Showing papers on "Hartmann number published in 2006"

Peristaltically induced motion of a MHD third grade fluid in a deformable tube

Abstract: We consider incompressible, magnetohydrodynamic (MHD) third grade fluid confined in a circular cylindrical tube. The tube surfaces are electrically non-conducting. Travelling sinusoidal wave is imposed on the tube which induces peristaltic motion in the fluid. The stream function, axial velocity and pressure gradient are determined analytically for small Deborah number ( Γ ) . The analysis consists of a perturbation expansion in terms of the Deborah number up to O ( Γ ) . Solutions for pressure rise and frictional force per wavelength are given through the use of numerical integration. The general solution of highly non-linear equation for the hydrodynamic third grade fluid is developed. The results are finally compared with the third grade hydrodynamic and Newtonian fluid cases. It is found that the axial velocity increases by increasing Deborah number but decreases for large values of Hartmann number.

Large eddy simulation of magnetohydrodynamic turbulent channel flows with local subgrid-scale model based on coherent structures

Abstract: For turbulent channel flows with a uniform magnetic field perpendicular to insulated walls, the performance of the coherent structure Smagorinsky model (CSM) is investigated in comparison to the Smagorinsky model (SM) and the dynamic Smagorinsky model (DSM). The Lorentz force acts against a streamwise flow. The effect of the Hartmann flattening leads to an increase in the wall shear stress, so that the skin friction coefficient increases. In contrast, the turbulence suppression by the magnetic field results in a decrease of the Reynolds shear stress near the wall, so that the skin friction coefficient decreases. As the magnetic field increases, a turbulent magnetohydrodynamic (MHD) flow transits to a laminar MHD flow at a critical Hartmann number. The CSM predicts a higher transition Hartmann number than the DSM and SM, because the model parameter of the CSM is locally determined based on coherent structures and the fluctuations are reflected in the shear stress. On the other hand, the model parameter of ...

On the flow past a magnetic obstacle

Abstract: This paper analyses numerically the quasi-two-dimensional flow of an incompressible electrically conducting viscous fluid past a localized zone of applied magnetic field, denominated a magnetic obstacle. The applied field is produced by the superposition of two parallel magnetized square surfaces, uniformly polarized in the normal direction, embedded in the insulating walls that contain the flow. The area of these surfaces is only a small fraction of the total flow domain. By considering inertial effects in the analysis under the low magnetic Reynolds number approximation, it is shown that the flow past a magnetic obstacle may develop vortical structures and eventually instabilities similar to those observed in flows interacting with bluff bodies. In the small zone where the oncoming uniform flow encounters the non-negligible magnetic field, the induced electric currents interact with the field, producing a non-uniform Lorentz force that brakes the fluid and creates vorticity. The effect of boundary layers is introduced through a friction term. Due to the localization of the applied magnetic field, this term models either the Hartmann braking within the zone of high magnetic field strength or a Rayleigh friction in zones where the magnetic field is negligible. Finite difference numerical computations have been conducted for Reynolds numbers Re=100 and 200, and Hartmann numbers in the range 1 ≤ Ha ≤ 100 (Re and Ha are based on the side length of the magnetized square surfaces). Under these conditions, a wake is formed behind the obstacle. It may display two elongated streamwise vortices that remain steady as long as the Hartmann number does not exceed a critical value. Once this value is reached, the wake becomes unstable and a vortex shedding process similar to the one observed in the flow past bluff bodies is established. Similarities and differences with the flow around solid obstacles are discussed.

Effects of a magnetic field on trapping through peristaltic motion for generalized Newtonian fluid in channel

Abstract: We investigate the effects of magnetic field on trapping at the centerline and at the channel wall for Carreau fluid through uniform channel. The problem is formulated using a perturbation method (to second order) in terms of Weissenberg number ( Wi ). It has been noted that the pressure rise and friction force for Newtonian and Carreau fluids increase with Hartmann number M except at certain values of volume flow rate. The trapping limit and the trapping occurrence region at the centerline increase with M but they are independent approximately of M at certain values of amplitude ratio. Furthermore, the trapping occurrence region (at the wall) decreases as M is increased. Also, the magnitude of vertical velocity and shearing extra stress increase with M in contraction region. The peristaltic pumping and the augmented pumping are discussed for various values of the physical parameters of interest.

Oscillatory hartmann two-fluid flow and heat transfer in a horizontal channel

Abstract: An unsteady Hartmann flow of two immiscible fluids through a horizontal channel with time-dependent oscillatory wall transpiration velocity is investigated. One of the fluids is assumed to be electrically conducting while the other fluid and the channel walls are assumed to be electrically insulating. Separate solutions for each fluid are obtained and these solutions are matched at the interface using suitable matching conditions. The partial differential equations governing the flow and heat transfer are transformed to ordinary differential equations and closed-form solutions are obtained in both fluids’ regions of the channel for steady and unsteady conditions. The closed-form results are presented graphically for various values of the Hartmann number, frequency parameter, periodic frequency parameter viscosity and conductivity ratios as well as the Prandtl number to show their effect on the flow and heat transfer characteristics.

Solution of magnetohydrodynamic flow problems using the boundary element method

Abstract: A boundary element solution is implemented for magnetohydrodynamic (MHD) flow problem in ducts with several geometrical cross-section with insulating walls when a uniform magnetic field is imposed perpendicular to the flow direction. The coupled velocity and induced magnetic field equations are first transformed into uncoupled inhomogeneous convection–diffusion type equations. After introducing particular solutions, only the homogeneous equations are solved by using boundary element method (BEM). The fundamental solutions of the uncoupled equations themselves (convection–diffusion type) involve the Hartmann number ( M ) through exponential and modified Bessel functions. Thus, it is possible to obtain results for large values of M ( M ≤300) using only the simplest constant boundary elements. It is found that as the Hartmann number increases, boundary layer formation starts near the walls and there is a flattening tendency for both the velocity and the induced magnetic field. Also, velocity becomes uniform at the center of the duct. These are the well-known behaviours of MHD flow. The velocity and the induced magnetic field contours are graphically visualized for several values of M and for different geometries of the duct cross-section.

Boundary element solution of unsteady magnetohydrodynamic duct flow with differential quadrature time integration scheme

Abstract: A numerical scheme which is a combination of the dual reciprocity boundary element method (DRBEM) and the differential quadrature method (DQM), is proposed for the solution of unsteady magnetohydrodynamic (MHD) flow problem in a rectangular duct with insulating walls. The coupled MHD equations in velocity and induced magnetic field are transformed first into the decoupled time-dependent convection–diffusion-type equations. These equations are solved by using DRBEM which treats the time and the space derivatives as nonhomogeneity and then by using DQM for the resulting system of initial value problems. The resulting linear system of equations is overdetermined due to the imposition of both boundary and initial conditions. Employing the least square method to this system the solution is obtained directly at any time level without the need of step-by-step computation with respect to time. Computations have been carried out for moderate values of Hartmann number (M⩽50) at transient and the steady-state levels. As M increases boundary layers are formed for both the velocity and the induced magnetic field and the velocity becomes uniform at the centre of the duct. Also, the higher the value of M is the smaller the value of time for reaching steady-state solution. Copyright © 2005 John Wiley & Sons, Ltd.

Skin-friction for unsteady free convection MHD flow between two heated vertical parallel plates

Abstract: Unsteady viscous incompressible free convection ∞ow of an electrically conducting ∞uid between two heated vertical parallel plates is considered in the presence of a uniform magnetic fleld applied transversely to the ∞ow. The induce fleld along the lines of motion varies transversely to the ∞ow and the ∞uid temperature changing with time. An analytical solution for velocity, induced fleld and the temperature distributions are obtained for small and large magnetic Reynolds numbers. The skin-friction at the two plates is obtained. Velocity distribution, induced fleld and skin-friction are plotted against the distance from the plates. It has been observed that with the increase in Rm, the magnetic Reynolds number, at constant M, the Hartmann number, leads to an increase in the skin-friction gradually. But with the increase in M, at constant Rm, the skin-friction decreases.

A new approach on MHD natural convection boundary layer flow past a flat plate of finite dimensions

Abstract: A new approach on MHD natural convection boundary layer flow from a finite flat plate of arbitrary inclination in a rotating environment, is presented. This problem plays a significant role on boundary layer flow control. It is shown that taking into account the pressure rise region at the leading edge of the plate leads to avoid separation and the back flow is reduced by the strong magnetic field. It is also shown that the frictional drag at the leading edge of the plate is reduced when the inclination angle α=π/4. In the case of isothermal flat plate, the bulk temperature becomes identical for any value of Gr (Grashof number) when the value of M 2 (Hartmann number) and K 2 (rotation parameter) are kept fixed.

Hydromagnetic natural convection of a binary fluid in a vertical porous enclosure

Abstract: An analytical and numerical investigation is conducted to study the effect of an electromagnetic field on natural convection in a vertical rectangular porous cavity saturated with an electrically conducting binary mixture. Uniform heat fluxes are applied to the vertical walls while the horizontal walls are adiabatic. Governing parameters of the problem under study are the thermal Rayleigh RT, Hartmann number Ha, buoyancy ratio ϕ, Lewis number Le, and aspect ratio A. An analytical solution, valid for tall enclosures (A > > 1), is derived on the basis of the parallel flow approximation. In the range of the governing parameters considered in this study, a good agreement is found between the analytical predictions and the numerical results obtained by solving the full governing equations.

Damping rate of magnetohydrodynamic vortices at low magnetic Reynolds number

Abstract: The damping rate of vortices in an electrically conducting fluid submitted to a uniform magnetic field is analyzed for a large Hartmann number Ha. The fluid is contained in a layer of constant thickness h, bounded by two insulating walls that are perpendicular to the magnetic field. The damping times and the eigenfunctions along the magnetic field are obtained from a linear eigenvalue problem. According to the damping times and these eigenfunctions, vortices are classified into several classes by the range of combinations of the mode number m in the magnetic field direction and the wave number k2D in the plane perpendicular to the magnetic field. It is found that the damping rate of vortices in the range of k2D∼[(m+12)πHa]1∕2h−1 and m=0,1,2 is of the same order as that of large-scale two-dimensional vortices. This fact suggests that actual quasi-two-dimensional magnetohydrodynamic turbulent flows include not only m=0 but also higher-mode (m⩾1) eigenfunctions of this wave-number range, although the eigenfu...

Magnetic field effects on laminar film condensation on a finite-size horizontal wavy disk

Abstract: This work aims to study the laminar film condensation heat transfer with magnetic field effects on a finite-size horizontal wavy disk. Mathematical analysis is used to obtain the dimensionless governing equations and boundary conditions, and the cubic spline collocation method is then used to calculate the flow and heat transfer characteristics along the wavy disk. The effects of the important parameters, such as Hartmann number, condensation parameter, wave number, amplitude-wavelength ratio, and Pr/Ja on the heat transfer characteristics have been successfully examined. The magnetic field effect increases the critical condensate thickness and thus decreases the condensation heat transfer. Odd wave number effects decrease the critical condensate thickness and thus enhance the condensation heat transfer.