Conjugate MHD flow past a flat plate

Summary A boundary layer solution for the conjugate forced convection flow of an electrically conducting fluid over a semi-infinite flat plate in the presence of a transverse magnetic field is presented. The governing nonsimilar partial differential equations are solved numerically using the Keller box method. Values of the temperature profiles of the plate are obtained for various values of the parameters entering the problem and are given in a table and shown on graphs.     

Hall effects on magnetohydrodynamic free convection about a semi-infinite vertical flat plate

A theoretical analysis is presented for the problem of free convection flow of a conducting fluid along a semi-infinite vertical flat plate when the fluid is permeated by a transverse magnetic field and the Hall effects are taken into account. The derived fundamental equations on the assumption of small magnetic Reynolds number are solved numerically by employing the difference-differential method in combination with the Simpson's rule. The velocity and temperature profiles as well as the local Nusselt number are computed for various values of the Hall and magnetic parameters. The results are compared with those known from the literature.     

Thermal boundary layers in magnetohydrodynamic flow over a flat plate in the presence of a transverse magnetic field

Summary A boundary layer solution for the heat transfer of an electrically conducting fluid over a semi-infinite flat plate in the presence of a transverse magnetic field has been studied. The heat due to viscous dissipation and stress work were also included into the energy equation. The governing nonsimilar partial differential equations are transformed into ordinary differential ones by means of difference-differential method. The temperature profiles and heat transfer coefficient are obtained for various values of the parameters entering the problem.     

Hydromagnetic Flow Past an Impulsively Started Infinite Vertical Plate with Variable Temperature and Mass Diffusion

An exact solution of the MHD Stokes problem for the flow of an electrically conducting, incompressible, viscous fluid past an impulsively started infinite vertical plate in the presence of variable temperature and mass diffusion is obtained. The dimensionless governing equations are solved using the Laplace-transform technique. The plate temperature and the concentration level near the plate increase linearly with time. The solutions for the velocity and skin friction are obtained for different magnetic field parameters and multiple buoyancy effects for aiding and opposing flows. It is observed that the velocity decreases in the presence of a magnetic field as compared to its absence and that the skin friction increases in the presence of aiding flows and decreases with opposing flows.__________Published in Inzhenerno-Fizicheskii Zhurnal, Vol. 78, No. 2, pp. 131–135, March–April, 2005.     

A study of induced magnetic field with chemically reacting and radiating fluid past a vertical permeable plate

The influence of thermal radiation and chemical reaction on the steady MHD heat and mass transfer by a mixed convective flow of a viscous, incompressible, electrically conducting Newtonian fluid (an optically thin gray gas) past a vertical permeable plate was investigated with account for the induced magnetic field. The similarity solutions of the transformed nondimensional governing equations are obtained by the series solution technique. The influence of numerous parameters on the process characteristics is studied.     

Theoretical magnetohydrodynamic analysis of mixed convection boundary-layer flow over a wedge with uniform suction or injection

Summary The purpose of this work is to study the effects of an applied magnetic field on the mixed convection boundary-layer flow over a wedge with suction or injection. The fluid is assumed to be viscous, incompressible and electrically conducting, and the magnetic field is applied transversally to the direction of the flow. Such a flow model has great significance not only of its own theoretical interest, but also for applications to aerodynamics and engineering. The governing partial differential equations of this problem, subjected to their boundary conditions, are solved numerically by applying an efficient solution scheme for local nonsimilarity boundary-layer analysis. Numerical calculations are carried out for different values of the dimensionless parameters of the problem, and the analysis of the obtained results showed that the flow field is appreciably influenced by the applied magnetic field.     

Convective and Absolute Instability in the Incompressible Boundary Layer on a Rotating Disk in the Presence of a Uniform Magnetic Field

The stability of a conducting fluid flow over a rotating disk with a uniform magnetic field applied normal to the disk, is investigated. It is assumed that the magnetic field is unaffected by the motion of the fluid. The mean flow and linear stability equations are solved for a range of magnetic field-strength parameters and the absolute/convective nature of the stability is investigated. It is found that increasing the magnetic field parameter is in general stabilizing.     

Unsteady MHD convective heat and mass transfer past a semi-infinite vertical permeable moving plate with heat absorption

The problem of unsteady, two-dimensional, laminar, boundary-layer flow of a viscous, incompressible, electrically conducting and heat-absorbing fluid along a semi-infinite vertical permeable moving plate in the presence of a uniform transverse magnetic field and thermal and concentration buoyancy effects is considered. The plate is assumed to move with a constant velocity in the direction of fluid flow while the free stream velocity is assumed to follow the exponentially increasing small perturbation law. Time-dependent wall suction is assumed to occur at the permeable surface. The dimensionless governing equations for this investigation are solved analytically using two-term harmonic and non-harmonic functions. The obtained analytical results reduce to previously published results on a special case of the problem. Numerical evaluation of the analytical results is performed and some graphical results for the velocity, temperature and concentration profiles within the boundary layer and tabulated results for the skin-friction coefficient, Nusselt number and the Sherwood number are presented and discussed.     

MHD flow over a moving flat plate with a step change in the magnetic field

Summary The boundary layer flow over a moving continuous flat plate in an electrically conducting ambient fluid with a step change in the applied magnetic field is considered. The governing equations are solved numerically using the Keller box method. It is shown that the skin friction decreases as the magnetic parameter increases.     

Wire coating analysis using MHD Oldroyd 8-constant fluid

The problem of wire coating by withdrawal from a bath of a magnetohydrodynamic Oldroyd 8-constant fluid is investigated. The fluid is electrically conducting in the presence of a uniform applied magnetic field. The obtained non-linear differential equation has been solved using homotopy analysis method. The solution is given in the form of a series. The convergence of the series is explicitly discussed. The effects of emerging non-Newtonian parameters and the Hartman number is seen. The results are presented graphically and discussed.     

A numerical solution of the steady MHD flow through infinite strips with BEM

The magnetohydrodynamic (MHD) flow of an incompressible, viscous, electrically conducting fluid in infinite channels in the presence of a magnetic field is investigated. The fluid is driven either by a pressure gradient or by the currents produced by electrodes placed parallel in the middle of the walls. The applied magnetic field is perpendicular to the infinite walls which are combined from conducting and insulated parts. A boundary element method (BEM) solution has been obtained by using a fundamental solution which enables to threat the convection-diffusion type equations in coupled form with general wall conductivities. Constant elements are used for the discretization of the walls by keeping them as finite since the boundary integrals are restricted to these boundaries due to the regularity conditions as x,y→±∞. The solutions are presented in terms of equivelocity and induced magnetic field contours for several values of Hartmann number and conducting lengths. The effect of the parameters on the solution is visualized.     

MHD flow between two parallel plates with heat transfer

Summary In the present paper, the steady flow of an electrically conducting, viscous, incompressible fluid bounded by two parallel infinite insulated horizontal plates and the heat transfe through it are studied. The upper plate is given a constant velocity while the lower plate is kept stationary. The viscosity of the fluid is assumed to vary with temperature. The effect of an external uniform magnetic field as well as the action of an inflow perpendicular to the plates together with the influence of the pressure gradient on the flow and temperature distributions are reported. A numerical solution for the governing non-linear ordinary differential equations is developed.     

The scattering of oblique flexural waves of a cracked conducting plate in a uniform magnetic field

Summary Following a classical plate bending theory for magneto-elastic interactions under quasistatic electromagnetic field, we consider the scattering of time harmonic flexural waves by a through crack in a conducting plate under a uniform magnetic field normal to the crack surface. It is assumed that the plate has the finite electric conductivity, and the electric and magnetic permeabilities of the free space. An incident wave giving rise to moments symmetric about the crack plane is applied in an arbitrary direction. Fourier transform method is used to solve the mixed boundary value problem which reduces to a pair of dual integral equations. These dual integral equations are further reduced to a Fredholm integral equation of the second kind. The dynamic moment intensity factor versus frequency for several values of incident angle is computed and the influence of the magnetic field on the normalized values is displayed graphically.     

Thermal radiation effects on magnetohydrodynamic mixed convection flow of a micropolar fluid past a continuously moving semi-infinite plate for high temperature differences

Summary An analysis is presented to study the effect of radiation on magnetohydrodynamic mixed convective steady laminar boundary layer flow of an optically thick electrically conducting viscous micropolar fluid past a moving semi-infinite vertical plate for high temperature differences. A uniform magnetic field is applied perpendicular to the moving plate. The density of the micropolar fluid is assumed to reduce exponentially with temperature. The usual Boussinesq approximation is neglected because of the high temperature differences between the plate and the ambient fluid. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The resulting governing equations are transformed using a similarity transformation and then solved numerically by applying an efficient technique. The effects of radiation parameter R, magnetic parameter M, couple parameter Δ and density/temperature parameter n on the velocity, angular velocity and temperature profiles as well as the local skin friction coefficient, wall couple stress and the local Nusselt number are presented graphically and in tabular form.     

Thermal instability in a micropolar fluid layer subject to a magnetic field

In the present paper we have considered thermal instability in a heat conducting micropolar fluid layer under the influence of a transverse magnetic field. Assuming the bounding surfaces to be rigid the eigenvalue problem is solved using finite-difference and Wilkinson's iteration techniques. Here it is seen that the instability sets in not only for adverse temperature gradient but also for positive temperature gradient. Both the microtation and the magnetic field are seen to stabilize the fluid layer. However, the stabilizing effect of microrotation becomes less significant when the strength of the magnetic field is large. In the case of heating from below, the critical wave number is seen to be insensitive to increase in the strength of the magnetic field, while it increases significantly when the fluid is heated from above.     

Magnetofluiddynamic flow with a pressure gradient and fluid injection

Summary The nonlinear partial differential equation of motion for an incompressible fluid flowing over a flat plate under the influence of a magnetic field and a pressure gradient, and with or without fluid injection (or ejection) through the plate is transformed to a nonlinear, third order ordinary differential equation by using a stream function and a similarity transformation.The necessary boundary conditions are developed for flow with and without fluid injection (or ejection), and an example is presented to illustrate the solution to the flow problem.The controlling equation reduces to the well known Falkner-Skan equation when the magnetic field is zero, and if additionally the pressure gradient is zero, the equation reduces to the Blasius equation.     

Effect of uniform suction or injection on a magnetohydrodynamic boundary layer flow along a flat plate with pressure gradient

Summary The effect of uniform suction or injection on the flow of an incompressible electrically conducting fluid past a flat plate with pressure gradient in the presence of a transverse magnetic field was theoretically investigated. The boundary layer equations were transformed into non-similar ones, and the numerical calculations of the resulting equations were performed by the difference differential method. The velocity profiles, the coefficient of skin friction, and the displacement thickness were given for various values of the pressure gradient, the magnetic and suction/injection parameters. The neutral stability curves for wavelike disturbances of Tollmien-Schlichting type and the critical Reynolds numbers were then presented for the velocity profiles obtained above.With 13 Figures     

传导薄板的非线性磁弹性振动问题

研究了磁场环境中传导薄板的非线性磁弹性振动问题。由虚功原理,给出了磁场中薄板的磁弹性耦合运动方程。并根据薄板薄壳的磁弹性基本假设及麦克斯威尔方程,得到了方程中电磁力及力矩的表达式。作为具体问题,采用多尺度法求出了横向磁场中条形板非线性振动的近似解析解。通过算例,分析了磁场环境对振动周期和幅值的影响。从而证实了,通过改变磁场因素,可达到控制该磁场环境中传导薄板振动的目的。所得的结论,对工程实际将有较大的应用参考价值。     

Solution of the boundary layer equation for a power law fluid in magneto-hydrodynamics

Summary The problem of a non-Newtonian power law conducting fluid past a semi-finite plate, in the presence of an external electromagnetic field, is studied. The electric conductivity is taken as a function of the velocity. The method of expansion for a small parameter is used to obtain the solution and for a special form of the free stream velocity, the method of similarity solutions is used to obtain the exact solutions of the boundary layer equations associated with this problem in a closed form. It was found that the presence of the electromagnetic field reduces the velocity of the fluid.     

Universal stability of magneto-micropolar fluid motions

Criteria for universal stability of the unsteady motion of an incompressible, electrically conducting linear micropolar fluid, i.e. with rigid microinclusions, in the presence of an arbitrary magnetic field, and in an arbitrary bounded time dependent domain are established. The model of the micropolar fluid employed is essentially the one proposed by Eringen. The interaction between the flow field and the magnetic field is manifested through the body force and body couple. Relativistic, Hall, and temperature effects are neglected. The stability method employed is an energy technique due to James Serrin. Certain uniqueness theorems for the unsteady and steady flows of magneto-micropolar fluid are also established.The theorems established for the stability and uniqueness are universal in the sense that they may be applied to any geometry of bounded domains and any distribution of the basic field variables. The present problem finds application in MHD generators with neutral fluid seedings in the form of rigid microinclusions.