Hydromagnetic ekman layer on convective heat generating fluid in slip flow regime

In this analysis, the velocity and temperature distributions on free convective heat generating rarefied gas in a rotating frame of reference are analysed for the case when a strong magnetic field is imposed in a plane which makes an angle with the normal to the plate. The effects of Hall currentm, heat source parameter and rarefaction have been discussed graphically followed by a discussion.     

Hydromagnetic Rayleigh problem for a porous wall in slip flow regime

An analysis of the Rayleigh problem in MHD for a porous wall in a slip flow regime is considered. The normal velocity of suction/injection at the wall is assumed to be time dependent. The solution of the problem is obtained in the form of a power series, in terms of known functions. The variations of the velocity field and the skin friction are shown graphically and are followed by a quantitative discussion.Science Update, The Pioneer, India, 21 July 1995 edition     

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     

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 .     

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.     

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 MHD free-convection flow past an accelerated vertical porous plate

The effect of Hall currents on the hydromagnetic free-convection flow of an electrically conducting and incompressible viscous fluid past a uniformly accelerated infinite vertical porous plate is discussed. The magnetic Reynolds number is assumed to be small so that the induced magnetic field can be neglected. The governing equations of the flow are solved by defining a complex velocity with the help of the Laplace transform method when the Prandtl number is equal to unity. The influence of the various parameters on the unsteady flow field is presented for both the cases, cooling and heating of the porous plate by free-convection currents.     

The effects of vigorous mixing in a convective model of zonal flow on the ice giants

Previous studies have used models of three-dimensional (3D) Boussinesq convection in a rotating spherical shell to explain the zonal flows on the gas giants, Jupiter and Saturn. In this paper we demonstrate that this approach can also generate flow patterns similar to those observed on the ice giants, Uranus and Neptune. The equatorial jets of Uranus and Neptune are often assumed to result from baroclinic cloud layer processes and have been simulated with shallow layer models. Here we show that vigorous, 3D convection in a spherical shell can produce the retrograde (westward) equatorial flows that occur on the ice giants as well as the prograde (eastward) equatorial flows of the gas giants. In our models, the direction of the equatorial jet depends on the ratio of buoyancy to Coriolis forces in the system. In cases where Coriolis forces dominate buoyancy, cylindrical Reynolds stresses drive prograde equatorial jets. However, as buoyancy forces approach and exceed Coriolis forces, the cylindrical nature of the flow is lost and 3D mixing homogenizes the fluid's angular momentum; the equatorial jet reverses direction, while strong prograde jets form in the polar regions. Although the results suggest that conditions involving strong atmospheric mixing are responsible for generating the zonal flows on the ice giants, our present models require roughly 100 and 10 times the internal heat fluxes observed on Uranus and Neptune, respectively.     

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.     

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.     

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 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.     

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.     

The effects of convective overshooting on naked helium stars

Using stellar evolutionary models, we investigate the effects of convective overshooting on naked helium stars. We find that a larger value of overshooting parameter δ_(ov) results in a larger convective core,which prolongs the lifetimes of naked helium stars on the helium main sequence and leads to higher effective temperatures and luminosities. For naked helium stars with masses lower than about 0.8 M_⊙, they hardly become giant stars as a result of a weak burning shell. However, naked helium stars with masses between about 0.8 M_⊙ and 1.1 M_⊙can evolve into giant branch phases, and finally become carbon oxygen white dwarfs.     

Effects of mass transfer on the hydromagnetic free convective flow in the Stokes' problem

The effects of the mass transfer on free convection flow of an electrically conducting viscous fluid (e.g., of a stellar atmosphere) past an impulsively started infinite vertical limiting surface (e.g., of a star) in presence of a transverse magnetic field is considered. Solutions for the velocity and skin-friction, in closed form are obtained with the help of the Laplace transform technique and the results obtained for various values of the parametersS _c (Schmidt number),P (Prandtl number) andM (Hartmann number) are given in graphical form. The paper is concluded with a discussion of the results obtained.     

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     

Hall effects on thermal hydromagnetic instability of a partially ionized medium

Thermal instability of a finitely conducting hydromagnetic composite medium is considered including the effects of Hall currents and the collisions with neutrals. The equilibrium magnetic field is assumed to be uniform and vertical. For stationary convection, the collissions have no effect, while the Hall currents are found to have a destabilizing effect on the thermal instability. It is further shown that whenM is finite andQ the asymptotic behaviours of the critical Rayleigh number, the critical wave number and the critical temperature gradient remain the same as those obtained by Chandrasekhar whereM is a nondimensional number which includes the Hall current effects andQ stands for the Chandrasekhar number.     

Heat flow and thickness of a convective ice shell on Europa for grain size-dependent rheologies

Although it is mostly accepted that the lower part of the ice shell of Europa is actively convective, there is still much uncertainty about the flow mechanism dominating the rheology of this convective layer, which largely depends on the grain size of the ice. In this work, we examined thermal equilibrium states in a tidally heated and strained convective shell, for two rheologies sensitive to grain size, grain boundary sliding and diffusion creep. If we take a lower limit of 70 mW m⁻² for the surface heat flow, according to some geological features observed, the ice grain size should be less than 2 or 0.2 mm for grain boundary sliding or diffusion creep respectively. If in addition the thickness of the ice shell is constrained to a few tens of kilometers and it is assumed that the thickness of the convective layer is related to lenticulae spacing, then grain sizes between 0.2 and 2 mm for grain boundary sliding, and between 0.1 and 0.2 mm for diffusion creep are obtained. Also, local convective layer thicknesses deduced from lenticulae spacing are more similar to those here derived for grain boundary sliding. Our results thus favor grain boundary sliding as the dominant rheology for the water ice in Europa's convective layer, since this flow mechanism is able to satisfy the imposed constraints for a wider range of grain sizes.     

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.