Free convection and mass transfer effects on the control of the unsteady boundary layer on an infinite vertical porous limiting surface

The present study presents an analytical solution to the flow field of the unsteady laminar accelerated flow of a viscous incompressible fluid past an infinite vertical porous limiting surface, when the freestream is accelerated and the limiting surface temperature and concentration are given functions of time. The expressions for the velocity, temperature and skin friction are obtained by using Laplace transform, when the Prandtl and Schmidt numbers are given. Graphs showing variations of the velocity and the skin friction, for different values ofG _r andG _c (modified Grashof number), as well as of the temperature are plotted and the results are discussed.     

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.     

Free convection effects on the oscillatory flow in the Stokes's problem past an infinite porous vertical limiting surface with constant suction,II

In this work we present the two-dimensional free convection flow of an incompressible viscous fluid past an infinite vertical limiting surface (porous wall) for the Stokes's problem when the fluid is subjected to a constant suction velocity. The flow is normal to the porous wall and the free stream oscillates about a mean value. As the mean steady flow has been presented in Part I, only the solutions for the transient velocity profiles, transient temperature profiles, the amplitude and the phase of the skin friction and the rate of heat transfer are presented in this work. As in the case of mean steady flow, the influence of the Grashof numberG and Eckert numberE on the unsteady flow field is discussed for air (P=0.71) and water (P=7) and for the cases of externally heating and cooling the porous limiting surface by free convection currents.     

Effects of mass transfer on the free convective flow in the Stokes' problem for an infinite vertical limiting surface

An exact analysis of the mass transfer effects on the free convection flow of an incompressible viscous fluid past an impulsively started infinite vertical (wall) limiting surface (Stokes's or Rayleigh's problem) has been carried out. Expressions for the velocity, temperature, species concentration and skin friction are obtained by using the Laplace transform technique. The velocity field and the skin friction are shown graphically for air (P=0.71) and mercury (P=0.025). The effects ofG (Grashof number),G _c (the modified Grashof number) andS _c (Schmidt number) are considered qualitatively during the course of discussion.     

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.     

Stokes problem for infinite vertical plate with constant heat flux

An exact solution for the Stokes problem for an infinite vertical plate has been derived on taking into account the constant heat flux at the plate. It has been observed that the velocity of the fluid increases with increasingt (time) orG (the Grashof number).     

Effects of free convection on the hydromagnetic accelerated flow past a vertical porous limiting surface

The effects of free convection on the accelerated flow of a viscous, incompressible and electrically conducting fluid (e.g. of a stellar atmosphere) past a vertical, infinite, porous limiting surface (e.g. of a star) in the presence of a transverse magnetic field, is considered. The magnetic Reynolds number of the flow is taken to be small enough, so that the induced magnetic field is negligible. Expressions for velocity and skin-friction are obtained by using Laplace transform, when the Prandtl number is equal to one (P=1). Graphs showing variations of velocity and skin-friction, for different values ofG (Grashof number) andM (magnetic parameter) are plotted, and the results of them are discussed.     

Cosmological models with the variable gravitational and cosmological constants

Cosmology with the gravitational and cosmological constants generalized as coupling scalars in Einsteins theory is considered. A general method of solving the field equations is given. Exact solution for Zeldovich fluid satisfying G=G ₀(R/R ₀) ⁿ is given.     

The relationship betweenG andh in a closed Universe

In a closed expanding-contracting Universe, matter will be subject to an inward acceleration large enough to prevent perpetual expansion. A closed Universe must also perform a simple harmonic motion, which might consist either of one single cycle or of an infinite series of oscillations about a central point. It is the purpose of this study to find the rate ofa ₀, the cosmic acceleration, from which the gravitational constantG can be determined. It will be shown from Ampère's equation and Planck's radiation law that it is possible to derivea ₀=7.623×10^–12 ms^–2, a value which also conforms with the uncertainty principle. The relationship betweena ₀ and electromagnetic radiation is based on the concept that charges (such as electrons) must emit radiation while accelerating. The rate ofa ₀ yields a universal gravitational constant ofG=6.645×10^–11 N m² kg^–2.     

Dust and atomic hydrogen nearρ Ophiuchi

We discuss the distribution of dust and atomic hydrogen in and around a small dark cloud near Ophiuchi. Although the obscuration reaches values as high as 8 magnitudes, the values ofN _H derived inside the cloud do not differ markedly from those found at nearby, less obscured points. At low values of the obscuration, dust and hydrogen isophotes show satisfactory agreement, i.e.,N _H increases withN _G. However, we find thatN _H starts decreasing for sufficiently large values ofN _G. In the entire range of optical extinctions investigated our observations are satisfied by an expression of the typeN _H=AN _G exp (-BN _G). Interpretation of this relationship suggests that an appreciable part of the hydrogen has been converted to molecular form inside the cloud. A tentative method for calculating the time elapsed since the conversion process began is proposed.Contribution No. 2 from the Argentine-Carnegie Radio Astronomy Station of the Instituto argentino de Radioastronomía and the Department of Terrestrial Magnetism of the Carnegie Institution of Washington.     

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.     

Free convection effects on the oscillatory flow in the Stokes's problem past an infinite porous vertical limiting surface with constant suction — I

An analysis of Rayleigh's problem (also Stokes's problem) for the flow of a viscous fluid (e.g. of a stellar atmosphere) past an impulsively started infinite, vertical porous limiting surface (e.g. of a star) with constant suction, when the free stream velocity oscillates in time about a constant mean, has been carried out. On solving the coupled non-linear equations in approximate way, expressions for the mean velocity, the mean temperature, the mean skin-friction and the mean rate of heat transfer, expressed in terms of Nusselt number, are obtained. The effects of Grashof numberG, Eckert numberE and Prandtl numberP, on these quantities, is discussed for the cases of an externally heating and cooling of the limiting surface, by the free convection currents, and the variations of them are shown graphically.     

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 .     

Phantom phase power-law solution in f(G) gravity

Power-law solutions for f(G) gravity coupled with perfect fluid have been studied for spatially flat universe. It is shown that despite the matter dominated and accelerating power-law solutions, the power-law solution exists for an special form of f(G) when this universe enters a Phantom phase.     

The shock-wave structure for arbitrary Prandtl numbers and high mach numbers

By use of a modified law of viscosity of the form =T ⁿ, wheren is a given function ofM, an analytical solution is obtained to the problem of strong shock waves. These analytical results agree very well with results obtained by using Boltzmann equation to the same problem.     

Exact statistical mechanics of a one-dimensional self-gravitating system

The statistical mechanics of an isolated self-gravitating system consisting ofN uniform mass sheets is considered using both canonical and microcanonical ensembles. The one-particle distribution function is found in closed form. The limit for large numbers of sheets with fixed total mass and energy is taken and is shown to yield the isothermal solution of the Vlasov equation. The order of magnitude of the approach to Vlasov theory is found to be 0(1/N). Numerical results for spatial density and velocity distributions are given.     

Bianchi II with time varying constants. Self-similar approach

We study a perfect fluid Bianchi II models with time varying constants under the self-similarity approach. In the first of the studied model, we consider that only vary G and Λ. The obtained solution is more general that the obtained one for the classical solution since it is valid for an equation of state ω∈(−1,∞) while in the classical solution ω∈(−1/3,1). Taking into account the current observations, we conclude that G must be a growing time function while Λ is a positive decreasing function. In the second of the studied models we consider a variable speed of light (VSL). We obtain a similar solution as in the first model arriving to the conclusions that c must be a growing time function if Λ is a positive decreasing function.     

Effects of the external temperature-dependent heat sources on the unsteady free convective and mass-transfer hydromagnetic flow in the stokes problem

There have been considered the effects of external temperature-dependent heat sources and mass transfer on free convection flow of an electrically conducting viscous fluid past an impulsively starting infinite vertical limited surface in presence of a transverse magnetic field as considered. Solutions for the velocity and skin-friction, in closed form are obtained by using the Laplace transform technique and the results obtained for various values of the parametersS _c (Schmidt number),M (Hartmann number), andS (Strength a Source or Sink) are given in graphical form. The paper is concluded with a discussion on the obtained results.     

Evening and morning twilight airglow emissions of 5577 Å and 5893 Å lines at Calcutta and Allahabad and their correlation with flare index

Evening and morning twilight enhancements of 5577 Å and 5893 Å lines were observed by Dunn-Manring type photometer at Calcutta during the period 1983–1985 and that of 5577 Å have been collected from Allahabad observatory. The following paper presents the correlation between the enhanced intensity of airglow lines (A _G ) and solar flare index (I _f ) which is calculated considering all the flares which occurred 24 hr before the times of occurrence of enhancements. It is observed that the intensity of airglow lines varies with the flare index in an oscillatory manner upto a certain limiting value ofI _f . Afterwards intensity of both lines increases with the increase ofI _f . The nature of variation is the same for both sunspot maximum and minimum periods. A possible explanation of such type of variation has also been invoked.