Heat and mass transfer of an oscillatory flow with Hall current,II

An analysis of Hall current on the combined effects of thermal and mass diffusion of an electrically conducting liquid past an infinite vertical porous plate is performed. Analytical expressions for the transient velocity, the transient temperature in the boundary layer and the skin-friction on the plate are derived. The effects of various parameters on the velocity, temperature, shearing stresses and rate of heat transfer are shown by graphs and tables.     

Heat and mass transfer in rotating fluid with Hall current,I

Hall effects on the hydromagnetic free convection resulting from the combined effects of thermal and mass diffusion of an electrically conducting liquid past an infinite vertical porous plate in a rotating system have been analysed. The expressions for the mean velocity, mean temperature in the boundary layer and the mean skin friction, the mean rate of heat transfer on the plate are derived. The effects of magnetic parameterM, Hall parameterm, Schmidt number Sc, and Ekman numberE on the flow field, are discussed with the help of graphs and tables.     

Heat and mass transfer in rotating fluid with Hall current,II

Effects of Hall current on the hydromagnetic free-convection resulting from the combined effects of thermal and mass diffusion of an electrically conducting liquid past an infinite vertical porous plate in a rotating frame of reference have been analysed. As the mean steady flow has been presented in Part I, only the solutions for the transient primary and secondary velocity profiles, transient temperature profiles in the boundary layer and the transient skin friction, the transient rate of heat transfer on the plate are presented in this work. The influence of the different parameters entering into the problem are discussed.     

Unsteady free-convective flow and mass transfer in a rotating porous medium with Hall current,I

The Hall effect on the unsteady hydromagnetic free-convection resulting from the combined effects of thermal and mass diffusion of an electrical-conducting liquid through a porous medium past an infinite vertical porous plate in a rotating system have been analysed. The expressions for the mean velocity, mean skin friction, and mean rate of heat transfer on the plate are derived. The effects of magnetic parameterM, Hall parameterm, Ekman numberE, and permeability parameterK ^* on the flow field are discussed with the help of graphs and tables.Nomenclature C _p specific heat at constant pressure - C the species concentration inside the boundary layer - C _w the species concentration at porous plate - C the species concentration of the fluid at infinite - C dimensionless species concentration - D chemical molecular diffusivity - E Ekman number - Ec Eckert number - g acceleration due to gravity - Gr Grashof number - Gm modified Grashof number - H ₀ applied magnetic field - (J _x, J_y, J_z) components of current density - M magnetic parameter - m Hall parameter - P Prandtl number - q _m mean rate of heat transfer - Sc Schmidt number - t time - t dimensionless time - T temperature of fluid - T _w temperature of the plate - T temperature of fluid at infinite - T dimensionless temperature - (u, v, w) components of the velocityq - w ₀ suction velocity - (x, y, z) Cartesian coordinates - z dimensionless coordinate normal to the plate Greek symbols coefficient of volume expansion - * coefficient of thermal expansion with concentration - frequency - dimensionless frequency - k thermal conductivity - K ^* permeability parameter - dinematic viscosity - density of the fluid in the boundary layer - coefficient of viscosity - _e magnetic permeability - angular velocity - electrical conductivity of the fluid - _m mean skin friction - _mn mean skin friction in the direction ofx - _mv mean skin friction in the direction ofy     

Heat and mass transfer of a viscous heat generating fluid with Hall currents

A study of natural convection in hydrodynamic flows of a viscous heat generating fluid in the presence of Hall currents and variable suction has been carried out. The governing equations for the magnetohydrodynamic fluid flow and heat transfer are solved. The effects of Hall currentm and heat source parameter on the velocity and temperature distributions are discussed.     

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.     

Hall effects on heat and mass transfer flow with variable suction and heat generation

A study of the combined buoyancy effects of thermal and mass diffusion on MHD convection flow in the presence of Hall currents with variable suction and heat generation has been carried out. Analytical expressions for the velocity and the temperature of the fluid are given. The effects of Hall currents, parameterm, and heat source parameter on the velocity are discussed.     

Free convection and mass transfer effects on the hydro-magnetic oscillatory flow past an infinite vertical porous plate

Two-dimensional unsteady free convection and mass transfer, flow of an incompressible viscous dissipative and electrically conducting fluid, past an infinite, vertical porous plate, is considered, when the flow, is subjected in the action of uniform transverse magnetic field. The magnetic Reynolds number is taken to be small enough so that the induced magnetic field is negligible. The solution of the problem is obtained in the form of power series of Eckert numberE, which is very small for incompressible fluids. Analytical expressions for the velocity field and temperature field are given, as well as for the skin friction and the rate of heat transfer for the case of the mean steady flow and for the unsteady one. The influence of the magnetic parameter,M, modified Grashof numberG _c , Schmidt numberS _c and frequency , on the flow field, is discussed with the help of graphs, when the plate is being cooled, by the free convection currents (G _r ,E>0), or heated (G _r ,E<0). A comparative study with hydrodynamic case (M=0) and the hydromagnetic one (M0) is also made whenever necessary.List of symbols B₀ applied magnetic field - |B| amplitude of the skin friction - C concentration inside the boundary layer - C concentration in the free stream - C _w concentration at the porous plate - C _p specific heat at constant pressure - D diffusion coefficient - E Eckert number - g _x acceleration due to gravity - G _c modified Grashof number - G _r Grashof number - M magnetic parameter - N _u Nusselt number - P Prandtl number - |Q| amplitude of the rate of heat transfer - S _c Schmidt number - T temperature of the fluid - T _w temperature of the plate - T temperature of the fluid in the free stream - T _r ,T _i fluctuating parts of the temperature profile - u, v velocity components in thex, y directions - u dimensionless velocity in thex direction - u ₀ mean steady velocity - u ₁ unsteady part of the velocity - u _r ,u _i fluctuating parts of the velocity profile - U dimensionless free stream volocity - U ₀ mean free stream velocity - v ₀ suction velocity - x, y co-rodinate system Greek Symbols phase angle of the skin-friction - coefficient of volume expansion - _* coefficient of expansion with concentration - phase angle of the rate of heat transfer - dimensionless co-ordinate normal to the plate - dimensionless temperature - ₀ mean steady temperature - ₁ unsteady part of temperature - k thermal conductivity - v kinematic viscocity - density of fluid in the boundary layer - density of fluid in the free stream - electrical conductivity of the fluid - skin friction - ₀ mean skin friction - frequency - dimensionless frequency     

Free convection and mass transfer effects on the oscillatory flow past an infinite moving vertical isothermal plate with constant suction and heat sources

An analysis of the two-dimensional flow of an incompressible, viscous binary fluid past an infinite, porous, vertical plate is presented under the following conditions: (i) the suction velocity is constant; (ii) the free stream oscillates in time about a constant mean; (iii) the plate moves in the upward direction in its own plane; (iv) the temperature of the plate is constant; (v) there are heat generation (absorption) in the fluid.Approximate solutions for the coupled non-linear equations are obtained for the velocity, temperature and their related quantities and the influence of the various parameters entering into the problem is discussed.     

Hall effects on oscillatory MHD boundary-layer flow under variable suction

The effects of Hall current on the oscillatory hydromagnetic boundary-layer flow under variable suction, past an infinite porous flat plate in the presence of a transverse magnetic field is discussed. The expressions for velocity and skin-friction are obtained and their variations for small and large frequency of oscillations are 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.     

Free convection and mass transfer in the hydromagnetic oscillatory flow past an infinite vertical porous plate with internal heat generation due to radiation absorption

the influence of radiation absorption on the flow-field of an unsteady laminar boundary layer due to free convection is considered. The flow is that of an incompressible viscous dissipative and electrically conducting fluid past an infinite vertical porous plate, when the flow is subjected to the action of a transverse magnetic field and the mainstream is oscillating around a mean value and an oscillating suction. The radiation is absorbed by a second material in a small concentration within the fluid and the absorption rate is proportional to the local concentration. The solution of the problem is obtained in the form of power series of Eckert numberE, which is very small for incompressible fluids, analytical expression for the velocity, temperature and the induced magnetic field are given for both the steady and the unsteady flows. The solution is also given in a number of figures that present the combined influence of the absorption withE,G _r , and the frequency of oscillation. In addition the influence of the absorption on the skin friction the heat flux is given. The results indicate the importance of the absorption which can be significant under certain conditions.     

Heat and mass transfer in convective flow of an incompressible rarefied visco-elastic fluid in presence of transverse magnetic field

Analytical study is performed to examine heat and mass transfer characteristics of natural convection flow of an incompressible, rarefied visco-elastic fluid past an infinite vertical porous plate with constant suction in the presence of transverse magnetic field under combined buoyancy force effects of thermal and mass diffusion. The effects of various parameters on mean velocity and mean skin-friction are shown graphically followed by a comparative study of Newtonian and non-Newtonian (visco-elastic). rarefied states.     

Hall effects on an oscillatory MHD flow in the Stokes problem past an infinite vertical porous plate,I

Hall effects on the hydromagnetic free convection flow of an electrically conducting incompressible viscous fluid past a steadily moving vertical porous plate has been analysed when the free stream oscillates in magnitude. The flow is subjected to a constant suction, through the porous plate, and the difference between 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. Approximate solutions for the components of velocity field 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.     

Effects of hall current on the oscillatory MHD free-convection flow

An analysis of Hall currents and heat generation on the free-convection flow resulting from the combined effects of thermal and mass diffusion is considered. Analytical expressions for the transient velocity and transient temperature field are derived. The influence of the different parameters entering into the problem are discussed by graphs.     

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.     

Heat and mass transfer on MHD heat generating flow through a porous medium in a rotating fluid

The problem of the free-convection flow of a viscous heat generating fluid through porous media in a rotating frame of reference is considered for the case when a strong magnetic field is imposed in a direction which is perpendicular to the free-stream and makes an angle to the vertical direction. Analytical expressions for the velocity field and temperature are given, and the influences of the various parameters on the velocity field are discussed.     

Effects of Hall current on hydromagnetic free-convective flow through a porous medium

An analysis of the effects of Hall current on hydromagnetic free-convective flow through a porous medium bounded by a vertical plate is theoretically investigated when a strong magnetic field is imposed in a direction which is perpendicular to the free stream and makes an angle to the vertical direction. The influence of Hall currents on the flow is studied for various values of .Nomenclature c _p specific heat at constant pressure - e electrical charge - E Eckert number - E electrical field intensity - g acceleration due to gravity - G Grashof number - H ₀ applied magnetic field - H magnetic field intensity - (j _x , j _y , j _z ) components of current densityJ - J current density - K permeability of porous medium - M magnetic parameter - m Hall parameter - n _e electron number density - P Prandtl number - q velocity vector - (T, T _w , T ) temperature - t time - (u, v, w) components of the velocity vectorq - U ₀ uniform velocity - v ₀ suction velocity - (x, y, z) Cartesian coordinates Greek Symbols angle - coefficient of volume expansion - _e cyclotron frequency - frequency - dimensionless temperature - thermal conductivity - coefficient of viscosity - magnetic permeability - kinematic viscosity - mass density of fluid - _e charge density - electrical conductivity - _e electron collision time     

MHD free-convection and mass transfer flow through a porous medium with heat source

An analytical study is performed to examine the heat source characteristics on the free-convection and mass transfer flow past an impulsively started infinite non-conducting vertical plate of a viscous, incompressible electrically-conducting fluid under the action of a uniform magnetic field through porous medium. The effects of various parameters on the velocity field are extensively discussed.     

Effects of Hall current and rotation

Effects of Hall current and rotation on the flow of electrically conducting rarefied gas due to combined buoyant effects of thermal and mass diffusion, past an infinite porous plate in the presence of transverse magnetic have been investigated. The equations governing the flow problem have been solved and the profiles are shown on graphs. Effects ofm (Hall parameter) andE (Ekman number) on velocity are discussed.