MHD free-convection flow in the stokes problem for a porous vertical plate

The effect of a uniform transverse magnetic field on the free-convection flow of an electrically-conducting fluid past an infinite, vertical, porous plate for both classes of impulsive as well as uniformly-accelerated motion of the plate is discussed. The magnetic lines of force are assumed to be fixed relative to the plate. Expressions for the velocity field and skin friction for both cases are obtained by the Laplace transform technique. The influence of the various parameters, entering into the problem, on the velocity field and skin-friction is extensively discussed with the help of graphs and tables.     

Stokes' problem for a vertical infinite plate with variable temperature

An exact analysis of Stokes' problem for an infinite vertical plate, whose temperature varies linearly with time, has been presented. It is observed that the velocity near the plate increases with the timet, and the Grashof numberGr. The skin-friction has been found to vary ast ^7/2 and the Nusselt number varies as or whereP is the Prandtl number.     

MHD free-convection flow in the stokes problem for a vertical porous plate in a rotating system

The flow past an infinite vertical isothermal plate started impulsively in its own plane in a viscous incompressible and electricalfy conducting fluid has been presented in a rotating system. 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 defining a complex variable with the help of the Laplace transform technique. The influence of the various parameters, occurring into the problem, on the axial and transverse components of the velocity and skin-friction is extensively discussed with the help of graphs and table.     

Free-convection and mass transfer effects on the flow past a vertical plate

In sequel to an earlier work (Mitra, 1984), I set out to find the appropriate equation of state of an isothermal (self-gravitating) cosmic gas sphere. It will be shown that because of self-gravitational interaction, a cosmic gas which is perfect otherwise, is destined to behave like an imperfect gas. It is found that for a cosmic gas in hydrostatic equilibrium the only mode of free expansion (or contraction) is by a homologous evolution. This theorem enables one to construct the equation of state in terms of the local thermodynamical parameters of the inhomogeneous medium in such a way that it is consistent with the boundary conditions at the centre and at the natural boundary of the system. This method can be extended even when there is a temperature gradient in the system. This analysis predicts that the density profile should be the same at least for all nondegenerate Newtonian stars having the same temperature profile and which can be considered to be in hydrostatic equilibrium. And the density profile will be that of a polytrope of indexn=3, modulated by a temperature profile.     

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.     

Free-convection flow past an exponentially accelerated vertical plate

The free-convection flow of an incompressible and viscous fluid past an exponentially accelerated infinite vertical plate is analysed. The Laplace transform method is used to obtain the expressions for velocity and skin-friction. The effect of various parameters, occuring into the problem, is discussed with the help of graphs and table.     

Hydromagnetic free convection flow in the stokes problem for a porous vertical limiting surface with constant suction

This paper provides a comprehensive analysis of the effects of a uniform transverse magnetic field on the free-convection flow of a viscous incompressible and electrically conductive fluid (e.g., of a stellar atmosphere) past an impulsively started, infinite, porous, vertical limiting surface (e.g., of a star) with a constant suction. The magnetic Reynolds number is assumed small so that the induced magnetic field is considered negligible. Exact solution of the equations governing the flow is obtained in closed form with the help of the Laplace transform technique when the Prandtl numberP=1. Expressions are given for the velocity field, for the temperature field and for their related quantities. The results thus obtained are discussed quantitatively in the last section of this paper.     

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.     

Finite-difference analysis of the MHD stokes problem for a vertical plate with Hall and ion-slip currents

An explicit finite-difference method is employed to study the MHD free convection heat generating fluid past an impulsively started vertical infinite plate when a strong magnetic field is applied perpendicular to the plate. The velocity and temperature profiles are shown on graphs and the results are discussed in terms of the non-dimensional parameters _e (Hall parameter), _i (ionslip parameter), (heat source parameter), and Gr (Grashof number).     

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.     

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.     

Convection flow over a uniform-flux vertical surface with variable viscosity

A regular perturbation analysis is presented for natural convection flow over an uniform flux vertical surface with temperature dependent viscosity. Numerical calculations are presented forP _r=6.7 which show that the first-order correction to the local temperature difference and to the local skin-fraction are negative whereas it is positive for the local Nusselt number. The effects of variable viscosity on the temperature, velocity profiles, the local temperature difference, the local Nusselt number and the local skin fraction are discussed.     

Free convection effects on the stokes problem for an infinite vertical limiting surface with constant suction

This paper studies the effects of free convection currents on the flow field of an incompressible viscous fluid past an impulsively started infinite vertical porous limiting surface when the fluid is subjected to a suction with uniform velocity. An exact analysis of the problem is obtained with the aid of the Laplace transform technique and the expressions for the velocity field, temperature field and for their related quantities of skin friction and rate of heat transfer are given. The results thus obtained are discussed quantitatively for air and water.     

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

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.     

Hall effects on MHD free-convection flow in the Stokes problem for a vertical porous plate

Hall effects on the MHD flow of an incompressible, electrically-conducting viscous fluid past an impulsively started infinite vertical porous plate has been analysed for the case of small magnetic Reynolds number. Exact solutions have been obtained for the axial and the transverse components of the velocity and the skin-friction by defining a complex velocity with the help of the Laplace transform technique. The velocity profiles are shown graphically and the numerical values of axial and transverse components of skin-friction are tabulated for different values of the dimensionless parameters occurring into the problem.     

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.     

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.     

Free-convection effects on MHD flow past a porous plate with step function change in suction velocity

Free convection effects on MHD flow past a semi infinite porous flat plate is studied when the time dependent suction velocity changes in step function form. The solution of the problem is obtained in closed form for the fluid with unit Prandtl number. It is observed that for both cooling and heating of the plate the suction velocity enhances the velocity field. The heat transfer is higher with increase in suction velocity.Notations B intensity of magnetic field - G Grashof number - H magnetic field parameter,H=(M+1/4) ^1/2–1/2 - M magnetic field parameter - N _u Nusselt number - P Prandtl number of the fluid - r suction parameter - T temperature of the fluid - T _w temperature of the plate - T temperature of the fluid at infinity - t time - t non-dimensional time - u velocity of the fluid parallel to the plate - u non-dimensional velocity - U velocity of the free stream - suction velocity - ₁ suction velocity att0 - ₂ suction velocity att>0 - x,y coordinate axes parallel and normal to the plate, respectively - y non-dimensional distance normal to the plate - coefficient of volume expansion - thermal diffusivity - kinematic viscosity - electric conductivity of the fluid - density of the fluid - non-dimensional temperature of the fluid - shear stress at the plate - non dimensional shear stress - erf error function - erfc complementary error function     

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.