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The problem of unsteady viscous incompressible fluid flow near a critical point is considered. Self-similar solutions describing plane and axisymmetric flows are constructed.

This paper presents a numerical study of the partially invariant solutions of the Navier-Stokes equations for the plane case which describes unsteady flow in a layer bounded by a straight solid wall and a free boundary parallel to it. It is found that for different values of the initial flow velocity, there may be the establishment a steady state with a decrease or an increase in the initial layer thickness can be established or the layer thickness can be increased infinitely due to liquid inflow from infinity.

A nonequilibrium phase transition of a generalized Burger-Fisher equation describing biological pattern formation with a periodic boundary condition is examined. In the presence of a weak external force, some approximate bifurcation solutions near a critical point and new spatially periodic patterns are obtained by using the perturbation method in an infinite-dimensional space. The result shows that the external force delays the bifurcation.

Two-dimensional unsteady exhaustion of a one-velocity gas-particle mixture into vacuum is analyzed in extreme equilibrium cases of heat transfer. Domains of existence of a one-dimensional Riemann wave and side expansion wave and the boundary of the expansion region are obtained. In the case of temperature equilibrium, the reverse flow is found to occupy a large region extending beyond the boundaries defined by the angles of expansion of an ideal gas and a gas-particle mixture with thermally insulated phases. Exhaustion of a nonequilibrium two-phase medium in terms of velocities and temperatures into vacuum is numerically simulated. It is demonstrated that a barrel structure with wavy expansion of the gas and combined discontinuities in the expanding gas-particle mixture is formed.

Results of simulations of the flow structure in a vertical monodisperse gas-liquid flow in a tube on the basis of the Euler approach with allowance for the effect of bubbles on the averaged characteristics and turbulence of the carrier flow are reported. The carrier phase turbulence is calculated by using the transport model for the Reynolds stress tensor components. A comparison of the simulation results with available experimental data shows that the proposed apprach provides an adequate description of turbulent bubble flows in wide ranges of the local gas content and gas inclusion sizes.

The problem of the stability of the sandy bottom surface in a rectangular pressure conduit with respect to spatially one-dimensional perturbations. The problem of bed stability is solved using an analytical formula of sediment discharge which takes into account the effect of bottom pressure on sediment movement. An analytical relationship of the bottom wavelength to the hydrodynamic flow parameters and the diameter of bottom particles is obtained and compared with experimental data.

An analysis of a three-dimensional viscoelastic fluid flow over an exponentially stretching surface is carried out in the presence of heat transfer. Constitutive equations of a second-grade fluid are employed. The governing boundary layer equations are reduced by appropriate transformations to ordinary differential equations. Series solutions of these equations are found, and their convergence is discussed. The influence of the prominent parameters involved in the heat transfer process is analyzed. It is found that the effects of the Prandtl number, viscoelastic parameter, velocity ratio parameter, and temperature exponent on the Nusselt number are qualitatively similar.

A 3D numerical study of convective instabilities in a horizontal liquid layer (silicone oil with a Prandtl number Pr = 102) with an upper free surface is presented. The liquid layer is subjected to an inclined gradient of temperature. The influence of both gravity and thermocapillary forces on the formation of convective patterns is studied for different values of the liquid layer depth. Numerical results are found to be in good agreement with experimental data of other authors.

An axisymmetric magnetohydrodynamic (MHD) boundary layer flow and heat transfer of a fluid over a slender cylinder are investigated numerically. The effects of viscous dissipation, thermal radiation, and surface transverse curvature are taken into account in the simulations. For this purpose, the governing partial differential equations are transformed to ordinary differential equations by using appropriate similarity transformations. The resultant ordinary differential equations along with appropriate boundary conditions are solved by the fourth-order Runge-Kutta method combined with the shooting technique. The effects of various parameters on the velocity and temperature profiles, local skin friction coefficient, and Nusselt number are analyzed.

The combustion of ultrahigh molecular weight polyethylene (UHMWPE) in airflow perpendicular to the polyethylene surface (counterflow flame) was studied in detail. The burning rate of pressed samples of UHMWPE was measured. The structure of the UHMWPE-air counterflow flame was first determined by mass spectrometric sampling taking into account heavy products. The composition of the main pyrolysis products was investigated by mass spectrometry, and the composition of heavy hydrocarbons (C₇ – C₂₅) in products sampled from the flame at a distance of 0.8 mm from the UHMWPE surface was analyzed by gas-liquid chromatography mass-spectrometry. The temperature and concentration profiles of eight species (N₂, O₂, CO₂, CO, H₂O, C₃H₆, C₄H₆, and C₆H₆) and a hypothetical species with an average molecular weight of 258.7 g/mol, which simulates more than 50 C₇ – C₂₅ hydrocarbons were measured. The structure of the diffusion flame of the model mixture of decomposition products of UHMWPE in air counterflow was simulated using the OPPDIF code from the CHEMKIN II software package. The simulation results are in good agreement with experimental data on combustion of UHMWPE.