Soret effects on free-convection and mass transfer flow in the stokes problem for a infinite vertical plate

An analytical study is performed to examine the free-convection and mass transfer flow for the Sokes problem for an infinite vertical plate on taking into account the Soret effect (thermal diffusion effect). The Laplace transform technique is used to obtain the expressions for velocity and skin-friction. The effect of Soret numberS on velocity field and skin-friction is extensively discussed with the help of graphs and table.     

Line Formation in Turbulent Media with Finite Correlation Length

The influence of a stochastic velocity field on the line formation is investigated. A method similar to the mean field electrodynamics is described, where only two-point correlations are taken into account. The influence of velocity model parameters, e. g. the correlation length and the dispersion of the velocity field, on the line profiles is discussed by simplified assumptions.     

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.     

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.     

Hydromagnetic free-convection laminar flow of an elasto-viscous fluid past an infinite plate

The effect of a transverse magnetic field on unsteady free-convection flow of an electrically conducting elasto-viscous fluid (Walters liquidB') past an impulsively started infinite vertical plate is discussed. The Laplace transform technique is used to obtain the expressions for velocity and shearing stress. The influence of the various parameters, entering in the problem, on the velocity field and shearing stress is extensively discussed.     

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.     

Numerical treatment of the unsteady hydromagnetic thermal boundary layer problem

This paper presents a suitable numerical method for the treatment of the unsteady hydromagnetic thermal boundary layer problem for flows past an infinite porous flat plate, the motion of which is governed by a general time-dependent law, under the influence of a transverse externally set magnetic field. The normal velocity of suction/injection at the plate is also assumed to be time-dependent. The results obtained on the basis of numerical approximations seem to compare favourably with earlier results (Pandeet al., 1976; Tokis, 1978). Analytical approximations are given for the cases of a plate (i) generally accelerated and (ii) harmonically oscillating. The direct numerical treatment is obviously advantageous since it allows, handling of cases where the known methods for analytical approximations are not applicable. This problem is closely related to the motions and heat transfer occurring locally on the surfaces of stars.     

Free convection effects on the hydromagnetic oscillatory flow in the stokes problem past an infinite porous vertical limiting surface with constant suction,II

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.     

Effects of the external temperature-dependent heat sources on the unsteady free convective and mass-transfer hydromagnetic flow in the stokes problem

There have been considered the effects of external temperature-dependent heat sources and mass transfer on free convection flow of an electrically conducting viscous fluid past an impulsively starting infinite vertical limited surface in presence of a transverse magnetic field as considered. Solutions for the velocity and skin-friction, in closed form are obtained by using the Laplace transform technique and the results obtained for various values of the parametersS _c (Schmidt number),M (Hartmann number), andS (Strength a Source or Sink) are given in graphical form. The paper is concluded with a discussion on the obtained results.     

Free convection in hydromagnetic flows of a viscous heat-generating fluid with wall temperature oscillation and Hall currents

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.     

Mass transfer effects on the flow past an accelerated vertical plate with constant heat flux

In the present paper, mass transfer effect on the free-convection flow of an incompressible viscous fluid past a uniformly accelerated infinite vertical plate is discussed when there is a constant heat flux between fluid and plate. The expressions for the velocity field and the skin-friction have been obtained by the Laplace-transform technique. The influence of the various parameters entering into the problem is extensively discussed with the help of graphs and table.     

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.     

MHD flow of an elasto-viscous fluid past a porous flat plate

An analytical study is performed to examine the laminar flow of an electrically-conducting elasto-viscous fluid (Walters's liquidB) past an infinite porous flat plate to a step function change in suction velocity in the presence of a transverse magnetic field. The influence of the various parameters, entering in the problem, on the velocity field and shearing stress is extensively discussed.     

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.     

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.     

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.     

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.     

On an alternative method for approximate solution of linear stochastic differential equations

An approximate method for solving formal linear stochastic differential equations of first order is proposed. On the basis of the Reynold averaging technique, the stochastic differential equation is transformed into an infinite hierarchical system. This infinite system is cut off in such a manner that uncorrelated (totally randomly) and totally correlated stochastic processes are exactly included. By this the applicability of the Reynold method is extended.     

Mass transfer effects on free-convection flow past an impulsively started porous infinite vertical limiting surface

The effects of heat and mass transfer on the flow field of a laminar boundary layer is considered. The flow is that of an incompressible viscous fluid past an impulsively started permeable vertical limiting surface with constant heat flux. The solution of the problem was obtained numerically, using an implicit finite difference scheme. The solution is given in a number of diagrams, which depict the influence ofG on velocity,P on temperature and Sc on concentration. The influence ofG on skin friction is also given.     

Laminar hydromagnetic thermal boundary layer in fluctuating flow past a limiting surface with variable suction

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.