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.     

Thermal and mass diffusion on MHD natural convective flow of a rarefied gas along vertical porous plate

The flow of an electrically conducting incompressible rarefied gas due to the combined buoyancy effects of thermal and mass diffusion past an infinite vertical porous plate with constant suction has been studied in the presence of uniform transverse magnetic field. The problem has been solved for velocity, temperature, and concentration fields. It has been observed that mean velocity and the mean temperature are affected by the Grashof numbersG ₁ andG ₂, the slip parameterh ₁, temperature jump coefficienth ₂, concentration jump coefficienth ₃ and magnetic field parameterM. The amplitude and the phase of skin-friction and the rate of heat transfer are affected by frequency in addition to the above parameters. They are shown graphically. The numerical values of the mean skin-friction and the mean rate of heat transfer are also tabulated.     

Finite Larmor radius and Hall effects on thermosolutal instability of a plasma

The thermosolutal instability of a plasma with finite Larmor radius and Hall effects is studied. When the instability sets in as stationary convection, finite Larmor radius effects are always stabilizing forx(=k ² d ²/² greater than two and forx less than two, they have a stabilizing or destabilizing influence depending on the Larmor radius parameterN in the presence of Hall currents. On the other hand the Hall currents have both stabilizing and destabilizing effects on the thermosolutal instability forx less than two and forx greater than two depending on the Hall parameterM. The stable solute gradient is found to have a stabilizing effect on stationary convection. The case of overstability is also considered wherein the sufficient conditions for the non-existence of overstability are derived.     

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.     

Hall effects on hydromagnetic convection flow in a rotating fluid

An analysis of Hall effects on the hydromagnetic free convection resulting from the combined effects of thermal and mass diffusion of an electrically-conducting liquid passed an infinite vertical porous plate in a rotating frame of reference is carried out when a strong magnetic field is imposed in a plane which makes an angle with the normal to the plate. 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 influence of Hall currents on the flow is studied for various values of .     

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.     

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.     

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 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.     

MHD thermal-diffusion effects on free-convective and mass-transfer flow over an infinite vertical moving plate

The Soret effect on MHD free-convective and mass-transfer flow of an incompressible, viscous, and electrically-conducting fluid, past a moving vertical infinite plate is studied. The flow is assumed to be at small Reynolds numbers so that the induced magnetic field is neglected. The problem is solved with the help of the Laplace transform method for two different values of the dimensionless functionf(t) signifying two different cases, e.g., (i) when the boundary surface, the flat plate, is impulsively started, moving in its own plane (I.S.P.) and (ii) when it is uniformly accelerated (U.A.P.). The effects on the velocity field as well as on the skin-friction of the various dimensionless parameters occurring into the problem, especially the magnetic parameterM and Soret number So, are discussed with the help of graphs.     

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.     

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.     

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.     

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.     

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.     

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     

Very massive stars: Evolution with mass loss

The evolution of mass-losing very massive stars in the 500–10000M _⊙ range has been investigated for two different initial compositions, (X, Z)=(0.8,0.0) and (X, Z)=(1.0,0.0). The evolutionary tracks are governed by two opposing factors which are the increase in the mean molecular weight in the convective core and the effect of mass loss. Conservative evolution of stars with massM?10000M _⊙ is similar to that of massive stars (20–100M _⊙), always moving to lower effective temperatures. For low values of the standard mass loss parameterN (50?N?200) the two opposing factors are almost in balance and the star is forced to move in a series of loops. For higher mass loss rates the loops disappear. In the 10000M _⊙ case no loops are observed and the tracks always move to higher effective temperatures. For a given mass loss rate the transition between right and left moving tracks occurs at higher masses the lower is the mass loss rate.     

The Plate Scale of the SODISM Instrument and the Determination of the Solar Radius at 607.1 nm

Knowledge of the Solar Diameter Imager and Surface Mapper (SODISM) plate scale is a fundamental parameter for obtaining the solar radius. We have determined the plate scale of the telescope on the ground and in flight onboard the Picard spacecraft. The results show significant differences; the main reason is that the conditions of observation are not the same. In addition, the space environment has an impact on the performance of a metrology instrument. Therefore, calibration in space and under the same conditions of observation is crucial. The transit of Venus allowed us to determine the plate scale of the SODISM telescope and hence the absolute value of the solar radius. The transit was observed from space by the Picard spacecraft on 5?–?6 June 2012. We exploited the data recorded by SODISM to determine the plate scale of the instrument, which depends on the characteristics of optical elements (mirrors, filters, or front window). The mean plate scale at 607.1 nm is found to be 1.0643 arcseconds?pixel^?1 with 3×10^?4 RMS. The solar radius at 607.1 nm from 1 AU is found to be equal to 959.86 arcseconds.