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A mathematical model of the flow of a thin layer of heavy liquid under an elastic shell filled with gas is constructed. By means of mass exchange with the environment, the gas phase is active and supports a self-organized wave motion in the liquid layer. The conditions under which small perturbations are transformed into quasiperiodic wave packets of finite amplitude, which move in the same direction, are found. It is shown that the structure of the waves is similar to that of roll waves in open channels.

The processes of heat and mass transfer and phase transformations during motion of a set of water droplets through high-temperature gases have been studied numerically. The regimes and conditions of formation of zones of significant joint influence of the droplets on the integral characteristics of heat and mass transfer are determined. The values of the dimensionless parameters describing the dependence of the temperature of the gases in the wake of a small set droplets on their volume concentration and arrangement are calculated. The variations in these dimensionless parameters during motion of droplets through high-temperature gases are described.

The influence of the wake vortex arising behind a perforated tab on the mixing process in heat exchangers and chemical reactors is analyzed. The preliminary step of this study, i.e., investigation of the turbulent field generated by a single perforated tab, is presented here. For this aim, laser Doppler velocimetry measurements are conducted downstream from a perforated trapezoidal vortex generator placed in a wind tunnel. It is shown that two shear layers are generated by the tab. The first shear layer is located at the upper edge of the tab, and the other is ejected from the perforation edges. These shear layers are characterized by high turbulent kinetic energy levels, which are profitable for meso-mixing enhancement. Finally, a spectral study shows that the turbulent macro-scale is nearly the same for typical locations in the shear layers shed from the tab and perforation edges.

This article addresses the heat transfer in a peristaltic flow of a reactive combustible viscous fluid through a porous saturated medium. The flow here is induced because of travelling waves along the channel walls. It is assumed that exothermic chemical reactions take place within the channel under the Arrhenius kinetics and the convective heat exchange with the ambient medium at the surfaces of the channel walls follows Newton's law of cooling. The analysis is carried out in the presence of viscous dissipation and without consumption of the material. The governing equations are formulated by employing the long-wavelength approximation. Closed-form solutions for the stream function, axial velocity, and axial pressure gradient are obtained. It is found that the temperature decreases at high Biot numbers, and the Nusselt number increases with increasing reaction parameter. The Biot number and reaction parameter produce the opposite effects on the Nusselt number.

In this paper, non-similarity solutions for natural convection heat and mass transfer along a vertical plate with a uniform wall temperature and concentration in a doubly stratified porous medium saturated by a fluid are obtained. The Darcy--Forchheimer-based model is employed to describe the flow in the porous medium. The nonlinear governing equations and their associated boundary conditions are initially cast into dimensionless forms by using pseudo-similarity variables. The resulting system of nonlinear partial differential equations is then solved numerically by using the Keller-box method. The effects of the buoyancy parameter, Forchheimer number, and thermal and solutal stratification parameters on the dimensionless velocity, temperature, concentration, and heat and mass transfer coefficients are studied.

A mathematical model of the effect of a medium on a homogeneous rigid body whose outer surface includes a circumferential cone is considered. The complete system of equations of motion under quasistationarity conditions is given. In the dynamic part forming an independent third-order system, an independent second-order subsystem is distinguished. A new two-parameter family of phase portraits on the phase cylinder of quasivelocities is obtained.

This paper presents a solution of a sequence of coupled problems of thermoelastoplasticity which study the occurrence and development of flow in a material layer under pure shear conditions, and its subsequent deceleration by slowly removing the load. The homogeneity of the stress state of the layer is excluded due to the coupling of thermal and deformation processes in the presence of a temperature dependence of the yield point. An additional source of heat is taken to be its production by friction of the material layer on a rough plane. The conditions for the occurrence of viscoplastic flow in the deformable material layer and the laws of motion of the boundaries between the elastic and plastic regions in this layer are determined, and the flow velocities and large irreversible and reversible deformations are calculated. It is shown that reversible deformations cause stresses in the flow region and the moving elastically deformed core.

This paper presents a theoretically study of the boiling of superfluid helium on a cylindrical heater placed in a coaxial porous shell in microgravity. Steady-state transfer processes at the interface are studied using molecular-kinetic methods. The Boltzmann transport equation is solved by the moment method based on the four-moment approximation in the form of a two-sided Maxwellian. The obtained solution is used to calculate the heat flux density in film boiling on a cylindrical heating surface in the case where the film thickness is comparable to the diameter of the heater. The motion of the normal component of the superfluid liquid in pores is described by equations that take into account heat and mass transfer in superfluid helium. The relation between the vapor film thickness and the structural characteristics and geometrical dimensions of the porous shell is obtained. Analysis of the results of the calculations is given.

In this paper, the effects of viscous dissipation, nonuniform heat source/sink, magnetic field, and thermal radiation on the heat transfer characteristics of a thin liquid film flow over an unsteady stretching sheet are analyzed by the homotopy analysis method. The effects of various physical parameters on the heat transfer characteristics are found. The study shows that the thermal radiation parameter has a significant effect on the surface temperature. It is also found that nonuniform heat sinks are better suited for cooling purposes. Furthermore, the limiting cases are obtained and are found to be in good agreement with numerical results previously published by other authors.

The dynamic antiplane strain of an incompressible cylindrical body is studied in a nonlinear formulation in actual variables. A representation of the velocity and acceleration through the displacement is obtained. The problem of the body deformation with account for geometrical and physical nonlinearities is reduced to an initial boundary-value problem for the displacement. The displacement found is used to determine the pressure and stresses. For a body with a quadratic elastic potential, plane waves and self-similar motion are studied. The linear potential is used to investigate the deformation of a hollow elliptical cylinder for which analytical expressions for displacement and stresses are found and the external load is determined. It is shown that, due to the degeneration of the inner cavity of the body to a plane section, the load on the section remains limited.