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1.
In this work an analysis of Stokes' problem for a two-dimensional unsteady hydromagnetic free convection flow, of an incompressible viscous electrically conducting fluid, past an infinite vertical porous limiting surface is presented, when the free stream velocity oscillates in time about a constant mean value. The flow is subjected to a constant suction, through the porous wall, and the difference between the 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. Analytical expressions for the velocity field, the temperature field and for their related quantities are obtained. The influence of the various parameters entering into the problem is extensively discussed. A comparative study with hydrodynamic case is also made wherever necessary.  相似文献   

2.
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.  相似文献   

3.
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.  相似文献   

4.
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.  相似文献   

5.
A study is made of the free convection in hydromagnetic flows through a porous medium of a heat generating fluid past an infinite vertical porous plate. A strong magnetic field is imposed in a direction which is perpendicular to the free stream and makes an alge to the vertical direction. The governing equations for the hydromagnetic fluid flow and the heat transfer are solved analytically. The influence of Hall currents, the permeabilityK and the inclination upon the velocity field are shown in figures.  相似文献   

6.
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.  相似文献   

7.
An analysis of Hall effects on the hydromagnetic free convection resulting from the combined effects of thermal and mass diffusion of an electrically-conducting liquid passed an infinite vertical porous plate in a rotating frame of reference is carried out when a strong magnetic field is imposed in a plane which makes an angle with the normal to the plate. 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 influence of Hall currents on the flow is studied for various values of .  相似文献   

8.
A similarity analysis for the free and forced convection hydromagnetic flow over a horizontal semi-infinite flat plate through a non-homogeneous porous medium is presented, taking into account the hydrostatic pressure variation normal to the flat plate. The similarity solution of the problem under consideration is obtained under certain valid simplifying assumptions when, (i) the plate temperature is inversely proportional to the square root of the distance from the leading edge, (ii) the intensity of the applied magnetic field, normal to the plate, changes with the inverse square root of the distance from the leading edge, and (iii) the permeability of the porous medium, occupying a semi-infinite region of the space bounded by the flat plate, is proportional to the distance measured in the direction of the flow. A numerical solution of the resulting system of ordinary differential equations of motion and energy is obtained, depending on the Prandtl number Pr, the magnetic parameterM n ,the bouyancy parameter , and the permeability parameterP m .The variations of the fundamental quantities of the problem are shown graphically followed by a quantitative discussion.  相似文献   

9.
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.  相似文献   

10.
Unsteady two-dimensional hydromagnetic free convection and mass transfer flow of an electrically-conducting viscous-incompressible fluid, through a highly porous medium bounded by a vertical plane surface of constant temperature is considered. The free-stream velocity of the fluid vibrates about a mean constant value and the surface absorbs the fluid with constant velocity. Expressions for the velocity, temperature, concentration are obtained. Effects of Gr (Grashof number), Gm (modified Grashof number),K (permeability of the porous medium), (frequency parameter), andM (magnetic parameter) upon the velocity field are discussed.  相似文献   

11.
Unsteady hydromagnetic boundary layer flow of a viscous incompressible and electrically conducting fluid past an infinite vertical non-conducting porous limiting surface in presence of a transverse magnetic field, is considered when the limiting surface is moving impulsively in its own plane and is subjected to a constant suction. The free stream oscillates in time about a constant mean value and the magnetic Reynolds number is taken to be small enough so that the induced magnetic field is negligible. 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 the heat transfer are presented in this work. The influence of the various parameters entering into the problem, especially of the magnetic parameterM, is extensively discussed. A comparative study with hydrodynamic case (M=0) is also made.  相似文献   

12.
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.  相似文献   

13.
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.  相似文献   

14.
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.  相似文献   

15.
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.  相似文献   

16.
Unsteady two-dimensional free convection flow of an electrically conducting, viscous, incompressible fluid, past an infinite vertical porous limiting surface in the presence of a transverse magnetic field is studied, when the limiting surface is moved impulsively with a constant velocity, either in the direction of the flow or in the opposite direction. The magnetic Reynolds number of the flow is not taken to be small enough so that the induced magnetic field is not negligible. The obtained results, for the mean steady flow phenomena, are discussed with the aid of graphs and tables for different values of the dimensionless parameters entering into the problem.  相似文献   

17.
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.  相似文献   

18.
An analytical study is performed to examine the effects of magnetic field and temperature-dependent heat source on the free and forced convection flow past an infinite vertical plate. The expressions for the velocity field, penetration distance and skin-friction have been obtained by Laplace transform technique. The influence of the various parameters entering into the problem is extensively discussed.  相似文献   

19.
The problem of unsteady hydromagnetic axial flow near the porous surface of a sphere or a cylinder is studied numerically. The fluid is considered to be electrically conducting, viscous and incompressible subjected to a magnetic field. Results are presented for the case of injected or sucked fluid with a constant velocity through the porous surfaces. The magnetic Prandtl number is set equal to one, while the magnetic Reynolds number is taken to be small enough so that the inducted magnetic field is negligible.  相似文献   

20.
An analysis of the temperature field in the case of the two-dimensional hydromagnetic flow of a viscous incompressible and electrically conducting fluid, (e.g., of a stellar atmosphere), past a porous, infinite, limiting surface in the presence of a transverse magnetic field, is considered when (i) the free stream velocity oscillates in time about a constant mean; (ii) the suction velocity normal to the limiting surface oscillates in magnitude but not in direction about a non-zero mean; and (iii) there is no heat transfer between the fluid and the wall. Approximate solution is obtained of the energy equation and are given expressions for the temperature field and for the temperature at the limiting surface, when the magnetic Prandtl numberP m =1 and the magnetic parameterM<1. They are shown graphically followed by a discussion.Research supported by the Alexander S. Onassis Foundation.  相似文献   

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