The unsteady hydromagnetic thermal boundary layer with suction

The unsteady two-dimensional laminar flow of a viscous incompressible and electrically conducting fluid near an oscillating porous plate in the presence of uniform suction, is investigated. The solutions for the velocity, magnetic field, electric current density, temperature and Nusselt number are given in a closed form for the case of the magnetic Prandtl number being equal to unity. The other significant constants are the Eckert number, the fluid Prandtl number and the frequency of oscillation. The influence of these parametres on the solutions is given in both tabulated and graphical forms.     

Magnetohydrodynamic flow past a plate by the presence of radiation

An analysis of the unsteady magnetohydrodynamic flow of a viscous and electrically conducting fluid past to a plate by the presence of radiation is considered. The fluid is a gray, absorbing-emitting but nonscattering medium and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. Analytical solutions for the mean temperature, velocity and the magnetic field have been derived and the effect of the radiation on the temperature is discussed. Received on 20 November 1997     

Effects of magnetohydrodynamic flow past a vertical plate with variable surface temperature

An analysis is performed to study the magnetohydrodynamic flow of an electrically conducting, viscous incompressible fluid past a semi-infinite vertical plate with variable surface temperature under the action of transversely applied magnetic field. The heat due to viscous dissipation and the induced magnetic field are assumed to be negligible. The dimensionless governing equations are unsteady, two-dimensional, coupled and non-linear governing equations. It is found that the magnetic field parameter has a retarding effect on the velocities of air and water.     

Series solutions of unsteady MHD flows above a rotating disk

The series solutions of unsteady flows of a viscous incompressible electrically conducting fluid caused by an impulsively rotating infinite disk are given by means of an analytic technique, namely the homotopy analysis method. Using a set of new similarity transformations, we transfer the Navier–Stokes equations into a pair of nonlinear partial differential equations. The convergent series solutions are obtained, which are uniformly valid for all dimensionless time 0 ≤ τ < ∞ in the whole spatial region 0 ≤ η < ∞. To the best of our knowledge, such kind of series solutions have never been reported. The effect of magnetic number on the velocity is investigated.     

Laminar unsteady magnetohydrodynamic flow in an annular channel under a radial magnetic field

Summary The paper discusses the unsteady flow of an electrically conducting viscous fluid in the region between two coaxial cylinders in the presence of a radial magnetic field emanating from the common axis in planes perpendicular to it. In the special case when the magnetic Reynolds number of the flow is the same as its Reynolds number, an exact solution in terms of Bessel functions has been obtained which after infinite time tends to the steady flow discussed by Globe.     

A nonuniform shock wave subjected to an oblique magnetic field

Summary A family of exact solutions for the one dimensional, unsteady, non-isentropic flow of an ideal, inviscid, perfectly conducting, compressible fluid subjected to an oblique magnetic field, is connected by a nonuniform shock wave to gas at rest in which the density distribution is nonuniform. The method of solution is inverse in the sense that the shock path is determined by the usual jump conditions, and then the density distribution in front of the shock is obtained in parametric form in terms of the equation of the shock locus.     

Two time scale solution for an unsteady MHD duct flow

The investigation deals with unsteady laminar flow of a viscous, incompressible, electrically conducting fluid between conducting or nonconducting flat plates. A constant magnetic field is suddenly applied perpendicular to the plates and the created electromagnetic effects modify the motion. An approximate solution is obtained using time scales t and t/ε, where ε is the small magnetic Prandtl number.     

MHD Couette two-fluid flow and heat transfer in presence of uniform inclined magnetic field

The MHD Couette flow of two immiscible fluids in a parallel plate channel in the presence of an applied electric and inclined magnetic field is investigated in the paper. One of the fluids is assumed to be electrically conducting, while the other fluid and the channel plates are assumed to be electrically insulating. Separate solutions with appropriate boundary conditions 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 fluid regions of the channel. The results for various values of the Hartmann number, the angle of magnetic field inclination, the loading parameter and the ratio of the heights of the fluids are presented graphically to show their effect on the flow and heat transfer characteristics.     

KINEMATICAL FORCE-FREE FIELDS OF A MAGNETIC ARCH

I.Introducti0nCosmicmagneticfieldswhichoccurinregionsofhighelectricalconductivityandlowdensitymightoftensatisfytheforce-freeconditioncurlH=a(r,t)H(l.l)whereHdenotesthedensityofthemagneticfleld,and2issomescalarfunctionofpositionandtime,sincethepressuregrad…     

Quasi-geostrophic motions in a rotating layer of an electrically conducting fluid

Large-scale nonlinear oscillations of an electrically conducting ideal fluid of varying depth are considered with the magnetic, Archimedean, and Coriolis forces taken into account. The main equations are derived from an analysis of the scales of quasi-geostrophic motions. Under the assumptions that the Rossby numbers (a measure of the ratio of the local and advective accelerations to the Coriolis acceleration) are of the same order, the problem is reduced to a system of three nonlinear equations for hydromagnetic pressure and two functions describing the magnetic field. For an infinitely long horizontal layer of an electrically conducting rotating fluid, the exact solution of the corresponding nonlinear equations and the dispersion relation are obtained under the assumption of an approximately constant slope of the upper boundary surface of the layer at a distance of the order of the wavelength. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 30–41, January–February, 2009.     

MHD UNSTEADY FLOWS DUE TO NON—COAXIAL ROTATIONS OF A DISK AND A FLUID AT INFINITY

Exact analytical solution for flows of an electrically conducting fluid over an infinite oscillatory disk in the presence of a uniform transverse magnetic field is constructed. Both the disk and the fluid are in a state of non-coaxial rotation. Such a flow model has a great significance not only due to its own theoretical interest, but also due to applications to geophysics and engineering. The resulting initial value problem has been solved analytically by applying the Laplace transform technique and the explicit expressions for the velocity for steady and unsteady cases have been established. The analysis of the obtained results shows that the flow field is appreciably influenced by the applied magnetic field, the frequency and rotation parameters.     

DTM-BF method and dual solutions for unsteady MHD flow over permeable shrinking sheet with velocity slip

An unsteady magnetohydrodynamic (MHD) boundary layer flow over a shrinking permeable sheet embedded in a moving viscous electrically conducting fluid is investigated both analytically and numerically. The velocity slip at the solid surface is taken into account in the boundary conditions. A novel analytical method named DTMBF is proposed and used to get the approximate analytical solutions to the nonlinear governing equation along with the boundary conditions at infinity. All analytical results are compared with those obtained by a numerical method. The comparison shows good agreement, which validates the accuracy of the DTM-BF method. Moreover, the existence ranges of the dual solutions and the unique solution for various parameters are obtained. The effects of the velocity slip parameter, the unsteadiness parameter, the magnetic parameter, the suction/injection parameter, and the velocity ratio parameter on the skin friction, the unique velocity, and the dual velocity profiles are explored, respectively.     

Unsteady laminar hydromagnetic fluid–particle flow and heat transfer in channels and circular pipes

The problem of unsteady laminar flow and heat transfer of a particulate suspension in an electrically conducting fluid through channels and circular pipes in the presence of a uniform transverse magnetic field is formulated using a two-phase continuum model. Two different applied pressure gradient (oscillating and ramp) cases are considered. The general governing equations of motions (which include such effects as particulate phase stresses, magnetic force, and finite particle-phase volume fraction) are non-dimensionalized and solved in closed form in terms of Fourier cosine and Bessel functions and the energy equations for both phases are solved numerically since they are non-linear and are difficult to solve analytically. Numerical solutions based on the finite-difference methodology are obtained and graphical results for the fluid-phase volumetric flow rate, the particle-phase volumetric flow rate, the fluid-phase skin-friction coefficient and the particle-phase skin-friction coefficient as well as the wall heat transfer for plane and axisymmetric flows are presented and discussed. In addition, these numerical results are validated by favorable comparisons with the closed-form solutions. A comprehensive parametric study is performed to show the effects of the Hartmann magnetic number, the particle loading, the viscosity ratio, and the temperature inverse Stokes number on the solutions.     

Unsteady MHD mixed convection flow over an impulsively stretched permeable vertical surface in a quiescent fluid

The unsteady mixed convection flow of an incompressible laminar electrically conducting fluid over an impulsively stretched permeable vertical surface in an unbounded quiescent fluid in the presence of a transverse magnetic field has been investigated. At the same time, the surface temperature is suddenly increased from the surrounding fluid temperature or a constant heat flux is suddenly imposed on the surface. The problem is formulated in such a way that for small time it is governed by Rayleigh type of equation and for large time by Crane type of equation. The non-linear coupled parabolic partial differential equations governing the unsteady mixed convection flow under boundary layer approximations have been solved analytically by using the homotopy analysis method as well as numerically by an implicit finite difference scheme. The local skin friction coefficient and the local Nusselt number are found to decrease rapidly with time in a small time interval and they tend to steady-state values for t*≥5. They also increase with the buoyancy force and suction, but decrease with injection rate. The local skin friction coefficient increases with the magnetic field, but the local Nusselt number decreases. There is a smooth transition from the unsteady state to the steady state.     

Magnetohydrodynamic flow through a rectangular duct due to a periodic pressure gradient

Summary The flow of an incompressible, viscous, electrically conducting fluid in a long channel of rectangular cross section due to a periodic pressure gradient, in the presence of a uniform transverse magnetic field is investigated. Exact solutions are obtained and asymptotic forms valid for large Hartmann numbers are discussed.     

An unsteady MHD duct flow

An exact solution is presented for unsteady laminar flow of a viscous, incompressible, electrically conducting fluid between nonconducting, parallel, flat plates. A constant magnetic field is suddenly applied perpendicular to the plates and the motion is modified by the induced current. Numerical results are given which show how the velocity profile changes from the parabolic profile of hydrodynamics to the Hartmann profile of magnetohydrodynamics.     

An unsteady MHD duct flow

An exact solution is presented for unsteady laminar flow of a viscous, incompressible, electrically conducting fluid between nonconducting, parallel, flat plates. A constant magnetic field is suddenly applied perpendicular to the plates and the motion is modified by the induced current. Numerical results are given which show how the velocity profile changes from the parabolic profile of hydrodynamics to the Hartmann profile of magnetohydrodynamics.     

Unsteady incompressible Couette flow in a uniform transverse magnetic field

Summary The unsteady plane Couette flow of an incompressible, viscous and infinitely conducting fluid in a uniformly imposed transverse magnetic field is studied. The problem is solved in general in a series form by means of a finite Fourier transform, and explicit solutions for two special cases are worked out.     

Evolution of planar and cylindrically symmetric magneto-acoustic waves in a van der Waals fluid

We consider a quasilinear system of partial differential equations (PDEs) governing the one-dimensional unsteady planar and cylindrically symmetric motion of an electrically conducting van der Waals fluid permeated with a transverse magnetic field. An asymptotic method is used to derive an evolution equation that governs the wave amplitude in the far field. Our main objective is to study the evolution equation, and to investigate as to how the presence of magnetic field and geometrical spreading (in cylindrical case) along with the cubic nonlinearity, inherently present in the system, influence the wave structure that finally develops.     

Flow of a Weakly Conducting Fluid in a Channel Filled with a Porous Medium

We investigate the fully developed flow in a fluid-saturated porous medium channel with an electrically conducting fluid under the action of a parallel Lorentz force. The Lorentz force varies exponentially in the vertical direction due to low fluid electrical conductivity and the special arrangement of the magnetic and electric fields at the lower plate. Exact analytical solutions are derived for fluid velocity and the results are presented in figures. All these flows are new and are presented for the first time in the literature.