恒磁场对刚性圆直管中脉动流的影响*

本文研究了恒磁场对于刚性圆直管中脉动流的影响,并根据现有的实验资料考虑了磁场对于血液粘度的影响,给出了恒磁场作用下刚性圆直管脉动流的分析解以及恒磁场对刚性圆直管中的流速分布、流量以及阻抗的影响的计算结果.这些结果对于深入研究磁场对于血液动力学的影响具有一定参考价值.     

低频交变磁场对于刚性直圆管中脉动流的影响*

本文通过求解灾变磁场作用下刚性直圆管脉动流的运动方程,得到了它的分析解.计算了流速分布及阻抗.计算结果对于深入了解低频磁场对于血液动力学的影响以及它的临床应用具有一定参考价值.     

Influence of moving magnetic field on three dimensional Couette flow

A three dimensional steady fully developed MHD Couette flow of a viscous incompressible electrically conducting fluid is analysed. The lower stationary porous plate is subjected to a periodic injection velocity and the upper porous plate in uniform motion to a constant suction velocity. A magnetic field of uniform strength applied normal to the planes of the plates is fixed with the moving plate. Neglecting the induced magnetic field, an approximate solution for the flow field is obtained and discussed with the help of graphs.     

Influence of moving magnetic field on three dimensional Couette flow

A three dimensional steady fully developed MHD Couette flow of a viscous incompressible electrically conducting fluid is analysed. The lower stationary porous plate is subjected to a periodic injection velocity and the upper porous plate in uniform motion to a constant suction velocity. A magnetic field of uniform strength applied normal to the planes of the plates is fixed with the moving plate. Neglecting the induced magnetic field, an approximate solution for the flow field is obtained and discussed with the help of graphs.     

Hydromagnetic instability of a power-law liquid film flowing down a vertical cylinder using numerical approximation approach techniques

The long-wave perturbation method is employed to investigate the hydromagnetic stability of a thin electrically-conductive power-law liquid film flowing down the external surface of a vertical cylinder in a magnetic field. The validity of the numerical results is improved through the introduction of the flow index and the magnetic force into the governing equation. In contrast to most previous studies presented in the literature, the solution scheme employed in this study is based on a numerical approximation approach rather than an analytical method. The normal mode approach is used to analyze the stability of the film flow. The modeling results reveal that the stability of the film flow system is weakened as the radius of the cylinder is reduced. However, the flow stability can be enhanced by increasing the intensity of the magnetic field and the flow index, respectively. In general, the optimum conditions can be found through the use of a system to alter stability of the film flow by controlling the applied magnetic field.     

A Method for Determining Linear Solutions in Magnetohydrodynamics

Given any two-dimensional and incompressible flow describedby a set of linear partial differential equations, a methodis presented for determining the solution for the dependentvariables (velocity, pressure, etc.). The method is then usedto investigate the following magnetohydrodynamic flows. (a) The flow of an irrotational and inviscid fluid. (b) The flow of a viscous fluid. (c) The flow of an electrically conducting, inviscid fluid inthe presence of a magnetic field aligned with the flow at infinity. (d) The flow of an electrically conducting, viscous fluid inthe presence of a magnetic field having arbitrary direction.     

A finite volume spectral element method for solving magnetohydrodynamic (MHD) equations

In this paper, the coupled equations in velocity and magnetic field for unsteady magnetohydrodynamic (MHD) flow through a pipe of rectangular section are solved using combined finite volume method and spectral element technique, improved by means of Hermit interpolation. The transverse applied magnetic field may have an arbitrary orientation relative to the section of the pipe. The velocity and induced magnetic field are studied for various values of Hartmann number, wall conductivity and orientation of the applied magnetic field. Comparisons with the exact solution and also some other numerical methods are made in the special cases where the exact solution exists. The numerical results for these sample problems compare very well to analytical results.     

Steady Magnetogasdynamic Flow Past a Source

This paper presents an asymptotic solution for the disturbanceat large distance from a source placed in a flow of conductingcompressible fluid in the presence of an applied magnetic field.The solution is obtained by a Fourier transform method usingtechniques developed for magnetohydrodynamic waves by Lighthill(1960). The results are discussed in detail for the cases ofthe undisturbed flow aligned with and perpendicular to the field,although they apply for any angle between the two, and showa Mach cone type of disturbance together with Alfvénwaves.     

Hydromagnetic forced flow against a porous rotating disk

This paper deals with the steady forced flow of a viscous, incompressible and electrically conducting fluid against a porous rotating disk when a uniform magnetic field acts perpendicular to the disk surface. For small suction the equations of motion are integrated numerically by Kármán-Pohlhausen method, but for large suction a series solution in the inverse powers of the suction parameter is obtained. The effects of disk porosity and magnetic field on the various flow parameters are discussed in detail.     

Couette flow of a third-grade fluid with variable magnetic field

This investigation deals with the analytic solution for the time-dependent flow of an incompressible third-grade fluid which is under the influence of a magnetic field of variable strength. The fluid is in an annular region between two coaxial cylinders. The motion is induced due to an inner cylinder with arbitrary velocity. Group theoretic methods are employed to analyse the nonlinear problem and a solution for the velocity field is obtained analytically.     

Influence of induced magnetic field and heat transfer on peristaltic transport of a Carreau fluid

The effect of an induced magnetic field on peristaltic flow of an incompressible Carreau fluid in an asymmetric channel is analyzed. Perturbation solution to equations under long wavelength approximation is derived in terms of small Weissenberg number. Expressions have been constructed for the stream function, the axial induced magnetic field, the magnetic force function, the current density distribution and the temperature. Trapping phenomenon is examined with respect to emerging parameters of interest.     

Linear oscillatory hydromagnetic flow between two coaxial cylinders

Hydromagnetic flow between two coaxial circular cylinders is discussed when the inner cylinder oscillates axially under a radial magnetic field. Exact solution is given for the case of a perfectly conducting fluid. Expressions for velocity, induced magnetic field, current density, electric field, viscous drag and energy transfer are derived and expressed in polar forms so as to facilitate the study of magnitude and phase variations. Current sheets are found to exist on the two boundaries.     

Unsteady hydromagnetic rotating flow of a conducting second grade fluid

The purpose of this work is to investigate the hydromagnetic oscillatory flow of a fluid bounded by a porous plate, when the entire system rotates about an axis normal to the plate. The fluid is assumed to be non-Newtonian (second grade), incompressible and electrically conducting. The magnetic field is applied transversely to the direction of the flow. Such a flow model has great significance not only of its theoretical interest, but also for applications to geophysics and engineering. The resulting initial value problem has been solved analytically for steady and unsteady cases. The analysis of the obtained results showed that the flow field is appreciably influenced by the material parameter of the second grade fluid, the applied magnetic field, the imposed frequency, rotation and suction and blowing parameters. It is observed in a second grade fluid that a steady asymptotic hydromagnetic solution exists for blowing and resonance which is different from the hydrodynamic situation.     

Strong solutions to the equations of electrically conductive magnetic fluids

We study the equations of flow of an electrically conductive magnetic fluid, when the fluid is subjected to the action of an external applied magnetic field. The system is formed by the incompressible Navier–Stokes equations, the magnetization relaxation equation of Bloch type and the magnetic induction equation. The system takes into account the Kelvin and Lorentz force densities. We prove the local-in-time existence of the unique strong solution to the system equipped with initial and boundary conditions. We also establish a blow-up criterion for the local strong solution.     

Flow of a second grade fluid over a sheet stretching with arbitrary velocities subject to a transverse magnetic field

The boundary layer flow of a second grade fluid over a permeable stretching surface with arbitrary velocity and appropriate wall transpiration is investigated. The fluid is electrically conducting in the presence of a constant applied magnetic field. An exact solution to the nonlinear flow problem is presented.     

Fundamental solution for coupled magnetohydrodynamic flow equations

In this paper, a fundamental solution for the coupled convection–diffusion type equations is derived. The boundary element method (BEM) application then, is established with this fundamental solution, for solving the coupled equations of steady magnetohydrodynamic (MHD) duct flow in the presence of an external oblique magnetic field. Thus, it is possible to solve MHD duct flow problems with the most general form of wall conductivities and for large values of Hartmann number. The results for velocity and induced magnetic field is visualized in terms of graphics for values of Hartmann number M?300$M?300$.     

Stability analysis of an interface between immiscible liquids in Hele-Shaw flow in the presence of a magnetic field

Hydrodynamic instabilities may occur when a viscous fluid is driven by a less viscous one through a porous medium. These penetrations are common in enhanced oil recovery, dendrite formation and aquifer flow. Recent studies have shown that the use of magnetic suspensions allow the external control of the instability. The problem is nonlinear and some further improvements of both theory and experimental observations are still needed and continue being a current source of investigation. In this paper we present a generalized Darcy law formulation in order to examine the growth of finger instabilities as a magnetic field is applied to the interface between the fluids in a Hele-Shaw cell. A new linear stability analysis is performed in the presence of magnetic effects and provides a stability criterion in terms of the non-dimensional physical parameters of the examined flow and the wavenumber of the finger disturbances. The interfacial tension inhibits small wavelength instabilities. The magnetic field contributes to the interface stability for moderate wavelength as it is applied parallel to the liquid-interface. In particular, we find an explicit expression, as a function of the susceptibility, for a critical angle between the interface and the magnetic field direction, in which its effect on the interface is neutral. We have developed a new asymptotic solution for the flow problem in a weak nonlinear regime. The first correction captures the second order nonlinear effects of the magnetic field, which tends to align the fingers with the field orientation and have a destabilizing effect. The analysis predicts that the non-linear effects at second order can counterbalance the first order stabilizing effect of a parallel magnetic field which results in a loss of effectiveness for controlling the investigated finger instabilities. The relevant physical parameters for controlling these finger instabilities are clearly identified by our non-dimensional analysis.     

Flow field of a third-grade non-Newtonian fluid in the annulus of rotating concentric cylinders in the presence of magnetic field

In this paper, the flow field of a third-grade non-Newtonian fluid in the annulus of rotating concentric cylinders has been investigated in the presence of magnetic field. For this purpose, the constitutive equation of such a fluid flow was simplified, and the existence of the solution to the governing equation was established using Schauder's fixed point theorem. Using the finite difference method, the numerical solution of the non-dimensionalized form of the established governing equation was obtained. The effect of sundry parameters such as the rotating speed of the cylinders, the physical properties of fluid, and magnetic field intensity on the fluid velocity field was studied as well.     

Mathematical modelling of flow control in a tundish using electro-magnetic forces

The control of flow in a tundish is important for improving the quality of the steel. Dams, Wiers and Pouring chamber are some of the devices used for controlling the flow in the tundish. The investigation about the role of electromagnetic forces as a replacement for these devices is an objective for the present work. Thus, 3-D MHD simulation was performed to study the effect of electromagnetic forces on flow behaviour in the tundish. The MHD model developed for carrying out the simulation was validated with the analytical solution of the Hartman problem. The results obtained shows improvement in the desired characteristics for inclusion flotataion with magnetic flow modifier of optimum strength of magnetic field.     

Hydromagnetic fluctuating flow of a couple stress fluid through a porous medium

The equations of a polar fluid of hydromagnetic fluctuating through a porous medium are cast into matrix form using the state space and Laplace transform techniques the resulting formlation is applied to a variety of problems. The solution to a problem of an electrically conducting polar fluid in the presence of a transverse magnetic field and to a probem for the flow between two parallel fixed plates is obtained. The inversion of the Laplace transforms, is carried out using a numerical approach. Numerical results for the velocity, angular velocity distribution and the induced magnetic field are given and illustrated graphically for each problems.