Том 58, № 2 (2017)

This paper presents a mathematical model and analytical solutions of the problem of the growth of a hydrate layer during contact of gas and water for two limiting regimes of gas hydrate formation determined by mass transfer and heat transfer. Critical values are obtained for thermal parameters and parameters that determine the flow properties of the hydrate layer (diffusion coefficient and permeability), on which the hydrate formation regime depends.

The accuracies of measuring the velocity field using clinical and research magnetic resonance imagers are compared. The flow velocity of a fluid simulating blood in a carotid artery model connected to a programmable pump was measured. Using phase-contrast magnetic resonance tomography, the velocity distributions in the carotid artery model were obtained and compared with the analytical solution for viscous liquid flow in a cylindrical tube (Poiseuille flow). It is found that the accuracy of the velocity measurement does not depend on the field induction and spatial resolution of the imagers.

An attempt is made to study a steady two-dimensional flow of a viscous incompressible fluid incident at some angle onto a plate lubricated with a thin layer of a power-law fluid. Similar and nonsimilar solutions of the governing partial differential equations are obtained numerically by imposing the continuity of velocity and shear stress at the interface layer between the fluid and the lubricant. The Keller box method is applied to obtain the solutions. The limiting cases for full and no-slip conditions are compared.

Numerical simulation was performed to study convective structures in a thin silicone oil layer heated from below, whose free surface is exposed to air flow generating drift flow. The basic equations are transformation to a form suitable for spectral methods. The steady flow velocity profile obtained in a laboratory experiment is calculated. It is shown that increasing the Reynolds number leads to the transition from polygonal convective cells to longitudinal rolls (elongated along the flow). The dependence of the transition Reynolds number on the temperature on the lower boundary of the layer is obtained. The calculation results are compared with experimental data.

The stability of steady convective flow in an inclined plane fluid layer bounded by ideally heat conducting solid planes is studied in the presence of a homogeneous longitudinal temperature gradient under unstable stratification conditions where the layer is inclined so that the temperature is higher in the lower part than in the upper part. It is shown that the inclination leads to the transition from critical perturbations to long-wavelength helical perturbations. Flow stability maps are given for the entire range of Prandtl numbers and inclination angles corresponding to unstable stratification.

This paper presents a physicomathematical model for the effect of air flow containing ice crystals on a water film moving along the surface of a solid body. Numerical studies were carried out for the case of a cylinder in transverse flow. The influence of the effective viscosity of the suspension of crystals in the carrier water and the finite time of their melting on the hydro-thermodynamics of the solidifying film. In this case, the employed model is nonlocal.

The thermal performance of a nanofluid in a cooling chamber with variations of the nanoparticle diameter is numerically investigated. The chamber is filled with water and nanoparticles of alumina (Al₂O₃). Appropriate nanofluid models are used to approximate the nanofluid thermal conductivity and dynamic viscosity by incorporating the effects of the nanoparticle concentration, Brownian motion, temperature, nanoparticles diameter, and interfacial layer thickness. The horizontal boundaries of the square domain are assumed to be insulated, and the vertical boundaries are considered to be isothermal. The governing stream-vorticity equations are solved by using a secondorder central finite difference scheme coupled with the mass and energy conservation equations. The results of the present work are found to be in good agreement with the previously published data for special cases. This study is conducted for the Reynolds number being fixed at Re = 100 and different values of the nanoparticle volume fraction, Richardson number, nanofluid temperature, and nanoparticle diameter. The results show that the heat transfer rate and the Nusselt number are enhanced by increasing the nanoparticle volume fraction and decreasing the Richardson number. The Nusselt number also increases as the nanoparticle diameter decreases.

This paper describes the method for solving the problems of linear viscoelasticity for thin plates under the influence of bending moments and transverse forces. The small parameter method was used to reduce the original problem to a sequence of boundary-value problems solved via complex potentials of the bending theory of multiply connected anisotropic plates. The general representations of complex potentials and boundary conditions for their determination are obtained. The method for determining the stress state of the plate at any time with respect to complex approximation potentials is developed by replacing the powers of the small parameter by the Rabotnov operators. The problem of a plate with elliptical holes is solved. The numerical calculation results in the case of a plate with one or two holes are given. The variation of bending moments in time until stationary condition is reached is studied, and the influence of geometric characteristics of the plate on these variable is described.

The development of macroscopic inhomogeneities in the form of Chernov–Luders bands and serrated deformation bands (Portevin–Le Chatelier effect) in plastic metal flow is studied. For these two cases, regularities in the development of deformation inhomogeneity were established and the kinetics of motion of the fronts of Chernov–Luders bands and serrated deformation bands was studied. It is shown that the Chernov–Luders fronts and the serrated Portevin–Le Chatelier deformation can be considered as macroscopic autowave switching and excitation processes, respectively, in deformable media of different nature.

The problem of the stress-strain state of thin-walled tubes in axisymmetric steady-state deformation is solved using the membrane theory of shells and the model of an ideal rigid-plastic material satisfying the Mises yield condition and the associated flow law. The obtained solution is used together with the empirical relation between the strain state at an arbitrary point of the free surface and the surface roughness parameters at the same point to determine the influence of some tube reduction parameters on the surface roughness parameters in the product. The employed empirical relation is derived assuming that the free surface roughness parameters depend on two independent kinematic variables.

An analytical solution of a plane stress problem for a cantilever beam made of a functionally graded material subjected to uniform loading is constructed. The material is assumed to be isotropic with constant Poisson’s ratio and exponentially varying Young’s modulus through the beam thickness. Expressions for displacements, strains, and stresses are obtained.

The energy balance of laser cutting of low-carbon and stainless steel sheets with the minimum roughness of the cut surface is experimentally studied. Experimental data obtained in wide ranges of cutting parameters are generalized with the use of dimensionless parameters (Peclet number and absorbed laser energy). It is discovered for the first time that the minimum roughness is ensured at a certain value of energy per unit volume of the melt (approximately 26 J/mm³), regardless of the gas type (oxygen or nitrogen) and laser type (fiber laser with a wavelength of 1.07 μm or CO₂ laser with a wavelength of 10.6 μm).