Effects of free convection on the hydromagnetic accelerated flow past a vertical porous limiting surface

The effects of free convection on the accelerated flow of a viscous, incompressible and electrically conducting fluid (e.g. of a stellar atmosphere) past a vertical, infinite, porous limiting surface (e.g. of a star) in the presence of a transverse magnetic field, is considered. The magnetic Reynolds number of the flow is taken to be small enough, so that the induced magnetic field is negligible. Expressions for velocity and skin-friction are obtained by using Laplace transform, when the Prandtl number is equal to one (P=1). Graphs showing variations of velocity and skin-friction, for different values ofG (Grashof number) andM (magnetic parameter) are plotted, and the results of them are discussed.     

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

An analysis of Rayleigh's problem (also Stokes's problem) for the flow of a viscous fluid (e.g. of a stellar atmosphere) past an impulsively started infinite, vertical porous limiting surface (e.g. of a star) with constant suction, when the free stream velocity oscillates in time about a constant mean, has been carried out. On solving the coupled non-linear equations in approximate way, expressions for the mean velocity, the mean temperature, the mean skin-friction and the mean rate of heat transfer, expressed in terms of Nusselt number, are obtained. The effects of Grashof numberG, Eckert numberE and Prandtl numberP, on these quantities, is discussed for the cases of an externally heating and cooling of the limiting surface, by the free convection currents, and the variations of them are shown graphically.     

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.     

Effects of the hydromagnetic free convection on the oscillatory flow of a viscous incompressible fluid past a porous limiting surface

The unsteady two-dimensional free convection flow of a viscous incompressible and electrically conducting fluid past an infinite non-conducting and non-magnetic porous limiting surface (e.g. of a star) through which suction with uniform velocity occurs is considered when the free-stream velocity, the temperature of the limiting surface and the induced magnetic field are oscillating in the time about a constant mean value. Expressions, in closed form for the velocity, the skin-friction, the displacement thickness, the induced magnetic field and the electrical current density are obtained by the help of the two-sided Laplace transform technique, when the magnetic Prandtl numberP _m, and the Prandtl numberP are equal to one, and the magnetic parameterM is smaller to one. During the course of analysis the effects of magnetic parameterM, Grashof numberG and non-dimensional frequency are discussed.     

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.     

Effects of mass transfer on the hydromagnetic flow past a vertical limiting surface

An analysis of a two-dimensional steady free convective flow of a conducting fluid, in the presence of a magnetic field and a foreign mass past an infinite, vertical porous and unmoving surface is carried out, when we have constant heat flux at the limiting surface and the magnetic Reynolds number of the flow is not small. If we assume constant suction at the surface, approximate solutions of coupled nonlinear equations are derived for the velocity field, temperature field, magnetic field and for their related quantities. During the course of discussion, the effectsM (magnetic parameter),Gr (Grashof number), andGm (modified Grashof number) have been presented.     

Transient hydromagnetic free-convection flow past an impulsively started vertical plate

The effect of rotation on unsteady free-convective started vertical plate is considered. It is assumed that the induced magnetic field is negligible compared to the applied magnetic field, which is fixed with the moving plate. Mathematical expressions for velocity and skin-friction are obtained by the Laplace transform technique. The profiles for velocity components are shown graphically with the effects of the rotation parameter, magnetic parameter and Grashof number. The numerical values of skin-friction components are given in tabalar form for different values of the parameters.     

Effects of mass transfer on the free convective flow in the Stokes' problem for an infinite vertical limiting surface

An exact analysis of the mass transfer effects on the free convection flow of an incompressible viscous fluid past an impulsively started infinite vertical (wall) limiting surface (Stokes's or Rayleigh's problem) has been carried out. Expressions for the velocity, temperature, species concentration and skin friction are obtained by using the Laplace transform technique. The velocity field and the skin friction are shown graphically for air (P=0.71) and mercury (P=0.025). The effects ofG (Grashof number),G _c (the modified Grashof number) andS _c (Schmidt number) are considered qualitatively during the course of discussion.     

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.     

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.     

Effects of mass transfer on the hydromagnetic free convective flow in the Stokes' problem

The effects of the mass transfer on free convection flow of an electrically conducting viscous fluid (e.g., of a stellar atmosphere) past an impulsively started infinite vertical limiting surface (e.g., of a star) in presence of a transverse magnetic field is considered. Solutions for the velocity and skin-friction, in closed form are obtained with the help of the Laplace transform technique and the results obtained for various values of the parametersS _c (Schmidt number),P (Prandtl number) andM (Hartmann number) are given in graphical form. The paper is concluded with a discussion of the results obtained.     

Oscillatory hydromagnetic flow through a porous medium in the presence of free convection and mass transfer flow

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.     

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 in the stokes problem for a vertical plate with variable surface temperature

The free-convection flow of an incompressible viscous fluid past an infinite, vertical plate for impulsive as well as uniformly accelerated motion of the plate is discussed when the plate temperatuve varies as the square root of time. The Laplace transform technique is used to obtain the expressions for velocity and skin-friction. The influence of the various parameters, entering into problem, on the velocity field and skin-friction is extensively discussed.     

Orbits of fluid elements accreting onto a black hole

An exact analysis of the unsteady free and forced convection flow of an incompressible viscous fluid is presented in the presence of thermal diffusion effect. The Laplace transform technique is used to obtain the expressions for velocity, leading edge effects, and skin-friction. During the course of the discussion, the effects ofS (thermal diffusion parameter), Pr (Prandtl number), andt (time parameter) on velocity, leading edge, and skin-friction are extensively 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.     

Photometry of the fast-rotating late-type star W92 in NGC 2264

The effect of a uniform transverse magnetic field on the free-convection flow of an electrically conducting fluid past a uniformly accelerated infinite vertical porous plate is discussed. Finite-difference method has been used to obtain the solution of the governing equations when the Prandtl number is not equal to unity. The velocity profiles have been shown graphically for both cases, cooling and heating of the porous plate. The numerical values of the skin-friction are entered in table and the effects of the various parameter are discussed on the flow field.     

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.     

Hydromagnetic free-convection flow near a time-varying accelerated vertical plate

The effect of a uniform transverse magnetic field on the free-convection flow of an electrically conducting fluid past an exponentially accelerated infinite vertical plate is analysed for both cases, when the magnetic lines of force are fixed relative to the fluid and the plate, respectively. The Laplace transform method is used to obtain the expressions for velocity and skin-friction. The effect of a magnetic parameter is to decrease the velocity of water when the magnetic field is fixed to the fluid, while it increases the velocity field when the magnetic lines of force are fixed relative to the plate.