The mathematical modeling of the non-isothermal flow of two-phase media in curved channels and pipes of complex geometric shapes is considered. Simplified equations of motion of a two-phase medium, taking into account the flow characteristics, written in an orthogonal coordinate system associated with the flow region, are solved by the method of equal flow surfaces. An algorithm for calculating the flow is constructed for the implementation of a computational experiment. This takes into account changes in the physical characteristics of the two-phase medium depending on temperature. Numerical calculations have been performed for channels of parabolic and conical shapes, taking into account changes in the effective viscosity of the medium from temperature, the initial section of the flow, and the influence of the centrifugal force field. Based on the conducted computational experiment, various flow regimes and the influence of various parameters on the hydrodynamic situation in the flow region are studied.

A mathematical model of the flow of a two-phase medium, whose state is defined by the nonlinear rheological equation, in a curvilinear channel of parabolic shape has been constructed. Numerical calculations of the flow of such a medium in this channel were performed with regard for the existence of its initial region and a centrifugal force in the channel. A computational experiment has been conducted, and, on its basis, different regimes of flow of a liquid in the indicated channel were investigated depending on the rheological properties of the liquid, governed by the Ostwald–de Waele law of state, and on the hydrodynamic situation in this channel. The numerical calculations have shown that, in the process of development of a liquid flow in the channel, in its initial region, the plane velocity profile of the flow is transformed into the parabolic one. In this case, the flow near the wall of the channel is decelerated, and the flow in the central region of the channel is, vice versa, accelerated. Because of this, in the initial region of the flow, its lines and the velocity fields on them have bends. The nonlinearity coefficient of a liquid substantially influences the shape of the velocity profile of its flow. In the case of rotation of the channel around its symmetry axis, the velocity profile of the liquid flow in it becomes asymmetrical.

Computer simulation of two-phase media flow in curvilinear channels and pipes of complex geometry is considered. The motion equations of a two-phase medium, simplified taking into account the features of the flow, which are written in an orthogonal coordinate system associated with the flow area, are solved by the method of surfaces of equal flow rates. An algorithm for calculating the flow for computer simulation has been constructed. Numerical calculations were carried out for channels of parabolic and conical shapes, taking into account the presence of the initial section of the flow and the influence of the centrifugal force field. Based on of computer simulation, various flow regimes and the influence of various parameters on the hydrodynamic situation in the flow area were studied.

The nonstationary heat transfer through the multilayer filler structures of a building in which the temperature of the air is unknown was investigated using the heat conduction equation with the asymmetric third-kind boundary conditions. For determining the change in the temperature inside a building, necessary for selecting the materials of its filler structures, the Cauchy problem was considered and solved by numerical methods. On the basis of computer simulation of the heat transfer through different multilayer filler structures of buildings, the regimes of heat transfer through such a structure were investigated for the cases where the temperature of the outdoor air changes by the linear and sinusoidal laws.

The process of non-stationary heat transfer through multilayer building envelopes is considered based on the heat conduction equation with asymmetric boundary conditions of the third kind and with an unknown indoor air temperature. Heat transfer coefficients on the inner and outer surfaces of the building envelope in the boundary conditions are calculated taking into account radiation and convection. In this case, natural convection is considered near the inner surface of the fence, caused by the difference in air and surface temperatures. At the outer surface of the fence, forced convection is considered, which is determined by the action of the wind. The influence of radiant heat transfer on the heat transfer coefficient on the inner and outer surfaces of the enclosing structure is determined based on the Stefan-Boltzmann law. To determine the temperature change inside the room, which is the basis for the choice of materials for the enclosing structures, the Cauchy problem is considered. To solve the problem, numerical methods were used; in the process of its numerical solution, an analysis of the stability of the constructed design scheme was carried out. The process of non-stationary heat transfer through multilayer structures depends on a large number of different factors, parameters and, therefore, to control the temperature regime inside the room, it must be considered as a cyber-physical system. Based on computer modeling, the modes of the process of unsteady heat transfer through various multilayer enclosing structures, which is a large and complex distributed system, are studied, i.e. cyber-physical system.

The process of non-stationary heat transfer through multi-layer enclosing structures of buildings is considered on the basis of the thermal conductivity equation with asymmetric boundary conditions of the third kind and with an unknown indoor air temperature. The Cauchy problem is considered to determine the change in temperature inside the room over time, which is the basis for the choice of materials for the enclosing structures. Numerical methods are used together with the method of establishment to solve the problem. The modes of heat transfer through various multilayer enclosing structures have been studied based on computer modeling.

The process of separation of granular materials into specific size fractions on sieve classifiers based on Poisson processes that relate to discontinuous Markov processes with discrete states is studied. The residence of particles of a certain size fraction on the surface of the sieves is defined as certain states, and a transition point from one state to another state (sieving) is defined as a random process. To determine the probabilities of states, a system of stochastic differential equations is constructed, the coefficients of which are calculated as dependent on the probability of sifting the particles into sieve cells. The solutions allow one to calculate the extraction rate and evaluate the separation efficiency. A computational experiment is conducted to study the main characteristics of the process.

A mathematical model of the process of separation of granular materials by specific weight in fluidized beds has been constructed on the basis of the conservation equations of mass and momentum of the heterogeneous media mechanics. Computational and physical experiments on studying the separation process have been carried out. The regime and design parameters of the apparatus that ensure the needed degree of granular material separation into fractions have been determined.

A mathematical model of film condensation is constructed which is obtained based on the equations for the conservation of mass, momentum, and energy for a heat-transfer fluid in the limited region of the condensate film and gas phase flowing down the surface of the wall of a heat exchanger in a two-dimensional setting. Equations for conserving the momentum of this model take into account the change in the physical properties of the heat-transfer fluid and condensate film depending on temperature. The boundary conditions of coupling are written for the regions on the inner wall of the flow range of the heat-transfer fluid and outer wall along which the condensate film flows, as well as at the film–gas interface. The boundary problem is solved by approximate and numerical methods, together with the condition for determining the unknown thickness of the film for different settings of the thermodynamic problem. Computational and physical experiments are conducted to study the main parameters and regularities of the process.

A mathematical model of the kinetics of thin-layer separation of granular materials on multiple-deck sieve classifiers was constructed based on the theory of Markovian processes. We identified the kinetic models using the oversize residues from sieves. The problem of optimization is formulated and solved in a multi-criteria formulation, where the criteria are selected device performance and the separation efficiency on its sieves.

МаТеМаТИЧеСКое МоДеЛИРоВаНИе ПРоЦеССоВКЛаССИФИКаЦИИ ЗеРНИСТЫХ МаТеРИаЛоВ На СИТаХ ахмадиев Ф.Г., Гиззятов Р

A mathematical model for calculating the thermohydrodynamic situation during film condensation based on the equations of conservation of mass, momentum and energy for the refrigerant in a limited area, the condensate film flowing and the gas phase in a two-dimensional formulation is constructed. The dependence of the viscosity of the working medium on the temperature is taken into account. The boundary conditions of conjugation are specified on the inner wall of the refrigerant flow region, the outer wall through which the condensate film flows, and also at the film-gas interface. The obtained boundary value problem is solved by approximate and numerical methods together with the condition for determining the unknown film thickness, which allows the calculation of all characteristics of the condensation process.

The mathematical model of the separation of granular materials on multiple-deck sieve classifiers has been constructed using the theory of Poisson processes and the model has been identified. The problem of the optimal implementation of the process in multicriterial setting has been formulated and solved; the engineering simulation of the classifier has been performed using this solution.

The hydrogasdynamics and kinetics of separation of disperse materials on a multistage classifier has been studied, and a kinetic model has been identified. The problem of optimum instrumentation of the classification process on the basis of constructed mathematical models in a multicriteria formulation has been set up and solved.

The hydrodynamic conditions in tubular filter cells operating under nonisothermal conditions are studied. The equations of mechanics of heterogeneous media are used to describe the separation process of two-phase suspensions, which are written and simplified in the cylindrical coordinate system taking into account characteristics of the flow. The challenge is solved semi-analytically. Using the methods of surfaces of equal consumptions and Slezkin, numerical calculations on the constructed mathematical model are presented for particular implementations of the separation process.

A method of calculating the kinetics of the separation of granular materials in a multi-tier classifier on the basis of the theory of random processes is considered and a kinetic model is identified. A problem of optimal hardware design of the classification process in a multi-criteria statement is formulated and solved. The performance of the apparatus and the efficiency of separation are selected as the optimization criteria.