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.     

Transient MHD free convection in a rotating system

The classical Rayleigh problem has been extended to the case of the hydromagnetic free-convective flow of an electrically-conducting and incompressible viscous fluid past an infinite vertical naturally permeable wall in a rotating system. The applied transverse magnetic field is fixed with the moving wall and the magnetic Reynolds number of the flow is taken small so that the induced magnetic field can be neglected in comparison to the applied magnetic field. The permeable wall starts moving from rest in the still fluid and thus arises an initial value problem whose solution has been obtained by the Laplace transform method for two important cases impulsive as well as accelerated start of the plate. Mathematical expression for skin friction components have been also obtained in a closed form. Asymptotic behaviour of the solution is analysed for both the cases, and some interesting particular cases have also been encountered. Influence of various physical parameters occurring into the problem has been discussed with the aid of graphs and tables.     

Finite difference analysis of unsteady hydromagnetic free-convection flow with constant heat flux

A numerical solution for unsteady hydromagnetic free-convection currents of a viscous incompressible and electrically conducting fluid induced by a vertical moving infinite plate is considered for constant heat flux at the plate. Velocity and skin-friction have been worked out for various values of the parameters occuring into the problem. It is found that magnetic parameter has a retarding effect on the velocity of air and water, while skin-friction increases with it.     

Thermal-diffusion effects on MHD free-convective and mass-transfer flow past a moving infinite vertical plate in a rotating fluid

An analytical study of MHD free-convective and mass-transfer flow past a moving infinite vertical plate, in a rotating fluid, is presented, taking into account the thermal diffusion effects. The solution of the problem is obtained with the help of the Laplace transform technique. Analytical expressions are given for the velocity field and for skin-friction for two different cases, e.g., when the plate is impulsively started, moving on its own plane (case I) and when it is uniformly accelerated (case II). The effects on the velocity field and skin-friction, of the various parameters entering into the problem, are discussed with the help of graphs.     

Free-convection flow past an impulsively started vertical plate in a porous medium by finite difference method

A numerical solution for the effects of the free-convection currents of a viscous fluid through a porous medium bounded by a vertical moving infinite vertical plate is considered, when the flow is unsteady. The graphs of velocity profiles for different values of permeability parameter of the porous medium and the Grashof number are discussed.     

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.     

Hydromagnetic flow past a continuously moving semi-infinite plate for large suction

The similarity solution for hydromagnetic flow of an incompressible viscous electrically conducting fluid past a continuously moving semi-infinite porous plate in the presence of a magnetic field has been obtained for the case of small magnetic Reynolds number. The perturbation method has been used to solve the similarity equations at large suction. The resulting equations have been solved by analytical method. The effect of the magnetic parameter is to increase the skin-friction coefficient while it has no significant effect on the Nusselt number.     

A numerical solution of MHD free-convection flow in the general nonlinear stokes problem by the finite-difference method

With viscous dissipation and Joule heating taking into account a numerical solution of magnetohydrodynamic free convection flow, in the Stokes's problem, is obtained for different values of Prandtl numberP. The fluid is viscous, incompressible, and electrically conducting and the magnetic lines of force are assumed to be fixed relative to the plate which is started moving impulsively in its own plane (ISP) or it is uniformly accelerated (UAP). The solution is obtained with an implicit second-order method, forP=0.71 (air) andP=7 (water) and the obtained results are shown on figures and tables.     

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.     

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.     

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.     

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.     

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.     

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.     

Numerical solution of MHD free-convection flow in the Stokes problem by the Crank-Nicolson method

A numerical solution of magnetohydrodynamic free-convection flow, in the Stokes' problem, for a porous vertical plate, is obtained, when Prandtl numberP is not equal to one. The magnetic lines of force are assumed to be fixed relative to the plate which is started moving impulsively in its own plane (I.S.P.) or it is uniformly accelerated (U.A.P.). The solution is obtained by the Crank-Nicolson method, which is an implicit second-order method, forP=0.71 (air) andP=7 (water). The obtained results are shown on figures and tables.     

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.     

Free convection and mass transfer effects on the magnetohydrodynamic flows near a moving plate in a rotating medium

An exact solution of the free-convection flow near an infinite vertical plate moving in a rotating medium in the presence of foreign mass and a transverse magnetic field is presented under a constant heating of the plate. It is apparent from this solution that the effects of the motion, the temperature, and the mass transfer are linear and, hence, can be studied independently. Three applications of physical interest are discussed. The non-magnetic case and non-rotating case are are also discussed.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, on 30 May 1988.     

Unsteady magnetohydrodynamic flows in a rotating elasto-viscous fluid

The unsteady flow of an incompressible electrically-conducting and elasto-viscous fluid (Walter's liquidB), filling the semi-infinite space, in contact with an infinite non-conducting plate, in a rotating medium and in the presence of a transverse magnetic field is investigated. An arbitrary time-dependent forcing effect on the motion of the plate is considered and the plate and fluid rotate uniformly as a rigid body. The solution of the problem is obtained with the help of the Laplace transform technique and the analytical expressions for the velocity field as well as for the skin-friction are given.     

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.     

Influence of viscous dissipation on a hydromagnetic field

The effect of a transverse magnetic field and of the viscosity diffusion on the free-convection flow of an electrically-conducting incompressible fluid past a uniformally accelerated vertical plate is discussed. A finite difference method has been used to obtain a numerical solution. The influence of the various parameters on the flow field is discussed.