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The overdetermined system of partial differential equations describing the two-dimensional isothermal motion of a polytropic gas is studied. The system is reduced to passive form and fully integrated. The resulting solutions are treated as ideal incompressible fluid flow bounded by a free surface or a moving solid wall.

The heat and mass transfer effects on the flow of a conducting third-grade fluid over an oscillating vertical porous plate with chemical reactions are considered. Highly nonlinear governing equations of the third-grade fluid are solved analytically by using a multi-parameter perturbation technique and compared with the numerical results obtained by the parallel shooting method. The fluid flow velocity, temperature, and concentration are analyzed as functions of the Hartmann number, suction parameter, Prandtl and Schmidt numbers, and chemical reaction parameter.

The problem of constructing asymptotics of the far fields of internal gravitational waves generated by an oscillating localized source of perturbations moving in a stratified flow of finite depth. The velocity of the perturbation source does not exceed the maximum group velocity of an individual wave mode. The wave pattern consists of waves of two types: annular and wedge-shaped. Solutions are obtained that describe the asymptotic behavior of ring waves, which are expressed in terms of the Hankel function. The asymptotics of wedge-shaped waves are expressed in terms of the Airy function and its derivative.

A complex mathematical model for hysteresis of relative permeabilities based on percolation theory is developed. The model take into account the change in the surface properties of the pore space and the rheology of percolating fluids during the transition from drainage to impregnation, which gives rise to hysteresis. It is shown that accounting for the change in the rheology of the percolation fluids, along with accounting for the hydrophobization of the surface of the pore space, provides a better agreement between the calculated and experimental curves of relative permeabilities.

Stability of plane and cylindrical Poiseuille flows of nanofluids to comparatively small perturbations is studied. Ethylene glycol-based nanofluids with silicon dioxide particles are considered. The volume fraction of nanoparticles is varied from 0 to 10%, and the particle size is varied from 10 to 210 nm. Neutral stability curves are constructed, and the most unstable modes of disturbances are found. It is demonstrated that nanofluids are less stable than base fluids; the presence of particles leads to additional destabilization of the flow. The greater the volume fraction of nanoparticles and the smaller the particle size, the greater the degree of this additional destabilization. In this case, the critical Reynolds number significantly decreases, and the spectrum of unstable disturbances becomes different; in particular, even for the volume fraction of particles equal to 5%, the wave length of the most unstable disturbances of the nanofluid with particles approximately 20 nm in size decreases almost by a factor of 4.

Results of experimental investigations and numerical simulations of supersonic gas flows in radial nozzles with different nozzle widths are presented. It is demonstrated that different types of the flow are formed in the nozzle with a fixed nozzle radius and different nozzle widths: supersonic flows with oblique shock waves inducing boundary layer separation are formed in wide nozzles, and flows with a normal pseudoshock separating the supersonic and subsonic flow domains are formed in narrow nozzles (micronozzles). The pseudoshock structure is studied, and the total pressure loss in the case of the gas flow in a micronozzle is determined.

The present analysis deals with a two-dimensional MHD flow of the Carreau fluid over a stretching sheet with a variable thickness. The governing partial differential equations are converted into an ordinary differential equation by using the similarity approach. The solution of the differential equation is calculated by using the Keller box method. The solution is studied for different values of the Hartmann number, Weissenberg number, wall thickness parameter, and power-law index. The skin friction coefficient is calculated. The present results are compared with available relevant data.

This paper describes free acoustic oscillations of gas in a chamber with a jet flowing through its nozzle in the case of nonstationary intensity component of vortex sheet flowing down from the edge of the nozzle. There is established feedback between acoustic oscillations and oscillations induced by a corresponding vortex sheet component. It is shown that, in the presence of given feedback, there could be instability of acoustic oscillations, which would result in acoustic self-vibrations in the chamber. The boundaries of the domain in which instability is formed are determined by developing a mathematical model of stable acoustic oscillations in the chamber with account for the influence of the vortex sheet.

The transverse injection of a pulsed jet into supersonic flow for thrust vectoring in solid rocket motors is investigated. The gas flow through the injection nozzle is regulated by a piston which performs reciprocating motion. Reynolds-averaged Navier-Stokes equations and the (k-e)-turbulence model equations are discretized using the finite volume method and moving grids. The pressure distributions on the plate surface obtained using various approaches to the description of the flow field and difference schemes are compared. The solution obtained for the case of injection of a pulsed jet is compared with the solution for the case where a valve prevents gas flow through the injection nozzle. The dependence of the control force produced by injection of gas on time is investigated.

A nanometric HMX-based polymer-bonded explosive (PBX) is prepared by using the solution-water slurry technique. The resultant PBX is composed of 94% of HMX, 5% of fluororubber Viton, and 1% of wax. The properties of the nanometric HMX-based PBX, such as sensitivity and compressive performance, are comprehensively researched. The results shown significant improvement for the nanometric HMX-based PBX as compared to the micron-sized HMX-based PBX. The friction sensitivity, impact sensitivity, and shock sensitivity of the nanometric HMX-based PBX are obviously lower by 30, 48, and 24%, respectively. Moreover, the compressive strength and strain of the nanometric HMX-based PBX are significantly higher by 273 and 33%, respectively. Thus, both the safety and mechanical resistibility of the PBX will significantly benefit from using nanometric HMX