Unsteady MHD flow of a viscoelastic fluid past an infinite porous plate with oscillating temperature

The unsteady flow of an electrically conducting fluid past an infinite plate with constant suction is investigated in the presence of an external magnetic field and buoyancy forces. The temperature of the plate is assumed to oscillate in time about a constant mean and the flow is considered to be free of convection. For the method of solution, we have employed a small parameter approach when this small parameter is a non-dimensional quantity which is related to the viscoelastic constant of the fluid. Analytical expressions are obtained for the temperature distribution and the velocity profile of the fluid. These analytical results clearly show that the velocity profile is strongly damped when the magnetic field is more intense. This means that the applied magnetic field causes the fluid to move slower as compared with the non-magnetic case.     

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.     

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.     

Mass-transfer effects on the flow past an impulsively started infinite vertical plate with variable temperature or constant heat flux

An exact solution of the flow of a viscous incompressible fluid past an impulsively started infinite vertical plate in the presence of foreign mass is presented under the condition of (i) variable plate temperature, (ii) constant heat flux. It is observed that an increase in the Schmidt number leads to an increase in the skin-friction.     

Unsteady magnetohydrodynamic free-convection flows in a rotating fluid

The three-dimensional free-convection flow near an infinite vertical plate moving in a rotating fluid in the presence of a transverse magnetic field is studied in the case when the plate temperature undergoes a thermal transient. An exact solution has been obtained by defining a complex velocity with the help of the Laplace-transform technique, when the plate is moving with a velocity which is an arbitrary function of time. Three special cases of physical interest are also discussed.     

Free convection and mass transfer effects on the oscillatory flow past an infinite moving vertical isothermal plate with constant suction and heat sources

An analysis of the two-dimensional flow of an incompressible, viscous binary fluid past an infinite, porous, vertical plate is presented under the following conditions: (i) the suction velocity is constant; (ii) the free stream oscillates in time about a constant mean; (iii) the plate moves in the upward direction in its own plane; (iv) the temperature of the plate is constant; (v) there are heat generation (absorption) in the fluid.Approximate solutions for the coupled non-linear equations are obtained for the velocity, temperature and their related quantities and the influence of the various parameters entering into the problem is discussed.     

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.     

MHD oscillatory flow through porous medium

In this work we present the 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 steady moving vertical porous plate through high porous medium when the free stream oscillates in magnitude. The flow is subjected to a constant suction through the porous plate. As the mean steady flow has been presented gy Gholizadeh (1990), only the solution for the transient velocity profiles, transient temperature profiles, the skin-friction (steady+unsteady), and rate of heat transfer are presented in this work.     

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.     

MHD free-convection flow near a vertical oscillating plate

The unsteady free-convection flow of an electrically-conducting fluid near an oscillating vertical plate of infinite extent, is studied in the presence of a uniform transverse magnetic field. Exact solutions for velocity, temperature and skin friction are obtained with the aid of the Laplace transform method, when the plate is oscillating harmonically in its own plane. The influence of various parameters, entering into the problem, is discussed for the velocity field and skin-friction.     

MHD free-convection flow in the stokes problem for a porous vertical plate by finite difference method

The flow past an infinite vertical isothermal plate started impulsively in its own plane in a viscous incompressible and electrically conducting fluid has been considered. The magnetic Reynolds number is assumed small so that the induced magnetic field can be neglected. The governing equations of the flow are solved by finite-difference method when the Prandtl number is not equal to unity. The influence of the various parameters, entering 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.     

Heat transfer in unsteady MHD couette flow of an electrically conducting,viscous, incompressible rarefied gas

An analytical study is performed to examine the heat transfer characteristics on the flow of a viscous, incompressible rarefied gas in a parallel plate channel under the action of transverse magnetic field when (i) suction velocity normal to the plate is constant, (ii) the second plate oscillates in time about a constant non-zero mean, (iii) fluid is subjected to a constant heat source of absorption type. Apprximate solutions for velocity, temperature, phase, and amplitude of skin-friction and rate of heat transfer are evaluated. Mean temperature profiles, phase and amplitude of rate of heat transfer at both plates are discussed graphically followed by a quantitative discussion. Mean rate of heat transfer is tabulated in Table I.     

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.     

Hydromagnetic unsteady flow due to an unsteady plate

The unsteady flow near an infinite flat plate, which is oscillating harmonically in its own plane, is studied in the presence of a magnetic field subjected to suction or injection. The magnetic field is perpendicular to the plate and the flow of viscous incompressible and electrically conducting fluid is regarded as being initially at rest. Exact solutions for velocity and skin-friction are obtained for the magnetic field fixed to the fluid or to the plate.     

Unsteady free convection flow past an infinite plate with constant suction and heat sources

An analysis of a two-dimensional unsteady free convective flow of an incompressible viscous fluid past an infinite vertical porous plate has been carried out under the following conditions: (i) constant suction, (ii) the plate temperature oscillating in time about a constant non-zero mean, (iii) presence of the temperature-dependent sources in the fluid. Approximate solutions have been derived for the mean velocity and temperature fields, the transient velocity and temperature fields, the amplitude and the phase of the skin-friction and the rate of heat transfer. It is shown that an increase inS (the source-strength), leads to an increase in the value of |B| (the amplitude of the skin-friction) and |Q| (the amplitude of the rate of heat transfer), in case of air, but in case of water |B| and |Q| decrease.     

Flow of elasto-viscous fluid past an accelerated porous plate

The flow problem of an elasto-viscous liquid (Walter-B type) due to impulsively accelerated motion of an infinite porous plate is considered. The effect of suction and flow parameters is analysed. It is found that at a fixed time the fluid velocity and skin friction at any point decrease with the increase in suction and fluid elastic parameters.     

A class of exact solutions of the unsteady magnetohydrodynamic free-convection flows

The unsteady free-convection flow of an electrically-conducting fluid near a moving vertical plate of infinite extent is investigated in the presence of uniform transverse magnetic field fixed to the fluid or to the plate. Exact solution of this problem is obtained with the aid of the Laplace transform technique, when the plate is moving with a velocity which is an arbitrary functiuon of time. The solution is exemplified for three particular cases of physical interest; the non-magnetic case is also discussed.     

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.     

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.