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The structure and heat transfer in a turbulent separated flow in a suddenly expanding channel with injection (suction) through a porous wall are numerically simulated with the use of two-dimensional averaged Navier-Stokes equations, energy equations, and v²-f turbulence model. It is shown that enhancement of the intensity of the transverse mass flux on the wall reduces the separation region length in the case of suction and increases the separation region length in the case of injection up to boundary layer displacement. The maximum heat transfer coefficient as a function of permeability is accurately described by the asymptotic theory of a turbulent boundary layer.

The stability of steady convective flow in an inclined plane fluid layer bounded by ideally thermally conductive 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-wave helical perturbations. Stability maps of flow regimes are given for the entire range of Prandtl numbers and inclination angles corresponding to unstable stratification.

The radial angular temperature distribution in a porous medium with nonuniform permeability is investigated by numerical simulation of nonisothermal filtration of live oil taking into account the degassing heat, the Joule-Thomson effect, and the adiabatic effect. It is shown that nonuniform permeability in the wellbore zone of the porous layer leads to anomalous cooling due to intense degassing in the well-permeable zone.

This paper presents a physicomathematical model for the effect of a flow of air 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 by the hydro-thermodynamics of the solidifying film. In this case, the model used is nonlocal.

The method of characteristics was used within the framework of the kinetic approach to construct an analytical solution of the problem of heat transfer in a channel whose walls were formed by two coaxial cylinders. The main equation was the Williams kinetic equation, and the boundary condition on the channel walls was the diffusion reflection model. The vector field of the heat in the channel was determined, and the specific heat flow through the cross section of the channel was calculated. It was shown that the results obtained for a limiting case, in which the cylinder radii were significantly greater than the mean length of free path of gas molecules, were in good agreement with the results obtained for a plane channel with infinite parallel walls.

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 second-order 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 block element method for spatial integral equations with a difference kernel in boundary-value problems of continuum mechanics and mathematical physics. The basis of the proposed method is the Wiener-Hopf method, whose generalization for a spatial case is called integral factorization method. The block element method is applied to solve problems in regions with piecewise smooth boundaries containing corner points. The developed method was used to solve the contact problem for a V-shaped stamp occupying the first quadrant. This paper describes in detail the methods of obtaining various characteristics of the solution constructed by reversing the system of one-dimensional linear integral equations typical for dynamics and static contact problems for stamps in the form of a strip.

This paper describes the method of 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 with 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 changes of bending moments in time until stationary condition is reached and the influence of geometric characteristics of the plate on these variable are studied.

In this article, a smoothed particle hydrodynamics method is developed to simulate the dynamic process of the impact of two viscoelastic droplets onto a rigid plate. The Oldroyd-B fluid is considered as the rheological model to describe the viscoelastic characteristics. An artificial stress is added into the momentum equation to remove the tensile instability. The solution of the problem of two successive impacts of droplets are demonstrated to be in good agreement with the literature data. The problem of two droplets impacting simultaneously onto a rigid plate is investigated.

The impact fracture behavior of a high-density polyethylene (HDPE) material is investigated experimentally and theoretically. Single-edge notched bending (SENB) specimens are tested in experiments with three-point bending and in the Charpy impact tests. An energy model is proposed for evaluating the HDPE impact toughness, which provides a description of both brittle and ductile fracture.