MHD free convective flow and mass transfer over a stretching sheet with chemical reaction

The effect of chemical reaction on free convective flow and mass transfer of a viscous, incompressible and electrically conducting fluid over a stretching surface is investigated in the presence of a constant transverse magnetic field. The non-linear boundary layer equations with the boundary conditions are transferred by a similarity transformation into a system of non-linear ordinary differential equations with the appropriate boundary conditions. Furthermore, the similarity equations are solved numerically by using a fourth order Runge-Kutta scheme with the shooting method. Numerical results of the skin friction coefficient, the local Nusselt number Nu, the local Sherwood number Sh, as will as the velocity, temperature and concentration profiles are presented for gases with a Prandtl number of 0.71 for various values of chemical reaction parameter, order of reaction, magnetic parameter and Schmidt number.     

Natural oscillations of a jet membrane under hydrostatic pressure

The natural oscillations of a submerged elastic jet membrane modeling an axisymmetric hydrodynamic direct-flow radiator are analyzed. The fundamental frequency is calculated as a function of the geometric and hydrodynamic characteristics of the jet. The principle possibility of adjusting the frequency by changing the elasticity of the fluid, which is a function of hydrostatic pressure, is demonstrated. Numerical and experimental data are compared.__________Translated from Prikladnaya Mekhanika, Vol. 40, No. 12, pp. 92–98, December 2004.     

Diffuser stall and rotating zones of separated boundary layer

Unsteady flows and rotating stall in vaneless diffusers were investigated by measuring both the wall fluctuating pressures and the unsteady velocity field using hot-wires and laser Doppler anemometers. Experiments were carried out with a fixed impeller and fixed diffuser inlet and outlet radii. However, the diffuser width was varied so that its effect on rotating stall could be examined. Results show that the variation of _r with b/r _i is in qualitative agreement with the prediction of Senoo et al. (1977). Therefore, the onset of stall is delayed as diffuser width is decreased. For diffusers with small width, stall emerges first with one stall cell and then develops into 2 and 4 stall cells as the mass flow rate is decreased. On the other hand, for the diffuser with the largest width tested, stall emerges with one stall cell and quickly develops into 3 stall cells. The ratio of the speed of rotation of the stall cell to impeller speed is independent of diffuser width, but decreases slightly as the number of stall cells increases. Finally, rotating stall is associated with reversed flow originating from the hub side rather than from the shroud side.     

Three-dimensional instability of an elliptic Kirchhoff vortex

The instability of a Kirchhoff vortex [1–3] with respect to three-dimensional perturbations is considered in the linear approximation. The method of successive approximations is applied in the form described in [4–6]. The eccentricity of the core is used as a small parameter. The analysis is restricted to the calculation of the first two approximations. It is shown that exponentially increasing perturbations of the same type as previously predicted and observed in rotating flows in vessels of elliptic cross section [4–9] appear even in the first approximation. As distinct from the case of plane perturbations [1-3], where there is a critical value of the core eccentricity separating the stable and unstable flow regimes, instability is predicted for arbitrarily small eccentricity.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 40–45, May–June, 1988.     

Non-linear flexural-flexural-torsional-extensional dynamics of beams—I. Formulation

The non-linear differential equations of motion, and boundary conditions, for Euler-Bernoulli beams able to experience flexure along two principal directions (and, thus, flexure in any direction in space), torsion and extension are formulated. The beam's material is assumed to be Hookean but its properties may vary along its span. The nonlinearities present in the differential equations include contributions from the curvature expression and from inertia terms. A set of differential equations with polynomial nonlinearities to cubic order, suitable for a perturbation analysis of the motion, is also developed and the validity of the inextensional approximation is assessed. The equations developed here reduce to those for an inextensional beam. In Part II of this paper, a specific example of application is analyzed and the results obtained are compared with those available in the literature where several non-linear terms have been neglected a priori.     

Dependence of slip coefficients on the nature of the interaction between gas molecules and a wall

A method of solution of the boundary-value problems of kinetic gas theory is developed, making it possible to use the boundary conditions in the most general form. The generalized Maxwell boundary condition that takes into account the dependence of the accommodation coefficient on the angle of incidence of gas molecules is considered as an example.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 149–152, September–October, 1986.     

Kinking of a crack emanating from the free surface of a beam under pure bending

A perturbation technique developed by Karihaloo et al. is employed to obtain the stress intensity factors at the tip of a kinking crack that emanates from the free surface of a beam under pure bending. Under the condition that the kink extends in the direction of vanishing K₁₁ the crack path is obtained as well as a path stability condition. From conditions on K₁ a material parameter r^* akin to that of Ramulu and Kobayashi's r_c is obtained. By analysis of the slope of the kinking crack a stability condition is obtained corroborating the stability condition from consideration of vanishing K₁₁. It is shown that for a beam in pure bending the nonsingular remote stress term T must be greater than some positive critical value for kinking to occur confirming the results of Sayir and Schindler.     

Influence of the initial conditions on axisymmetric jets in a parallel flow

An experimental investigation was made of the initial-section flow of axisymmetric helium, air, and freon-12 jets in a parallel air flow for two different velocity profiles at the nozzle exit near the boundary of the jet. In one case, the velocity profile was determined by boundary layers on the nozzle walls; in the other case, it was produced artificially by means of a honeycomb of tubes of variable length. Measurements were made of the profiles of the mean and the pulsation velocity and the temperature. The flow was also photographed. The investigations showed that, depending on the initial conditions, the intensity of mixing of the jets in the initial section at Reynolds numbers Re 10⁴ (calculated using the jet diameter) can change from the level determined by molecular diffusion to the level characteristic of developed turbulent flow. The flow structure in the annular mixing layer also depends strongly on the initial conditions. The observed ordered structures in the mixing layer are related to a section of development of perturbations near the nozzle. The ordered structures are strongly influenced by the effect on the jet of acoustic vibrations from an external source. When the initial velocity profile is produced by the honeycomb, the transition to developed turbulence may be due to the development of long-wavelength perturbations or to the development of small-scale turbulence generated by the flow over the end of the honeycomb.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 18–24, July–August, 1980.We thank V. M. levlev and K. I. Artamonov for assistance and for discussing the work.     

Integral inequalities in the dynamics of a gravitating gas

In the framework of Newtonian mechanics, a study is made of the spherically symmetric problem of the adiabatic motion of a gravitating perfect gas in the presence of a shock wave produced by inhomogeneous gravitational collapse or a point explosion. The method of Golubyatnikov [1, 2] is used to construct a system of integro—differential inequalities that determine, in particular, the law of motion of the shock wave if the initial state of the gas is known. The investigated examples include some self-similar and nearly self-similar solutions to the problem of the gravitational contraction of dust with the formation of a strong shock wave, possibly with the release of energy; the self-similar problem of a point explosion in a gas at rest; and also the problem of the equilibrium of a gas sphere for =4/3 and arbitrary distribution of the entropy. In these cases, the inequalities reduce to algebraic relations and can be solved numerically.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 169–173, September–October, 1980.