MHD flow of an elasto-viscous fluid past a porous flat plate

An analytical study is performed to examine the laminar flow of an electrically-conducting elasto-viscous fluid (Walters's liquidB) past an infinite porous flat plate to a step function change in suction velocity in the presence of a transverse magnetic field. The influence of the various parameters, entering in the problem, on the velocity field and shearing stress is extensively discussed.     

MHD free-convection and mass transfer flow of an elasto-viscous fluid

The effects of magnetic field and mass transfer on the flow of an elasto-viscous fluid past an infinite vertical plate, when the plate is moving with uniform velocityU, are discussed. The magnetic lines of force are assumed to be fixed relative to the plate. The Laplace transform method is used to obtain the expression for velocity. The effect of various parameters, occurring into the problem, is discussed with the help of tables.     

Rayleigh waves in an orthotropic thermoelastic medium under gravity field and initial stress

The aim of the present paper is to investigate the influence both of gravity field and initial stress on the propagation of Rayleigh waves in an orthotropic thermoelastic medium subject to certain boundary conditions. We suppose that the body is under initial stress alonqx ₁-direction and incremental thermal stresses. The wave velocity equation has been obtained. Many special cases and comparison with the previous results have been studied.     

Unsteady hydromagnetic rotating flow near an oscillating plate

The three-dimensional flow of a viscous incompressible electrically conducting fluid near an infinite plate (or wall) of non-conductor, which is oscillating harmonically in a uniform rotating medium, is studied in the presence of a uniform magnetic field. The impressed uniform magnetic field is perpendicular to the plate and the induced magnetic field is considered. Exact solution of this problem is obtained for the velocity and magnetic fields. Neglecting the induced magnetic field we readily obtain the results of all the previous investigations. The effects of the rotation and the magnetic field are comparable with one another and are discussed for the whole problem. Also, the drag and the lateral stress on the plate are discussed.     

Role of magnetic field on transient forced and free-convection flow past an infinite vertical porous plate through porous medium with heat source

Effects of magnetic field and permeability of the porous medium on unsteady forced and free-convection flow past an infinite vertical porous plate in presence of temperature-dependent heat source have been analysed. The Laplace transform method is used to obtain the expression for velocity field, skin friction, and leading edge effects. During the course of discussion, the effects ofM (magnetic parameter),S (heat source parameter), (suction parameter), andK (permeability of porous medium) on velocity field, skin friction, and leading edge effect have been extensively discussed.     

A plane-symmetric inhomogeneous cosmological model of perfect fluid distribution with electromagnetic field

A plane-symmetric inhomogeneous cosmological model of perfect fluid distribution with electromagnetic field, is obtained.F ₁₂ is the non-vanishing component of the electromagnetic field tensor. To get a determinate solution, we assume the free gravitational field is Petrov type-II non-degenerate. In general, the model represents an expanding, shearing, non-rotating universe in which the flow vector is geodetic. The behaviour of the electromagnetic field tensor together with some geometrical and physical aspect of the model are also discussed.     

Unsteady magnetic boundary-layer flow of power-law non-Newtonian conducting fluid through a porous medium past an infinite porous flat plate

In this paper, the nonsteady flow of non-Newtonian power-law conducting fluid through a porous medium past an infinite porous plate is investigated. The system is stressed by a constant transverse magnetic field. The velocity outside the boundary layer depends exponentially on time. The rheological effects are shown and discussed on the shear stress in terms of rheological parameter of power-law fluid. The approximate solution in a closed form were obtained by using the Galerkin method. Also the effect of the magnetic field and permeability parameter are discussed.     

Bulk viscous fluid hypersurface–homogeneous cosmological models with time varying G and Λ

Hypersurface–homogeneous cosmological models containing a bulk viscous fluid with time varying G and Λ have been presented. We have shown that the field equations are solvable for any arbitrary cosmic scale function. The viscosity coefficient of bulk viscous fluid is assumed to be a power function of the energy density. Exact solutions of Einstein’s field equations are obtained which represent an expanding, shearing and accelerating/decelerating models of the universe. The physical and kinematical behaviours of the models are also discussed.     

MHD thermal-diffusion effects on free-convective and mass-transfer flow over an infinite vertical moving plate

The Soret effect on MHD free-convective and mass-transfer flow of an incompressible, viscous, and electrically-conducting fluid, past a moving vertical infinite plate is studied. The flow is assumed to be at small Reynolds numbers so that the induced magnetic field is neglected. The problem is solved with the help of the Laplace transform method for two different values of the dimensionless functionf(t) signifying two different cases, e.g., (i) when the boundary surface, the flat plate, is impulsively started, moving in its own plane (I.S.P.) and (ii) when it is uniformly accelerated (U.A.P.). The effects on the velocity field as well as on the skin-friction of the various dimensionless parameters occurring into the problem, especially the magnetic parameterM and Soret number So, are discussed with the help of graphs.     

Hydromagnetic free convection and mass transfer flow of non-Newtonian fluid through a porous medium bounded by an infinite vertical limiting surface with constant suction

An analysis of a two-dimensional steady-free convection and mass transfer flow of an incompressible, viscous, and electrically conductive non-Newtonian fluid through a porous medium bounded by a vertical infinite limiting surface (plane wall) has been presented in the presence of a transverse magnetic field. Approximate solutions to the coupled nonlinear equations governing the flow are derived and expression for the velocity, temperature, concentration, the rate of heat transfer, and the skin-friction are derived. Effects of Gr (Grashof number), Gm (modified Grashof number),M ^* (non-Newtonian parameter),N (magnetic parameter), and permeabilityK of the porous medium on the velocity, the skin-friction and the rate of heat transfer are discussed when the surface is subjected to a constant suction velocity.     

Free convection and mass transfer effects on the control of the unsteady boundary layer on an infinite vertical porous limiting surface

The present study presents an analytical solution to the flow field of the unsteady laminar accelerated flow of a viscous incompressible fluid past an infinite vertical porous limiting surface, when the freestream is accelerated and the limiting surface temperature and concentration are given functions of time. The expressions for the velocity, temperature and skin friction are obtained by using Laplace transform, when the Prandtl and Schmidt numbers are given. Graphs showing variations of the velocity and the skin friction, for different values ofG _r andG _c (modified Grashof number), as well as of the temperature are plotted and the results are discussed.     

Magnetic diffusion and flare energy buildup

Photospheric motion shears or twists solar magnetic fields to increase magnetic energy in the corona, because this process may change a current-free state of a coronal field to force-free states which carry electric current. This paper analyzes both linear and nonlinear two-dimensional force-free magnetic field models and derives relations of magnetic energy buildup with photospheric velocity field. When realistic data of solar magnetic field (B ₀ 10³ G) and photospheric velocity field (v _max 1 km s^–1) are used, it is found that 3–4 hours are needed to create an amount of free magnetic energy which is of the order of the current-free field energy. Furthermore, the paper studies situations in which finite magnetic diffusivities in photospheric plasma are introduced. The shearing motion increases coronal magnetic energy, while the photospheric diffusion reduces the energy. The variation of magnetic energy in the coronal region, then, depends on which process dominates.     

Free convection effects on the oscillatory flow in the Stokes's problem past an infinite porous vertical limiting surface with constant suction,II

In this work we present the two-dimensional free convection flow of an incompressible viscous fluid past an infinite vertical limiting surface (porous wall) for the Stokes's problem when the fluid is subjected to a constant suction velocity. The flow is normal to the porous wall and the free stream oscillates about a mean value. As the mean steady flow has been presented in Part I, only the solutions for the transient velocity profiles, transient temperature profiles, the amplitude and the phase of the skin friction and the rate of heat transfer are presented in this work. As in the case of mean steady flow, the influence of the Grashof numberG and Eckert numberE on the unsteady flow field is discussed for air (P=0.71) and water (P=7) and for the cases of externally heating and cooling the porous limiting surface by free convection currents.     

Soret effects on free-convection and mass transfer flow in the stokes problem for a infinite vertical plate

An analytical study is performed to examine the free-convection and mass transfer flow for the Sokes problem for an infinite vertical plate on taking into account the Soret effect (thermal diffusion effect). The Laplace transform technique is used to obtain the expressions for velocity and skin-friction. The effect of Soret numberS on velocity field and skin-friction is extensively discussed with the help of graphs and table.     

Free molecular flow of rarefied gas over an oscillating plate under a periodic external force

The free molecular flow over an infinite oscillating plane wall under external periodic force is considered. The Boltzmann equation is solved by using moments method with two-stream distribution functions. The boundary condition is obtained by assuming that the reflection of the particles from the solid surface takes place with complete energy accommodation. An analytical form for the velocity (X) and shear stress (Y) at any point is obtained. The results show that the amplitude of both the velocity change (X ₁) and the shear stress change (Y ₁) due to the periodic external force at the boundary (y=0) is an increasing function of time (t).     

Magnetohydrodynamic free convection effects on the stokes problem for an incompressible viscous fluid past an infinite vertical limiting surface

An analysis of the transverse magnetic field effects on the free convective flow of an incompressible, electrically conducting viscous fluid past an infinite non-conducting and non-magnetic, vertical limiting surface (e.g., of a star), has been carried out. The limiting surface is assumed to move after receiving an initial impulse. Exact solutions to equations governing the flow are derived with the help of the Laplace transform technique. The velocity, the induced magnetic field, the skin-friction and the electric current density are shown graphically. The effects of the Grashof numberG, the Prandtl numberP, and the magnetic parameterM are described during the course of discussion.     

Heat and mass transfer of an oscillatory flow with Hall current,II

An analysis of Hall current on the combined effects of thermal and mass diffusion of an electrically conducting liquid past an infinite vertical porous plate is performed. Analytical expressions for the transient velocity, the transient temperature in the boundary layer and the skin-friction on the plate are derived. The effects of various parameters on the velocity, temperature, shearing stresses and rate of heat transfer are shown by graphs and tables.     

Self‐similar evolutionary solutions for an accreting magneto‐fluid around a compact object with finite electrical conductivity

In this paper, we investigate the time evolution of an accreting magneto‐fluid with finite conductivity. For the case of a thin disk, the fluid equations along with Maxwell's equations are derived in a simplified, one‐dimensional model that neglects the latitudinal dependence of the flow. The finite electrical conductivity of the plasma is taken into account by Ohm's law; however, the shear viscous stress is neglected, as well as the self‐gravity of the disk. In order to solve the integrated equations that govern the dynamical behaviour of the magneto‐fluid, we have used a self‐similar solution. We introduce two dimensionless variables, S₀ and ε_ϱ, which represent the size of the electrical conductivity and the density behaviour with time, respectively. The effect of each of these on the structure of the disk is studied. While the pressure is obtained simply by solving an ordinary differential equation, the density, the magnetic field, the radial velocity, and the rotational velocity are presented analytically. The solutions show that the S0 and ε_ϱ parameters affect the radial thickness of the disk. Also, radial velocity and gas pressure are more sensitive to the electrical conductivity in the inner regions of disk. Moreover, the parameter ε_ϱ has a more significant effect on the physical quantities for small radii. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mass transfer effects on free-convection flow past an impulsively started porous infinite vertical limiting surface

The effects of heat and mass transfer on the flow field of a laminar boundary layer is considered. The flow is that of an incompressible viscous fluid past an impulsively started permeable vertical limiting surface with constant heat flux. The solution of the problem was obtained numerically, using an implicit finite difference scheme. The solution is given in a number of diagrams, which depict the influence ofG on velocity,P on temperature and Sc on concentration. The influence ofG on skin friction is also given.     

A numerical study of the unsteady MHD free convection with hall current

Effect of Hall current on the hydromagnetic free-convection flow of an electrically-conducting viscous incompressible fluid past an impulsively accelerated vertical porous plate in the presence of a uniform transverse magnetic field subjected to a constant transpiration velocity is analyzed for the case of small magnetic Reynolds number. Numberical solutions are obtained for the axial and transverse components of the velocity as well as the skin-friction by employing the Crank-Nicolson implicit finite-difference method for all probable values of the Prandtl number. The results are discussed with the effects of the Grashof number Gr, the transpiration velocity parameter , the Hall current parameterm, and the magnetic field parameterM for the Prandtl number Pr=0.71 which represents air at 20° C.