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.     

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.     

Unsteady hydromagnetic flow through a porous medium between two infinite parallel porous plates with time-varying suction

Unsteady two-dimensional flow of a viscous incompressible and electrical-conducting fluid through a porous medium bounded by two infinite parallel plates under the action of a transverse magnetic field is presented when there is time-varying suction at the plates. The lower plate is at rest while the upper plate is oscillating in its own plane about a constant mean velocity. Expressions for the velocity, fluctuating parts of the velocity, amplitude, and phase of the skin-friction are obtained. The flow phenomenon has been characterized by the parametersK (permeability of the porous medium),N(magnetic parameter) (frequency parameter), andA(variable suction parameter) and the role of these parameters on the flow characteristics has been studied.     

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.     

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 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.     

Unsteady forced and free convective flow past an infinite vertical porous plate with oscillating wall temperature and constant suction

A study of the two-dimensional unsteady flow of a viscous, incompressible fluid past an infinite vertical plate has been carried out under the following conditions: (1) constant suction at the plate, (2) wall temperature oscillating about a constant non-zero mean, and (3) constant free-stream. Approximate solutions to coupled non-linear equations governing the flow have been carried out for the transient velocity, the transient temperature, the amplitude and phase of the skin friction, and the rate of heat transfer. The velocity, temperature and amplitude are shown graphically whereas the numerical values of the phases are given in a table. It has been observed that the amplitude of the skin friction decreases with increasing (frequency) but increases with increasingG (Grashof number), while the amplitude of the rat of heat transfer increases with increasing .     

Hall effects on natural convective flow in slip flow regime

Hall effects on the flow of electrically conducting rarefied gas due to combined buoyant effects of thermal and mass diffusion past an infinite porous plate with constant suction in the presence of strong transverse magnetic field have been investigated. The equations governing the flow poblem have been solved for primary, secondary velocities and temperature. The effects of Hall current, magnetic field and the effect of rarefication have been discussed graphically followed by a discussion.Nomenclature x,y coordinate system - u velocity inx direction - v ₀ suction velocity - w velocity inz direction - E Eckert number - G, G^* Grashof numbers - h ₁ velocity slip coefficient - h ₂ temperature jump coefficient - h ₃ concentration jump coefficient - M, m magnetic field parameter, Hall parameter - Pr Prandtl number - Sc Schmidt number - T, T _w, T temperature in flow regime, plate temperature, temperature outside the boundary layer very away from the plate - C, C _w, C concentration of the gas in flow, concentration at the plate, concentration far away from the plate - thermal conductivity - D coefficient of chemical molecular diffusion - coefficient of kinematic viscosity - coefficient of viscosity - electrical conductivity - C _p specific heat of gas at constant pressure density     

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).     

The skin friction in the unsteady free-convection flow past an accelerated plate

In this paper the unsteady laminar free-convection flow of a viscous incompressible fluid, past an accelerated infinite vertical porous plate subjected to a constant suction (or injection) in considered. Numerical results for the skin-friction on the plate are obtained for the class of accelerated motions whose velocity is of the formU ₀ t ⁿ wheret is time,U ₀ a constant, andn is a positive integer. The skin friction tends to zero with increasingt when the Grashof number Gr=², the Prandtl number =1,n=0, and >0 which corresponds to suction.On leave of absence from the Department of Mathematics, University of Dhaka, Bangladesh.On leave from absence from the Department of Mathematics, University of Dar-es-Salaam, Tanzania.     

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.     

Role of magnetic field on transient forced and free-convection flow past an infinite vertical porous plate through porous medium with heat source

Effects of magnetic field and permeability of the porous medium on unsteady forced and free-convection flow past an infinite vertical porous plate in presence of temperature-dependent heat source have been analysed. The Laplace transform method is used to obtain the expression for velocity field, skin friction, and leading edge effects. During the course of discussion, the effects ofM (magnetic parameter),S (heat source parameter), (suction parameter), andK (permeability of porous medium) on velocity field, skin friction, and leading edge effect have been extensively discussed.     

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.     

Wall temperature oscillation on convection flow in a rotating fluid with hall and ion-slip currents

An analysis of Hall and ion-slip current effects on the MHD free-convection flow of a partiallyionised gas past an infinite vertical porous plate in a rotating frame of reference is carried out. A strong magnetic field is applied perpendicular to the plate and the plate temperature oscillates in time about a constant non-zero mean. The problem has been solved for the velocity and temperature fields and the effects of _e (the Hall parameter), _i (the ion-slip parameter),E _r (rotation parameter), and have been discussed and shown graphically.     

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     

Free-convection flow of water at 4°C past an infinite vertical porous plate with constant heat flux

An analysis of the two-dimensional flow of water at 4°C past an infinite porous plate is presented, when the plate is subjected to a normal suction velocity and the heat flux at the plate is constant. Approximate solutions are derived for the velocity and temperature fields and the skin-friction. The effects ofG (Grashof number) andE (Eckert number) on the velocity and temperature fields are discussed.Nomenclature u, v velocity components of the fluid inx, y direction - g acceleration due to gravity - coefficient of thermal expansion of water at 4°C - v kinematic viscosity - density - T temperature inside thermal boundary layer - T free-stream temperature - k thermal conductivity - C _p specific heat at constant pressure     

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.     

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 mixed convection flow past an infinite vertical porous plate with constant heat source

An exact analysis of the unsteady free and forced convection flow of an incompressible viscous fluid past a porous plate has been presented in presence of a constant heat source. A solution has been derived by Laplace-transform technique. Velocity profiles, skin-friction and leading edge effects have been obtained. During the course of the discussion, the effects ofS (heat source parameter), (suction parameter) on velocity, skin-friction and leading edge effect have been extensively discussed with the help of graphs and the table.