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.     

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.     

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.     

Unsteady MHD flow past a porous plate with step function change in suction at slip flow regime

Unsteady two-dimensional hydromagnetic flow of an electrically conducting viscous incompressible fluid past a semi-infinite porous flat plate with step function change in suction velocity is studied allowing a first order velocity slip at the boundary condition. The solution of the problem is obtained in closed form and the results are discussed with the aid of graphs for various parameters entering in the problem.Notations B intensity of magnetic field - H magnetic field parameter,H=(M+1/4)^1/2–1/2 - h rarefaction parameter - L ₁ slip coefficient; ;I, mean free path of gas molecules;f, Maxwell's reflection coefficient - M magnetic field parameter - r suction parameter - t time - t dimensionless time - u velocity of the fluid - u dimensionless velocity of the fluid - U velocity of the fluid at infinity - v suction velocity - v ₁ suction velocity att<=0 - v ₂ suction velocity att>0 - x distance parallel to the plate - y distance normal to the plate - y nondimensional distance normal to the plate - v kinematic viscosity - electric conductivity of the fluid - density of the fluid - shear stress at the wall - nondimensional shear stress at the wall - erf error function - erfc complementary error function     

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.     

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.     

Free convection effects on the flow past a moving vertical infinite porous plate

An analysis of the effects of free convection currents on the flow field of an incompressible viscous fluid past an infinite porous plate, which is uniformly accelerated upwards in its own plane, is presented, when the fluid is subjected to a variable suction (or injection) velocity. It is assumed that this normal velocity at the porous plate varies att^–1/2, wheret denotes time. The equations governing the flow are solved numerically, using two-point boundary value shooting techniques.     

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     

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.     

Similarity solution for free and forced convection hydromagnetic flow over a horizontal semi-infinite plate through a non-homogeneous porous medium

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.     

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     

Magnetohydrodynamic flow of a non-Newtonian fluid past a porous plate

This article studies the laminar flow of an electrically conducting non-Newtonian fluid (Rivlin-Encksen type) past an infinite porous flat plate to a step function change in suction velocity in the presence of a transverse magnetic field. The Laplace transform technique has been employed to solve the basic differential equations. The solutions of the velocity profile and skin-friction are obtained and the effects of the visco-elastic parameter, the magnetic field and the time parameter on the fluid flow have been studied in several tables.     

Unsteady hydromagnetic free convection flow past an accelerated infinite vertical porous plate

Unsteady laminar free convection flow of a viscous incompressible and electrically conducting fluid past an accelerated vertical infinite porous plate subjected to a suction velocity proportional to (time)^–1/2 is studied in presence of a uniform horizontal magnetic field. Results are discussed with the effects of the Grashof number Gr, and the magnetic field parameterM for Pr (the Prandtl number)=0.71 and 7.0 representing air and water respectively at 20 °C.Nomenclature a suction/injection parameter - C _p specific heat at constant pressure - B ₀ magnetic induction - g acceleration due to gravity - Gr Grashof number (vg(T'_w-T')/U ₀ ³ ) - K thermal conductivity - M magnetic field parameter (B ₀ ² _e ² /U ₀ ² ) - Pr Prandtl number (C _p/K) - T' temperature of the fluid near the plate - T' _w temperature of the plate - T' temperature of the fluid at infinity - t' time variable - t dimensionless time (t' U ₀ ² /v) - u non-dimensional velocity (u'/U ₀) - U' velocity of the plate - U dimensionless velocity of the plate (U'/U _o) - U ₀ reference velocity - v' ₀ suction velocity - v ₀ nondimensional suction velocity (v' ₀/U ₀)=at^–1/2 - v' normal velocity component - v dimensionless normal velocity - Ec Eckert number ((vU ₀)^2/3/C _p(T' _w -T' )) - T dimensionless temperature of the fluid near the plate ((T'-T' )/T' _w –T' )) - x',y' coordinates along and normal to the plate - y dimensionless ordinate (=y' U _o/v) - v kinematic viscosity - coefficient of volume expansion - electric conductivity of the fluid - similarity variable (y/2t) - _w density of the fluid at the plate - density of the fluid at infinity - ' skin-friction - dimensionless skin-friction - coefficient of viscosity - _e magnetic permeability     

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.     

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.     

MHD oscillatory flow through porous medium

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.     

Hall effects on heat and mass transfer flow through porous medium

Effects of Hall current on free convection and mass transfer flow through a porous medium bounded by a vertical surface has been analysed. The problem is solved analytically. The velocity profiles are shown on graphs. Effects ofm (Hall parameter).K ^* (permeability parameter), and Sc (Schmidt number) on velocity are discussed.     

Hydromagnetic stability of some non-dissipative flows subject to non-axisymmetric disturbances

We study the linear stability of nondissipative flow of an electrically conducting fluid subject to non-axisymmetric disturbances in the following cases: (i) the radial flow of an incompressible fluid between two concentric porous circular cylinders in the presence of a radial magnetic field and (ii) axial flow of a compressible fluid between two concentric circular cylinders permeated by a helical magnetic field (0,B ₀(r),B _0z) in a cylindrical coordinate system. It is shown that in case (i), the flow is stable if the Alfvén velocity based on the undisturbed radial magnetic field exceeds the radial velocity due to suction or injection at the cylinder surfaces. In case (ii), it is found that under certain conditions the complex wave speed for an unstable mode lies within a circle of diameterW _max-W _min, whereW _max andW _min are the maximum and minimum values of the axial velocity in the flow region. In the presence of a purely axial magnetic field, however, the complex wave speed for an unstable mode always lies within the above circle.     

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 .     

MHD oscillatory flow past a vertical porous plate through porous medium in the presence of thermal and mass diffusion with constant heat source

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.