The effects on the flow field of retaining the Joule heating and viscous dissipation term in the energy equation for the hydromagnetic free-convective oscillatory flow past a porous limiting surface,II

As the mean steady flow has been presented in Part I, only the solutions for the transient velocity profiles, transient induced magnetic field, and transient temperature profiles and the related to them quantities are presented in this work. The influence of the various parameters entering into the problem, especially of the Eckert numberE, which represents the contribution of heat in the boundary layer due to viscous dissipation and to Joule heat, is extensively discussed.     

The effects on the flow field of retaining the Joule heating and viscous dissipation term in the energy equation for the hydromagnetic free-convective oscillatory flow past a porous limiting surface,I

With viscous dissipation and Joule heating taking into account the hydromagnetic two-dimensional oscillating free-convection flow, of a viscous, incompressible and electrically conducting fluid, past an infinite vertical porous limiting surface, is studied. For the solution of the problem it is considered that, the free-stream velocity, the plate temperature and the induced magnetic field are oscillating in the time about constant mean values. The flow is subjected to a constant suction velocity, through the porous surface, and a magnetic field of uniform strength is applied transversely to the direction of the flow. Analytical expressions for the flow field are obtained by solving the coupled non-linear system of equations which describe the flow. The influence of the various parameters entering into the problem is also extensively discussed signifying the importance of retaining the Joule heating and viscous dissipation term in the energy equation.     

Effect of anisotropy and viscous dissipation on turbulence production

The paper is concerned with turbulent flow of incompressible, spatially homogeneous viscous fluid. A model for turbulence energy equation is obtained, ignoring the pressure redistribution term in dynamical equations for the Reynolds stresses. The mechanism of dissipation on turbulence production is discussed and shown that the turbulence kinetic energy decays upto a constant value as time becomes infinitely large, i.e., for isotropy, dissipation inhibits the production process and if > initially then dissipation causes reduction in anisotropy.     

The effect of asymmetry on toroidal hydromagnetic waves in a dipole field

The meridional and azimuthal electric wave fields are considered as the characteristic toroidal and poloidal components. Neglecting the exchange of energy between these fields leads to a toroidal mode wave equation which retains the principal longitudinal or asymmetric contribution. The asymmetric spectrum appears as a logical extension of the results for the symmetric field line oscillations. The model for this study consists of a dipole field magnetized plasma, whose density is commensurate with conditions in the plasmapause. Eigenperiods are calculated for a broad range of asymmetric modes. Because of the similarity in the latitudinal variation between the symmetric and asymmetric periods, it is imperative to revise current idealized magnetospheric models and incorporate such similarity in future models.     

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.     

The effects of induced magnetic field on unsteady hydromagnetic flows in a rotating medium

Unsteady flows of a viscous incompressible electrically conducting fluid filling the semi-infinite space in contact with an infinite conducting plate in a rotating medium in the presence of a transverse induced magnetic field are investigated under an arbitrary time-dependent forcing effect on the motion of the plate where the plate and the fluid rotate uniformly as a rigid body. By using the Laplace transform technique, the Greens function of the problem is determined and certain asymptotic expansions of the exact solutions are analyzed. the steady-state oscillatory flow problem is solved, and structure of waves and displacement thickness of the boundary layers are discussed for different cases of some natural parameters in the problem. The results are compared with similar flows in the presence of a constant magnetic field.     

On the energy dissipation of fast hydromagnetic shock waves in the solar chromosphere

MHD equations including dissipation terms are applied to study the most important irreversible processes occurring in fast hydromagnetic shock waves under the conditions of the outer solar atmosphere. The atmosphere is assumed to be permeated by a nearly horizontal, uniform magnetic field, the magnitude and inclination angle of which being parameters of the analysis. Numerical examples, corresponding to situations which might occur in the upper chromosphere, are computed in order to demonstrate the procedure.     

Free convection in hydromagnetic flows of a viscous heat-generating fluid with wall temperature oscillation and Hall currents

A study is made of the free convection in hydromagnetic flows through a porous medium of a heat generating fluid past an infinite vertical porous plate. A strong magnetic field is imposed in a direction which is perpendicular to the free stream and makes an alge to the vertical direction. The governing equations for the hydromagnetic fluid flow and the heat transfer are solved analytically. The influence of Hall currents, the permeabilityK and the inclination upon the velocity field are shown in figures.     

Compression of magnetic field in a viscous boundary layer

Galloway, Proctor, and Weiss have shown by numerical experiment that the magnetic field extending across a convective cell in a highly conducting viscous fluid may be concentrated into sheets with energy density B ²/8 larger than the kinetic energy density 1/2v ² of the convection by a factor (v/)^1/2 or more. This paper employs conventional boundary layer theory for high Reynolds number to provide a simple analytical example illustrating this remarkable effect of field concentration.This work was supported by the National Aeronautics and Space Administration under grant NGL 14-001-001.     

Accurate approximate formulae for toroidal standing hydromagnetic oscillations in a dipolar geomagnetic field

Calculations of the toroidal eigenmodes of oscillation of the magnetospheric plasma have been important in explaining the nature of Pc3, Pc4 and Pc5 geomagnetic pulsations. In this paper perturbation solutions of the governing equations are presented. These are much more accurate than the WKB approximation which has often been used, and much simpler to compute than the numerical solutions which have been used. A method of including the finite ionospheric conductivity is also presented.     

The instability of hydromagnetic planetary-gravity waves in a zonal flow and transverse magnetic field

Hydromagnetic planetary-gravity waves propagating on a β-plane through a zonal flow and transverse magnetic field are examined for instability. Such instabilities may be related to same physical phenomena in the atmospheres of the Sun and planets and in the Earth's core. It is found that the onset of instability depends on the directions of the vertical and transverse wave-numbers and the zonal flow. It is also shown that as the magnetic field intensity is kept uniform instability can onset provided that the zonal flow strength does not exceed a certain factor, which depends on the parameters of the medium, and then the zonal wavenumbers that can become unstable are limited to a given range. If the basic Alfvén wave speed is allowed to vary whereas the zonal flow is kept uniform the zonal wavenumbers that can exhibit instability are again limited but the basic Alfvén wave speed can assume any value.     

The effect of Joule dissipation on field line resonance

Damped hydromagnetic eigenmodes are calculated numerically for a simple inhomogeneous plasma that is assumed to be contained within rigid perfectly conducting walls, and subject only to Joule dissipation. It is found that E_∥ must be included in order to obtain well-behaved damped eigenmodes that include resonant field lines, even though E_∥ is relatively very small. The thickness of the resonant region in the equatiorial plane, estimated from the model, is of order 10^?3 of an L number, which seems about two orders of magnitude too small to match observed long period micropulsations. The fact that mid-latitude micropulsations sometimes lead in phase at the lower latitudes is shown probably to be an effect of the local increase in resonant period with latitude.     

Effects of boundary conditions and viscous energy dissipation on carbon burning in thermonuclear supernova models

Based on a one-dimensional hydrodynamic model, we investigate carbon burning in a thermonuclear type-Ia supernova in the approximation of unsteady convection. The relatively broad range of convective parameters, 1×10^?3≤α_c≤2×10^?3, in which delayed detonation from the edge takes place was found to be preserved only for cases with a low boundary temperature at the presupernova stage, T _b ^(PS) = 6.4 × 10⁶ K, and with a high envelope mass, m_ex ? 2 × 10^?3M_⊙. In cases with a more realistic temperature, T _b ^(PS) = 2 × 10⁸ K, which corresponds to helium burning in the shell source, and with a lower mass m_ex, delayed detonation from the edge takes place only at α_c = 2 × 10^?3, while at α_c = 1 × 10^?3, numerous model pulsations occur during t?500 s. Artificial viscosity is shown to give a determining contribution to the increase in entropy in outer model shells, which is caused by the generation of weak shock waves during pulsations. We also show that the entropies calculated by two independent methods are equal.     

Unsteady hydromagnetic boundary-layer flow on a semi-infinite wall

Unsteady two-dimensional flow of a viscous, incompressible and electrically conducting fluid which is confined on one side of a semi-infinite wall, in presence of a transverse magnetic field is investigated. The wall is initially at rest and then it is suddenly accelerated in its own plane with a velocity which is an arbitrary function of the time. Solution of the problem is obtained, for two particular cases, i.e., corresponding to two free-stream velocities, with the help of the finite difference approximation technique using the explicit method for uniformly accelerated motion of the wall.     

Acceleration covariance in hydromagnetic dusty turbulence in the presence of a very strong uniform magnetic field

We have found the Electric Dipole Radiation Fields and an estimative of the power radiated by an electric dipole in Einstein and de Sitter's cosmological backgrounds. A possible connection with the quasar problem is suggested.     

Cosmological evolution driven by viscous dissipation and monopole condensation in ten dimensions

A ten dimensional cosmology is studied wherein the stringy state of the early universe is simulated by a combination of viscous effects and monopole condensation in the primeval ten dimensions.     

Comparative effect of viscous dissipation on heat transfer in mixed convection flow: UWT and UHF cases

The effect of viscous dissipation on mixed convection flow about a rotating sphere with a prescribed uniform surface heat flux (UHF) has been investigated analytically. Merk's type of series expansions is used to obtain the heat transfer rate and the skin-friction coefficients. The results are presented for Pr=1;B=0, 1; ^*0, 0.5, 1 and various values of the dissipation parameter Ec^* at various angular positions. As in the case of uniform wall temperature (UWT), the heat transfer rate decreases with viscous dissipation. It is also observed that for an equivalence viscous dissipation effect, heating by UHF yields larger Nusselt number than heating by UWT.     

Magnetic field energy dissipation in neutral current sheets

An extended current sheet characterized by two peculiarities was formed in a configuration with opposite magnetic fields in a laboratory plasma on a -pinch device. First, development of the small scale turbulence leads to abnormal low sheet conductivity, through-sheet plasma diffusion and establishes the sheet thickness an order greater than the skin thicknessc/ _pe ( _pe is electron plasma frequency). Second, there develops and quickly stabilizes in a sheet the magnetic force line reconnection. As a result, a stable neutral sheet has the complicated structure of a magnetic field, including closed magnetic loops elongated along the axis of the system. The neutral sheet plasma becomes intensively heated, probably due to ion-sound turbulence, while a group of accelerated electrons, which on the energy spectrum lead to a plateau formation, are observed. The absence of any predominant direction is a typical feature for the motion of accelerated particles. The experimental data, obtained over a broad range of plasma densities and magnetic field values typical for the solar atmosphere, show that the antiparallel magnetic field turbulent dissipation could play an important role in the mechanism of solar energy release. The parameters of accelerated particles (energy 4–12 keV, the energy content being 10^–1–10² of all the energy dissipated in a sheet) agree nicely with the data of astrophysical observations.     

Axially-symmetric viscous fluid interacting with the gravitational field

The problem of an axially-symmetric viscous fluid interacting with the gravitational field has been investigated. Exact solutions have been obtained for the pressure and density of the viscous fluid. Physical interpretation of the solutions in respect of the expansion factor, acceleration components reality conditions of the distribution, etc., have been made.