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A stratified laminar flow of several fluids in a channels with an arbitrarily shaped cross section is considered. It is assumed that the hydrostatic problem of finding free boundaries between different fluids is solved and domains of motion of individual fluids are known. Under the assumption that the medium motion arises under the action of an applied pressure gradient and volume gravity forces (or forces of inertia), the property of reciprocity between the applied forces F_j and the flows of different components Q_i, which is manifested as symmetry of the matrix of the flow rate coefficients L_ij(Q_i = L_ijF_j), is proved in the general form. General symmetric solutions of the problem for a plane channel and a circular tube are presented. Formulas for the coefficient of increasing of the fluid flow rate owing to the presence of a near-wall layer of the gas are derived. It is shown that the flow rate of water in a partly filled channel may exceed the flow rate in a completely filled channel by more than an order of magnitude.

Available experimental data on aerodynamics of the Darrieus rotor with straight blades are analyzed. Ranges of the main parameters of the rotor at which it has high energy characteristics and is able to start its motion independently and to rotate uniformly around its vertical axis are found. Based on these results, a method for calculating the geometric parameters of the rotor satisfying prescribed conditions of its exploitation is developed.

The present paper focuses on the problem of a mixed convection fluid flow and heat transfer of an Al₂O₃–water nanofluid with the thermal conductivity and effective viscosity dependent on temperature and nanoparticle concentration inside a lid-driven cavity having a hot rectangular obstacle. The governing equations are discretized by using the finite volume method, and the SIMPLE algorithm is employed to couple the velocity and pressure fields. By using the developed code, the effects of the Richardson number and the diameter and volume fraction of Al₂O₃ nanoparticles on the flow, thermal fields, and heat transfer inside the cavity are studied. The obtained results show that the average Nusselt number for the entire range of the solid volume fraction decreases with an increase in the Richardson number and the nanoparticle diameter. The results also clearly indicate that addition of Al₂O₃ nanoparticles produces a remarkable enhancement on heat transfer with respect to that of the pure fluid.

Results of a numerical study of the influence of a positive pressure gradient in an axisymmetric diffuser with sudden expansion of a circular tube on aerodynamics and turbulent heat transfer in regions of flow separation, reattachment, and relaxation are reported. The air flow prior to separation is assumed to be fully turbulent and to have a constant Reynolds number Re_D1 = 2.75×10⁴. The tube expansion degree is 1.78, and the apex half-angle of the diffuser is varied from 0 to 5 ^oC. It is found that an increase in the pressure gradient leads to a decrease in the heat transfer intensity in the separation region, and the maximum heat release point moves away from the flow separation point. The calculated results are compared with experimental data. It is shown that the behavior of the separated flow behind the step becomes significantly different as the streamwise pressure gradient changes.

This paper presents a solution of the boundary-value problem of the stress-strain state of a friction unit placed in the gap between rigid rotating cylinders. It is assumed that the two-layer incompressible material of these unit has elastic, viscous, and plastic properties and different values of the elastic moduli, stress limit, and viscosity. The conditions of the occurrence of viscoplastic flow, motion of the elastoplastic boundary in a deformable medium, and interaction of the latter with the contact boundary of the materials were determined. Limiting values of the characteristic rotation parameters at which the damping layer of the friction unit is not deformed plastically are given. The velocity and stress fields for acceleration and deceleration of the lubricant flow are calculated.

A new approach to the solution of high dimension spectral problems, which is based on the use of the moment method (kernel polynomial method), is applied to study many-particle effects in a series of alkali fluorides. The electronic structure, absorption spectra, the features of the electronic charge distribution caused by the formation of bound electron-hole states and changes in these distributions in a series of fluorides due to distinctions in their electronic structure are analyzed.

The structural features and the distribution of cations over crystallographic sites of copperchromite, copper ferrite, and mixed chromite-ferrites with the spinel structure obtained by thermal decomposition at 600°C and 900°C of mixed hydroxy compounds of copper, iron, and chromium with the composition Cu ²⁺/(Fe ³⁺+Cr ³⁺) = 1/2 and different Fe ³⁺/Cr ³⁺ ratios are studied using a set of physicochemical methods. It is shown that the spinel-structure phases formed exist in two modifications: cubic and tetragonal, depending on the Fe ³⁺/Cr ³ ratio. The crystallographic relationship between the cubic and tetragonally distorted phases of spinel is analyzed. The distribution of cations over crystallographic sites, the character and degree of tetragonal distortion of Cu-Fe-Cr spinel depend on the Fe ³⁺/Cr ³⁺ ratio: when Fe ³⁺/Cr ³⁺ > 1, the ratio of unit cell parameters c */ а * > 1; when Fe ³⁺/Cr ³⁺ < 1, the ratio c */ а * < 1; when Fe ³⁺/Cr ³⁺ = 1, the spinel is cubic irrespective of the temperature of thermal treatment. The oxygen coordination of copper ions in the spinel structure has a significant effect on the catalytic properties of the samples in the low-temperature water gas shift reaction.

The second overtone band shape of water and its temperature dependence are identical to those of melted and distilled water.

The crystal structure of a novel chained metal-organic coordination polymer [Cd(dmf)(ntca)] obtained by heating of cadmium nitrate and naphthalene-1,4,5,8-tetracarboxylic acid monoanhydride (H ₂ntca) in N,N'-dimethylformamide (DMF) is determined.

The X-ray crystallographic method is used to determine the crystal structure and characteristic features of the molecular structure of 3-(2-(2-nitrophenyl)hydrazono)-5-phenyl-3 H-furan-2-one produced by the reaction of azo coupling of 2-nitrophenyldiazonium salt with 5-phenyl-3 Н-furan-2-one.