high velocities are present. T...
This paper is devoted to the analysis of unsteady 2-D dynamic, thermal and diffusion magnetohydrodynamic laminar boundary layer flow over a horizontal circular cylinder of incompressible and electrical conductivity fluid, in a porous medium, in the presence of a heat source or sink, and chemical reactions. The present magnetic field is homogenous and perpendicular to the body surface. It is assumed that the induction of the outer magnetic field is the function of the longitudinal coordinate and time. Fluid electrical conductivity is constant. The outer electric field is neglected and the magnetic Reynolds number is significantly lower than one i. e. the considered the problem is in induction-less approximation. Free stream velocity, temperature and concentration on the body are arbitrary differentiable functions. The developed governing boundary layer equations and associated boundary conditions are converted into a non-dimensional form using a suitable similarity transformation and similarity parameters. The system of dimensionless equations is solved using the finite difference method and iteration method. Numerical results are obtained and presented for incompressible fluid for different numbers, such as Sc, Pr, Ec and magnetic number, and the parameter of the porous medium, temperature parameters, thermal parameter, diffusion parameters and chemical reaction parameter. The solutions for the flow, temperature and diffusion transfer and other integral characteristics, boundary layer, are evaluated numerically for different values of the magnetic field. Transient effects of velocity, temperature and diffusion are analyzed. A part of obtained results is given in the form of figures and corresponding conclusions.
Laminar forced convection from a rotating horizontal cylinder in cross flow
Journal of Thermal Science, 2017
The influence of non-dimensional rotational velocity, flow Reynolds number and Prandtl number of the fluid on laminar forced convection from a rotating horizontal cylinder subject to constant heat flux boundary condition is numerically investigated. The numerical simulations have been conducted using commercial Computational Fluid Dynamics package CFX available in ANSYS Workbench 14. Results are presented for the non-dimensional rotational velocity α ranging from 0 to 4, flow Reynolds number from 25 to 40 and Prandtl number of the fluid from 0.7 to 5.4. The rotational effects results in reduction in heat transfer compared to heat transfer from stationary heated cylinder due to thickening of boundary layer as consequence of the rotation of the cylinder. Heat transfer rate increases with increase in Prandtl number of the fluid.
A Numerical Study of MHD Laminar Flow in a Rotating Curved Pipe with Circular Cross Section
Open Journal of Fluid Dynamics, 2015
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.
Journal of Applied Mechanics and Technical Physics
Abstract - In the current paper, axisymmetric magnetohydrodynamic (MHD) boundary layer flow and heat transfer of a fluid over a slender cylinder is investigated numerically. The effects of viscous dissipation, thermal radiation and surface transverse curvature are taken into account in the simulations. To do this, using the appropriate similarity transformations, the governing partial differential equations are transformed to ordinary differential equations. Resultant ordinary differential equations along with the appropriate boundary conditions are solved using fourth order Runge-Kutta method featuring by a shooting technique. Results are presented via diagrams and tables that clearly indicate the effect of each parameter on velocity and temperature profiles as well as local skin friction factor and Nusselt number.
Heat Transfer and MHD Boundary Layer Flow over a Rotating Disk
An analysis of heat transfer with MHD boundary layer flow of an electrically conducting viscous fluid over a rotating disk in the presence of magnetic field has been carried out. The governing partial differential equations have been transformed in to ordinary differential form by using similarity transformations. The resulting equations have been solved numerically by Successive over relaxation (SOR) method and Simpson's (1/3) rule. The numerical results have been improved by Richardson extrapolation to the limit. The effects of magnetic parameter M , Prandtl number Pr and temperature index parameter n are investigated on the features of fluid flow and temperature profiles.
FME Transactions
The present research work investigates the MHD braking and Joules heating effect in a confined rotating cylindrical cavity packed with liquid metal. All walls, except the top and bottom portion of the sidewall, of the cylindrical cavity, are made of electrically as well as thermally conducting material. The cavity is exposed to both axial magnetic fields along with the axial temperature gradient, packed with the incompressible electrically conducting liquid. The MHD braking effect is experienced within the rotating liquid metal flow due to the presence of a strong axial magnetic field. It is discerned that MHD braking governs the primary, as well as secondary flow, and, reduces Joules heating effect. Moreover, the internal heat generation due to Joules heating is governed by rotating speed, Hartmann strength, and temperature gradient.