Numerical Simulation of Non-Axisymmetric Homann's Stagnation-Point Flow of Nanofluid

This paper addresses numerical results for nanofluid near Homann's non-axisymmetric stagnation-point flow. The nanofluids model shows Brownian motion and thermophoresis effects. Recently, Weidman modify the Homann's stagnation-point problem to non-axisymmetric on rigid surface by superposing additional periodic terms to outer potential flow. The numerical results for couple differential system are obtained by means of shooting method. The solution is achieved for diverse values of involved parameter and ratio γ = b/a (b is shear and a is strain rate), which ranges from (–∞, ∞). The distributions for shear stresses, heat and mass transfer rate, temperature and nanoparticle concentration compared to their large- asymptotic behaviors also presented. For nanofluids, properties may vary considerably near solid boundary due to thermophoresis and Brownian motion of the fluid particles. These effects can result in decreasing viscosity within the boundary layer for heated fluids, thus leading to heat transfer enhancement.

Freedom as a Structural Component of Personality in Philosophical and Religious Doctrine of Czeslaw Stanislaw Bartnik

In this article, the author represents the aspect of philosophical and religious doctrine of Czeslaw Stanislaw Bartnik, a Polish personalist, which deals with the way the philosopher understands freedom as a structural component of a personality that enables a man to realize his inner and outer potential in both individual and social planes, in all dimensions of human existence: soul, body, intellect, will, actions, perception and creation of existence. Interrelation and interdependence between freedom and responsibility of a personality, as well as between freedom and will of a person, are the issues of principle for a Catholic thinker. As interpreted by Bartnik, responsibility is a measure of freedom, because of direct relationship between them: the more freedom a person possesses, the greater responsibility it takes to implement and use it. The relationship between freedom and will explains the dialectic character of structure of a personality. Freedom of a man is manifested through auto- determination, which means the ability of will to make free choices, and ultimately the will determines itself, being evaluated by practical mind. Freedom in personal existence concerns personality as a whole, but not the will or actions taken separately. That is why, Bartnik believes, it is better to speak about personal freedom and free existence of a personality. Choice -making proves freedom of a man, but when choosing an option, a person chooses himself, thus creating his own spiritual image. Existence consists of possibilities to choose from and means the core and backbone structure of a personality in the dynamic process of self-realization.

Non-axisymmetric Homann stagnation-point flows

A modification of Homann’s axisymmetric outer potential stagnation-point flow of strain rate $a$ is obtained by adding periodic radial and azimuthal velocities of the form $b\hspace{0.167em} r\sin 2\theta $ and $b\hspace{0.167em} r\cos 2\theta $, respectively, where $b$ is a shear rate. This leads to the discovery of a new family of asymmetric viscous stagnation-point flows depending on the shear-to-strain-rate ratio $\gamma = b/ a$ that exist over the range $\ensuremath{-} \infty \lt \gamma \lt \infty $. Numerical solutions for the wall shear stress parameters and the displacement thicknesses are given and compared with their large-$\gamma $ asymptotic behaviours. Sample similarity velocity profiles are also presented.

Effects of different mean velocity ratios on dynamics characteristics of a coaxial jet

The flow field of a coaxial jet configuration having inner and outer diameter ratio Di /Do = 0.33 is studied for four values of the velocity ratios and m = Ui /Uo = 5.17, 1.13, 0.77, and 0.54. The profiles of the mean axial velocity, of the axial turbulence intensities, and of the shear stress are described for the initial and fully zones. The obtained results show the inner potential core length of the coaxial jet strongly depends on the velocity ratio while the outer potential core for jets having velocity ratios greater than unity seems to be insensitive to the velocity ratio. As expected, the inner jet core length is seen to decrease with decreasing velocity ratio; jets with velocity less than unity develop faster than those with m greater than unity and the Reynolds stress show a zero-crossing in the near-region. .

Probing Non-Axisymmetry with Proper Motions

The potential of the Milky Way is almost certainly not axisymmetric: the centre is believed to be dominated by a bar, and beyond the solar radius some non-axisymmetric feature of the potential appears to warp the disk. There are grounds for believing that the outer potential is mildly elliptical. Sub mas yr–1 proper motions of objects that lie near the plane several kiloparsecs from the Sun would play a crucial role in refining our understanding of these non-axisymmetries.

The viscous interaction between sound waves and the trailing edge of a supersonic splitter plate

We consider the flow resulting from the interaction between the trailing edge of a supersonic splitter plate and sound waves incident on the trailing edge from upstream, as a model problem of relevance to understanding the unsteady flow in the vicinity of a supersonic jet nozzle. Morgan has previously shown that there is only one plausible solution to the outer potential-flow problem in this supersonic system, in which the vortex-sheet deflection close to the trailing edge varies linearly with the distance from the trailing edge, and that, in contrast to the subsonic version of the problem, it is not possible to construct an outer solution in which the vortex sheet leaves the plate smoothly (i.e. with zero gradient). In this paper our aim is to establish that this supersonic potential-theory solution is consistent with the equations governing the viscous flow close to the plate, and to provide a description of the nature of this inner flow, and we proceed by applying asymptotic analysis in the limit of large Reynolds number. For appropriate choices of the incident-wave amplitude and frequency, the canonical triple-deck structure at the trailing edge is realized, and the governing equations are then simplified by linearizing about the steady base flow in the lower deck; upstream of the trailing edge the unsteady flow is calculated analytically, whilst downstream a two-region parabolic scheme is employed. Our inner viscous flow is seen to match onto the outer potential-theory solution, and in particular we verify that the downstream evolution of the lower-deck flow as it emerges into the outer region corresponds exactly to the behaviour of the vortex sheet at the trailing edge in the outer flow. Once the consistency of the outer solution has been established, the dependence on the various flow parameters can be investigated, and we demonstrate in particular that significant unsteady shear-layer disturbances can be generated at the trailing edge over a wide range of values of the incidence angle, and that the amplitude of these disturbances decreases with increasing supersonic flow speed.

Scattering of sound by a heavily loaded finite elastic plate

A plane wave is incident onto a finite plate set in a rigid baffle, and the scattered field is examined in the limit when fluid-plate coupling effects are large. An asymptotic solution is obtained, matching an outer region with inner regions at either edge of the plate. Waves are found to be present on the flexible surface, and resonance is shown to occur for particular values of the plate half-length, a . Away from a resonance, the leading term in the expansion of the outer potential is the solution of the boundary value problem in the absence of the plate. As a resonance is approached, however, eigensolutions, with singularities at the plate edges, also become present at this order.