MHD oscillatory flow past a vertical porous plate through porous medium in the presence of thermal and mass diffusion with constant heat source

Effects of temperature-dependent heat source on hydromagnetic free-convection flow (set up due to temperature as well as species concentration) of an electrically-conducting incompressible viscous fluid past a steadily moving vertical porous plate through high porous medium has been analysed when the free stream oscillates in magnitude. The flow is subjected to a constant suction, through the porous plate. The mathematical analysis is presented for the hydromagnetic flow without taking into account the induced magnetic field. This is a valid assumption for small magnemtic Reynold number. Approximate analysis for the velocity and temperature field and their related quantities are obtained. The influence of various parameters entering into the problem is extensively discussed with the help of graphs and tables.     

Oscillatory free-convective flow of an elastico-viscous fluid past an impulsively started infinite vertical porous plate,II

In this work we present the two-dimensional free-convective flow of an elastico-viscous fluid past an infinite vertical porous plate for the Stokes problem when the flow is subjected to a constant suction velocity through the porous plate. As the mean steady flow has been presented in Part I, obly the solution 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 various parameters on the unsteady flow field is discussed for both the cases cooling and heating of the porous plate by free-convection currents.     

Hall effects on an oscillatory MHD flow in the Stokes problem past an infinite vertical porous plate,I

Hall effects on the hydromagnetic free convection flow of an electrically conducting incompressible viscous fluid past a steadily moving vertical porous plate has been analysed when the free stream oscillates in magnitude. The flow is subjected to a constant suction, through the porous plate, and the difference between wall temperature and the free-stream is moderately large causing the free convection currents. The mathematical analysis is presented for the hydromagnetic boundary layer flow without taking into account the induced magnetic field. This is a valid assumption for small magnetic Reynolds number. Approximate solutions for the components of velocity field and temperature field and their related quantities are obtained. The influence of various parameters entering into the problem is extensively discussed with the help of graphs and tables.     

Hall effects on the oscillatory MHD flow in the stokes problem past an infinite vertical porous plate,II

In this work we present the effects of Hall current on the hydromagnetic free-convection flow of a viscous, incompressible and electrically conducting fluid past an infinite vertical porous plate for the Stokes problem when the fluid is subject to a constant suction velocity. The flow is normal to the porous plate and the free-stream oscillates about a mean value. As the mean steady flow has been presented in part I, only the solution for the transient primary velocity profiles, transient secondary velocity profiles, transient temperature profiles; the amplitude and phase of skin-friction components and the rate of heat transfer are presented in this work. As in the case of mean steady flow, the influence of the various parameters on the unsteady flow field is discussed with the help of graphs and tables for both the cases cooling and heating of the porous plate.     

MHD free-convection flow past an accelerated vertical porous plate in a rotating fluid

The three-dimensional flow of an electrically conducting and incompressible viscous fluid past a uniformly accelerated infinite vertical porous plate is studied in a rotating fluid. The flow is assumed to be at small magnetic Reynolds number so that the induced magnetic field is neglected. An exact solution has been obtained by defining a complex velocity with the help of the Laplace transform method for the Prandtl number equal to unity. The effects of rotation, magnetic and free-convection parameters are discussed for the whole problem. Also, the skin-friction components on the plate are discussed.     

Hall effects on MHD free-convection flow past an accelerated vertical porous plate

The effect of Hall currents on the hydromagnetic free-convection flow of an electrically conducting and incompressible viscous fluid past a uniformly accelerated infinite vertical porous plate is discussed. The magnetic Reynolds number is assumed to be small so that the induced magnetic field can be neglected. The governing equations of the flow are solved by defining a complex velocity with the help of the Laplace transform method when the Prandtl number is equal to unity. The influence of the various parameters on the unsteady flow field is presented for both the cases, cooling and heating of the porous plate by free-convection currents.     

MHD free-convection and mass-transform flow through a porous medium

The effect of a uniform transverse magnetic field on the free-convection and mass-transform flow of an electrically-conducting fluid past an infinite vertical plate for uniformly accelerated motion of the plate through a porous medium is discussed. The magnetic lines of force are assumed to be fixed relative to the plate. Expression for the velocity field and skin-friction are obtained by the Laplace transform technique. The influence of the various parameters, entering into the problem, on the velocity field and skin-friction is extensively discussed.     

MHD free-convection flow in the stokes problem for a porous vertical plate

The effect of a uniform transverse magnetic field on the free-convection flow of an electrically-conducting fluid past an infinite, vertical, porous plate for both classes of impulsive as well as uniformly-accelerated motion of the plate is discussed. The magnetic lines of force are assumed to be fixed relative to the plate. Expressions for the velocity field and skin friction for both cases are obtained by the Laplace transform technique. The influence of the various parameters, entering into the problem, on the velocity field and skin-friction is extensively discussed with the help of graphs and tables.     

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.     

Oscillatory hydromagnetic free-convection flow in the stokes problem past an infinite vertical porous plate in a rotating system,I

Rotation effect on the hydromagnetic free-convection flow of an electrically conducting, viscous, and incompressible fluid past a steadily moving vertical porous plate has been analysed in the presence of a transverse magnetic field. The free-stream velocity oscillates in time about a constant mean, while the suction velocity, normal to the porous plate, is constant. The magnetic Reynolds number of the flow is taken small enough so that the induced magnetic field can be neglected. The plate temperature is constant and the difference between the temperature of the plate and the free stream is moderately large causing the free-convection currents. The flow field is described by nonlinar coupled system of equations. With viscous dissipative heat taken into account, approximate solutions of the problem are obtained for the components of velocity field and temperature field as well as for the skin-friction components and rate of heat transfer.     

MHD free-convection and mass transfer flow through a porous medium with heat source

An analytical study is performed to examine the heat source characteristics on the free-convection and mass transfer flow past an impulsively started infinite non-conducting vertical plate of a viscous, incompressible electrically-conducting fluid under the action of a uniform magnetic field through porous medium. The effects of various parameters on the velocity field are extensively discussed.     

Hall effects on oscillatory MHD boundary-layer flow under variable suction

The effects of Hall current on the oscillatory hydromagnetic boundary-layer flow under variable suction, past an infinite porous flat plate in the presence of a transverse magnetic field is discussed. The expressions for velocity and skin-friction are obtained and their variations for small and large frequency of oscillations are extensively discussed.     

Stokes problem for a porous vertical plate with heat sinks by finite difference method

The effect of heat sinks on the free-convection flow of an incompressible viscous fluid past an impulsively started infinite vertical porous plate is considered. Finite difference method has been used to obtain the numerical solution of the governing equations. The influence of the various parameters, occurring into the problem, on the velocity field, the temperature field and on their related quantities is extensively discussed with the help of graphs and tables.     

The effects on the flow field of retaining the Joule heating and viscous dissipation term in the energy equation for the hydromagnetic free-convective oscillatory flow past a porous limiting surface,I

With viscous dissipation and Joule heating taking into account the hydromagnetic two-dimensional oscillating free-convection flow, of a viscous, incompressible and electrically conducting fluid, past an infinite vertical porous limiting surface, is studied. For the solution of the problem it is considered that, the free-stream velocity, the plate temperature and the induced magnetic field are oscillating in the time about constant mean values. The flow is subjected to a constant suction velocity, through the porous surface, and a magnetic field of uniform strength is applied transversely to the direction of the flow. Analytical expressions for the flow field are obtained by solving the coupled non-linear system of equations which describe the flow. The influence of the various parameters entering into the problem is also extensively discussed signifying the importance of retaining the Joule heating and viscous dissipation term in the energy equation.     

Heat and mass transfer in rotating fluid with Hall current,I

Hall effects on the hydromagnetic free convection resulting from the combined effects of thermal and mass diffusion of an electrically conducting liquid past an infinite vertical porous plate in a rotating system have been analysed. The expressions for the mean velocity, mean temperature in the boundary layer and the mean skin friction, the mean rate of heat transfer on the plate are derived. The effects of magnetic parameterM, Hall parameterm, Schmidt number Sc, and Ekman numberE on the flow field, are discussed with the help of graphs and tables.     

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.     

Unsteady magnetohydrodynamic flow through a porous medium between two infinite parallel plates

An analysis of a two-dimensional unsteady flow of a viscous, incompressible electrically-conducting fluid through a porous medium bounded by two infinite parallel plates under the action of a transverse magnetic field is presented. The lower plate is fixed while the other is oscillating in its own plane. Expressions for the transient velocity, the amplitude, the phase angle, and the skin-friction are derived. The effects of the magnetic parameters, permeability of the porous medium, and the frequency parameter are discussed.     

Magnetohydrodynamic flow of a non-Newtonian fluid past a porous plate

This article studies the laminar flow of an electrically conducting non-Newtonian fluid (Rivlin-Encksen type) past an infinite porous flat plate to a step function change in suction velocity in the presence of a transverse magnetic field. The Laplace transform technique has been employed to solve the basic differential equations. The solutions of the velocity profile and skin-friction are obtained and the effects of the visco-elastic parameter, the magnetic field and the time parameter on the fluid flow have been studied in several tables.     

Unsteady hydromagnetic flow through a porous medium between two infinite parallel porous plates with time-varying suction

Unsteady two-dimensional flow of a viscous incompressible and electrical-conducting fluid through a porous medium bounded by two infinite parallel plates under the action of a transverse magnetic field is presented when there is time-varying suction at the plates. The lower plate is at rest while the upper plate is oscillating in its own plane about a constant mean velocity. Expressions for the velocity, fluctuating parts of the velocity, amplitude, and phase of the skin-friction are obtained. The flow phenomenon has been characterized by the parametersK (permeability of the porous medium),N(magnetic parameter) (frequency parameter), andA(variable suction parameter) and the role of these parameters on the flow characteristics has been studied.     

Free convection effects on oscillatory hydromagnetic boundary layer flow

Unsteady flow of an incompressible, viscous, electrically conducting fluid past an infinite porous plate has been analysed under the following assumptions: (i) suction velocity oscillates in time about a constant mean, (ii) the free-stream velocity oscillates in time about a constant mean, (iii) the plate temperature is constant, (iv) the difference between the temperature of the plate and the free-stream is moderately large causing the free-convection currents, (v) a uniform transverse magnetic field is applied, (vi) the magnetic Reynolds number is very small and hence the induced magnetic field is neglected. Approximate solutions to the coupled non-linear equations governing the flow are derived for the transient velocity, the transient temperature, the amplitude and the phase of the skin-friction and the rate of heat transfer. During the course of analysis the effects of ±G (Grashof number),P (Prandtl number),M (magnetic field parameter),A (suction parameter) and ω (frequency) are discussed.