#### Volume 90, №5

**IDEAL HEAT EXCHANGE SYSTEM**

The requirements with which a heat exchange system should comply in order that at certain values of the total contact surface and heat load the entropy production in it should be minimal have been determined. It has been shown that this system can serve as a standard for real systems of irreversible heat exchange. We have found the conditions for physical realizability of a heat exchange system in which heat exchange occurs by a law linear with respect to the temperature difference between contacting fl ows. Analogous conditions are given without deriving for the case of heat exchange by the Fourier law.

**Author:**
A. M. Tsirlin

**Keywords:**
heat exchange system, contact surface, heat load, entropy production

**Page:**
1035

**REFLECTION OF ACOUSTIC WAVES FROM A POROUS MATERIAL AT OBLIQUE INCIDENCE**

The process of refl ection of acoustic waves through a porous medium in the case of their oblique incidence have been considered. It has been shown that as the angle of incidence increases, there is a decrease in the transmission coeffi cient.

**Author:**
I. K. Gimaltdinov, L. F. Sitdikovа, V. L. Dmitriev,b UDC 534-18 T. M. Levina, N. S. Khabeev, and Song Wanqing

**Keywords:**
acoustic wave, porous medium, refl ection and transmission coeffi cients

**Page:**
1043

**HARMONIC PRESSURE WAVES IN FRACTURES OCCURRING IN OIL AND GAS STRATA**

Consideration has been given to the problem on propagation of harmonic pressure waves in a fracture produced by hydraulic fracturing in a porous and permeable medium. A dispersion analysis has been made on the basis of the theoretical model in the form of a system of integro-differential equations; the infl uence of the reservoir characteristics of the stratum and the fracture (e.g., of the porosity and permeability of the stratum and the width of the fracture) on the features of propagation of harmonic waves in the fracture and beyond it is studied. It has been established that the fracture in a porous and low-permeability stratum is a wave channel of sorts for low-frequency pressure oscillations in wells.

**Author:**
V. Sh. Shagapov and Z. M. Nagaeva

**Keywords:**
: hydraulic fracturing of the stratum, fracture, pressure wave, integro-differential equation, dispersion analysis

**Page:**
1053

**GRAVITY SEDIMENTATION OF A SET OF SOLID SPHERICAL PARTICLES IN THE REGIME OF A PARTIALLY BLOWN CLOUD **

Results of experimental study of the process of gravity sedimentation of a set of solid spherical particles in the regime of a partially blown cloud in a wide range for Reynolds numbers have been presented. A new method to create a spherical cloud of particles has been proposed. Based on the experimental data on the change in the settling velocity of the particles as a function of time and of the covered distance, a criterial dependence has been obtained for the coeffi cient of resistance of the set of particles in the sedimentation regime under study.

**Author:**
V. A. Arkhipov and A. S. Usanina

**Keywords:**
gravity sedimentation, solid sphere, set of particles, blown-cloud regime

**Page:**
1061

**NUMERICAL INVESTIGATION OF THE PROCESS OF HEAT TRANSFER OF A SYSTEM OF TRANSPIRATION COOLING UNDER THE EFFECT OF SMALL ENERGY DISTURBANCES**

Based on a two-temperature inert porous medium, the interaction of high-enthalpy fl ow with a system of porous cooling in the presence of small periodic disturbances of a gas cooler is considered. The possibility of controlling the process of heat transfer in a heatproof material is investigated.

**Author:**
V. A. Ovchinnikov and A. S. Yakimov

**Keywords:**
heatproof material, pulsations of a gas cooler, heat transfer

**Page:**
1069

**HYDROGASDYNAMICS AND KINETICS OF SEPARATION OF DISPERSE MEDIA ON SIEVE CLASSIFIERS**

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

**Author:**
G. F. Akhmadiev, R. F. Gizzyatov, and I. T. Nazipov

**Keywords:**
mathematical model, hydrogasdynamics, kinetics of separation, Markovian processes, disperse material, probability of sieving, optimization

**Page:**
1077

**KINETICS OF CAPILLARY SOAKING IN AN INHOMOGENEOUS ELECTRIC FIELD**

The effect of an external inhomogeneous electric fi eld on the speed of capillary soaking of Newtonian fl uids into fi ne capillaries, representing a model of pore structures, is considered. The results of calculations are compared with experiment. The action of the fi eld is most evident at the fi nal stage of capillary soaking

**Author:**
I. N. Karpovich

**Keywords:**
cylindrical capillary, column of liquid, wetting angle, inhomogeneous electric fi eld, mass transfer, porous body

**Page:**
1087

**INFLUENCE OF THE STEFAN FLOW ON HEAT TRANSFER IN THE SYSTEM "GAS–SOLID PARTICLE" IN THERMOCHEMICAL CONVERSION OF A SOLID FUEL**

Recommendations are presented on calculating interphase heat transfer in gas-disperse systems of plants for thermochemical conversion of ground solid fuel. An analysis is made of the infl uence of the gas release of fuel particles on the heat transfer during their heating. It is shown that in the processes of thermal treatment of oil shales, the presence of gas release reduces substantially the intensity of interphase heat transfer compared to the heat transfer in the absence of thermochemical decomposition of the solid phase.

**Author:**
Yu. Ya. Pechenegov and A. N. Mrakin

**Keywords:**
solid fuel, pyrolysis, Stefan fl ow, heat transfer, temperature, gas, heat of formation, heat capacity

**Page:**
1093

**PROCESSING OF OIL SLUDGE WITH THE USE OF THE ELECTROHYDRAULIC EFFECT**

The designed and assembled installation for recycling complex compounds with the use of Yutkin’s electrohydraulic effect is described. The results of using this effect for processing oil sludge are presented. To analyze the products of processing, the methods of gas chromatography, as well as chromato-mass and infrared spectroscopy, are used. Liquid fractions are shown to include paraffi ns, isoparaffi ns, aromatic hydrocarbons, naphthenes, olefi ns, and oxygenates. The possibility of using this effect for processing and recycling oil sludge, heavy oil, and solidifi ed oil products is shown.

**Author:**
D. U. Bodykov, M. S. Abdikarimov, M. A. Seitzhanova, M. Nazhipkyzy, Z. A. Mansurov, A. O. Kabdoldina, and Zh. R. Ualiyev

**Keywords:**
oil sludge, electrohydraulic effect, cavitation, discharge, gasoline fraction, processing, hydrocarbon

**Page:**
1096

**GROWTH OF SILICON CARBIDE NANOLAYERS ON CONTACT OF POROUS CARBON WITH MOLTEN SILICON**

The mathematical model of the growth of a silicon carbide layer includes two diffusion equations for silicon and carbon atoms and an equation describing the motion of the chemical conversion front. Analytical estimates and results of calculations are presented. Parametric calculations for different values of silicon solubility in silicon carbide are carried out. It is shown that the effective density of carbon exerts its infl uence on the duration of the process of silicon impregnation and the composite morphology

**Author:**
P. S. Grinchuk, H. M. Abuhimd, S. P. Fisenko and Yu. A. Khodyko

**Keywords:**
silicon solubility, diffusion, chemical conversion front, quasi-stationarity

**Page:**
1102

**APPLICATION OF THE MONTE CARLO METHOD TO THE SOLUTION OF HEAT TRANSFER PROBLEM IN NANOFLUIDS**

The algorithm of modeling heat transfer in steady-state fl ow of a nanofl uid in a plane channel on the basis of the Monte Carlo method is described. With the use of this algorithm, the profi les of temperature and of the volume fraction of nanoparticles in the channel are obtained. The dependence of the relative Nusselt number of fl ow on the volume fraction of nanoparticles in it and on the thermal conductivity of the fl uid is shown.

**Author:**
A. V. Kravchuk and A. A. Avramenko

**Keywords:**
nanofl uid, heat transfer, Monte Carlo method

**Page:**
1107

**OBTAINING THREE-DIMENSIONAL NANOSIZE OBJECTS ON A "3D PRINTER + ELECTROSPINNING" MACHINE**

The possibility of obtaining three-dimensional nanosize polymeric fi bers has been shown. The obtained fi bers are oriented, which makes it possible to create three-dimensional objects. The proposed method allows alignining strongly directive nanofi bers from a polymethylmethacrylate polymer with a diameter of 50 to 500 nm. The use of different types of electrodes enables one to vary the nanofi ber size. Oriented polymeric nanofi bers were used to construct bioskeletons for biological cells.

**Author:**
Ch. B. Daulbaev, T. P. Dmitriev, F. R. Sultanov, Z. A. Mansurov, and E. T. Aliev

**Keywords:**
3D printer, electrospinning, nanosize fi bers, nanoobjects

**Page:**
1115

**ON THE STRUCTURAL SIMILARITY OF STABLE FORMS OF SPIRAL-VORTEX MOTION**

On the basis of the thermodynamic approach, inferences of the stability theory, and the method of dimensional analysis, we have obtained analytical dependences defi ning the relations between geometric sizes and rotation frequencies in three-dimensional spiral-vortex formations. To describe the vortex structure of the swirling fl ow of viscous and nonviscous fl uids, we propose to introduce into consideration the notion the order parameter. It has been shown that helicity as a characteristic of the measure of decrease in the symmetry of a moving medium connected with its order is not only an invariant of the vortex fl ow of nonviscous media, but can also be used as the order parameter for describing the geometrical similarity of spiral-vortex structures in real fl uids.

**Author:**
O. V. Mitrofanova

**Keywords:**
vortex structures, helicity, screw motion, stability, invariance

**Page:**
1119

**FEATURES OF CONVECTIVE TURBULENT FLOWS BEHIND THE MIXING SPACER GRIDS OF THE TVS-KVADRAT OF THE PWR-TYPE REACTOR**

This paper presents the results of experimental investigations of the infl uence of mixing spacer grids with different types of defl ectors on the coolant fl ow in the TVS-Kvadrat fuel assembly of the PWR-type reactor. Investigations were conducted on an aerodynamic stand with the use of a multichannel pneumometric probe. Analysis of the spatial distribution of projections of the absolute fl ow velocity permitted detailing the coolant fl ow pattern behind the mixing spacer grid with various types of defl ectors of mixing grids. The results obtained in the present paper are used to verify three-dimensional CFD programs, and in applied cell by cell codes they also serve as a database in calculations of thermotechnical reliability of the cores of PWR-type reactors with the TVS-Kvadrat.

**Author:**
S. M. Dmitriev, A. V. Varentsov, D. V. Doronkov, M. A. Legchanov, V. D. Sorokin, and A. E. Khrobostov

**Keywords:**
reactor core, fuel assembly, mixing spacer grid, coolant hydrodynamics

**Page:**
1131

**FLOW OF COMBUSTION PRODUCTS CONTAINING CONDENSED-PHASE PARTICLES OVER A RECESSED VECTORABLE JET NOZZLE**

The fl ow of combustion products containing condensed-phase particles over the recessed vectorable nozzle of a solid-propellant rocket motor was investigated with the use of the Reynolds-averaged Navier–Stokes equations, equations of the k–ε model of turbulence, and the Lagrange approach. The fi elds of fl ows of combustion products and the mechanical trajectories of condensed-phase particles in the charge channel, the prenozzle space, and the nozzle unit of this motor were calculated for different angles of swing of the nozzle. The formation of vortices in the gas fl ow in the neighborhood of the downstream cover of the nozzle and their infl uence on the movement of particles different in size were considered.

**Author:**
K. N. Volkov, S. V. Denisikhin, V. N. Emel′yanov, and I. V. Teterina

**Keywords:**
solid-propellant rocket motor, recessed vectorable nozzle, combustion products, gas flow.

**Page:**
1138

**ON THE THEORY OF FORMATION OF A GAS HYDRATE IN A HEAT-INSULATED SPACE COMPACTED WITH METHANE**

The formation of a gas hydrate in a closed adiabatic space saturated with snow and a gas in the initial state is considered. The formation of a gas hydrate in this gas–snow system in the case where in the initial state it hasa negative temperature was investigated. It was established that, depending on the initial snow saturation of the indicated system, a gas hydrate can be formed in it at both negative and positive temperatures as well as at the melting point of ice. It is shown that there exists any initial snow saturation of the gas–snow system at which the hydrate saturation of the heat-insulated space reaches a maximum value depending on its initial temperature and pressure. It was established that the intensity of hydrate formation in this space increases with increase in the pressure in it and decrease in its temperature. Charts of different possible fi nal states of the gas–snow system depending on its initial temperature, pressure, and snow saturation were constructed.

**Author:**
V. Sh. Shagapov, A. S. Chiglintseva, and S. V. Belova

**Keywords:**
gas hydrate, snow, saturation, ice particles, adiabatic space

**Page:**
1147

**FORMATION OF SCLEROTIC HYDRATE DEPOSITS IN A PIPE FOR EXTRACTION OF A GAS FROM A DOME SEPARATOR**

The theory of formation of hydrate deposits on the walls of a pipe for extraction of a gas from a dome separator designed for the accident-related collection of hydrocarbons on the ocean fl oor is considered. A mathematical model has been constructed for defi nition of a steady movement of a gas in such a pipe with gas-hydrate deposition under the conditions of changes in the velocity, temperature, pressure, and moisture content of the gas flow.

**Author:**
R. R. Urazov, I. A. Chiglinstev, and A. A. Nasyrov

**Keywords:**
sclerotic deposits, hydrate, pipe, dome separator

**Page:**
1162

**DIFFRACTION OF A SHOCK WAVE ON A WEDGE IN A DUSTY GAS**

Within the framework of one- and multivelocity dusty-gas models, the author has investigated, on a curvilinear grid, fl ow in refl ection of a shock wave from the wedge-shaped surface in an air–droplet mixture using the Godunov method with a linearized Riemannian solver

**Author:**
V. S. Surov

**Keywords:**
dusty gas, hyperbolic system of equations, Godunov method, mathematical modeling

**Page:**
1170

**HALL EFFECTS ON UNSTEADY MHD REACTIVE FLOW THROUGH A POROUS CHANNEL WITH CONVECTIVE HEATING AT THE ARRHENIUS REACTION RATE**

This paper deals with the study of an unsteady magnetohydrodynamic (MHD) fl ow and heat transfer of a reactive, viscous, incompressible, electrically conducting fl uid between two infi nitely long parallel porous plates where one of the plates is set into impulsive/uniformly accelerated motion in the presence of a uniform transverse magnetic fi eld at the Arrhenius reaction rate, with the Hall currents taken into account. The transient momentum equations are solved analytically with the use of the Laplace transform technique, and the velocity fi eld and shear stresses are obtained in a unifi ed closed form. The energy equation is tackled numerically using Matlab. The effects of the pertinent parameters on the fl uid velocity, temperature, shear stresses, and the heat transfer rate at the plates are investigated. The results reveal that the combined effects of magnetic fi eld, suction/injection, exothermic reaction, and variable thermal conductivity have a signifi cant impact on the hydromagnetic fl ow and heat transfer

**Author:**
S. Das, R. R. Patra, R. N. Jana, and O. D. Makindec

**Keywords:**
magnetohydrodynamics (MHD), Hall currents, reactive fl uid, heat transfer, porous channel

**Page:**
1178

**PLASMA PROCESSING OF MODEL RESIDENTIAL SOLID WASTE**

The authors have tested the technology of processing of model residential solid waste. They have developed and created a pilot plasma unit based on a plasma chamber incinerator. The waste processing technology has been tested and prepared for commercialization.

**Author:**
V. E. Messerle, A. L. Mossé, A. N. Nikonchuk,c, A. B. Ustimenko, and R. V. Baimuldind

**Keywords:**
plasma processing, plasma chamber incinerator, residential waste

**Page:**
1192

**CRATER FORMATION ON HIGH-VELOCITY COLLISION OF A METALLIC PROJECTILE WITH POLYMETHYLMETHACRYLATE TARGETS**

The possibility of using targets made of polymethylmethacrylate for determining the velocity of metallic projectiles is considered. Results of experimental investigations of the interaction of single spherical steel particles of diameter 2.5 mm with polymethylmethacrylate targets in the velocity range 0.94–2.4 km/s are presented. The acceleration of particles is achieved with the aid of a light-gas magnetoplasma launcher. A semiempirical dependence of the depth of penetration of steel projectiles into a polymethylmethacrylate target on the collision velocity has been obtained.

**Author:**
P. P. Khramtsov, V. A. Vasetskii, A. I. Makhnach, V. M. Grishchenko, M. Yu. Chernik, M. V. Doroshko, and I. A. Shikh

**Keywords:**
polymethylmethacrylate, high-velocity impact, light-gas magnetoplasma launcher, crater formation

**Page:**
1198

**DETERMINATION OF ION TEMPERATURE FROM THE VOLT–AMPERE CHARACTERISTICS OF ELECTROLYTES**

The author presents experimental volt–ampere characteristics measured in various media. From them, the density of ions and their temperature have been determined. An estimating formula has been derived for the thickness of a space-charge layer. It has been proposed in this work that the Fermi distribution function be used to calculate the thickness of a space-charge layer. A procedure has been presented to determine the ion temperature in electrolytes. The error of the described procedure amounts to 15–20%. To correct the ion temperature in the media, it is necessary to take account of the shielding of electrodes in the ion layer

**Author:**
S. A. Gutsev

**Keywords:**
volt–ampere characteristic, ion–ion plasma, ion temperature, concentration of ions, space-charge layer

**Page:**
1205

**ON THE APPLICABILITY OF THE OSTWALD–DE WAELE MODEL IN SOLVING APPLIED PROBLEMS**

By comparing the results of calculation of power-law fl uid fl ow in a slit with the Ellis fl uid fl ow, the inaccuracy of the power-law model is shown as much in describing the velocity profi le as in determining the non-Newtonian fl uid flow rate. Moreover, the error of the power-law model in the description of temperature distribution in the case of dissipative heating of non-Newtonian fl uid over a stabilized segment is shown. The boundary condition of fi rst kind was used.

**Author:**
V. M. Shapovalov

**Keywords:**
fl ow rate, shear stress, pressure, rheological model, temperature, velocity

**Page:**
1213

**DEGRADATION OF POLYMER SOLUTIONS IN A HYDRODYNAMIC FIELD WITH A LONGITUDINAL VELOCITY GRADIENT **

A fl ow diagram of degradation of polymer solutions under the action of a hydrodynamic fi eld with a longitudinal velocity gradient has been established. Intra- and intermolecular branchings (cross-linkings) that dominate over the rupture of macromolecular chains are initiated by the hydrodynamic fi eld.

**Author:**
A. V. Pogrebnyak, I. V. Perkun, and V. G. Pogrebnyak

**Keywords:**
polymer solution, hydrodynamic activity, velocity gradient, deformation action, degradation, degree of uncoiling, molecular chain, light-scattering indicatrix

**Page:**
1219

**INVESTIGATION OF CONTACT THERMAL RESISTANCE IN A FINITE CYLINDER WITH AN INTERNAL SOURCE BY THE FAST EXPANSION METHOD AND THE PROBLEM OF CONSISTENCY OF BOUNDARY CONDITIONS**

By the fast expansion method, the authors have obtained the approximate solution of the problem in analytical form, which holds true at all points of the cylinder up to the boundary. From an analysis of the solution, it follows that the broken thermal contact between annular regions gives rise to a weak thermal resistance. Beginning with four annular regions, the thermal resistance remains constant, in practice. This result was obtained for the fi rst time. When no more than three terms in a Fourier series are used, the maximum residual of the differential heatconduction equation is 10^{–2}.

**Author:**
A. D. Chernyshov, V. M. Popov, V. V. Goryainov, and O. V. Leshonkov

**Keywords:**
contact thermal resistance, fi nite cylinder, fast expansions, temperature fi eld, internal source, residual of the differential equation

**Page:**
1225

**HEAT EXCHANGE IN A LIQUID WITH ENERGY DISSIPATION**

A method of analytical solution of the problem on the heat exchange in a liquid moving in a tube with dissipation of its energy at the fi rst-kind boundary conditions, i.e., under the conditions of heat shock at the walls of the tube, was developed on the basis of the integral method of heat balance. The approach proposed involves the introduction of an additional desired function and additional boundary conditions, which allows one to reduce the solution of the partial differential equation to the integral ordinary differential equation for the additional desired function determined by only the longitudinal space variable. In this method there is no need to perform integration of the differential equation with respect to the transverse coordinate, involving the use of the heat-balance integral, which enables it to be used for solving the problem on the heat exchange in a medium with variable physical properties as well as nonlinear boundary-value problems.

**Author:**
A. V. Eremin, I. V. Kudinov, A. I. Dovgyallo, and V. A. Kudinov

**Keywords:**
heat exchange, laminar flow, dissipation of energy, integral method of heat balance, additional desired function, additional boundary conditions, coordinate function

**Page:**
1234

**THERMOPHYSICAL ANALYSIS OF THE EFFICIENCY OF REGULATING HEAT CONSUMPTION OF A BUILDING**

Analysis has been made of the methods of improving the energy consumption effi ciency of buildings by controlling the heat consumption by various devices (including individual heat points) without and with account for the air temperature control in a room (presence of feedback). Particular consideration was given to the low-cost method of energy saving by decreasing the air temperature in the absence of people, which at present is used inadequately, although its potential can reach 15–20%. The investigations carried out by us have shown that to effectively regulate the energy consumption with the aim of its saving, it is necessary to introduce feedback between the rooms of the building and the individual heat points. Analysis of the thermal state of an old offi ce building with a low energyeffi ciency has enabled us to develop methods for decreasing energy consumption by up to 4% for district heating and up to 10% for individual heating.

**Author:**
P. G. Krukovskii, O. Yu. Tadlya, A. I. Daineko and D. I. Sklyarenko

**Keywords:**
building, energy effi ciency, heating system, individual heat point

**Page:**
1243

**INFLUENCE OF JOULE DISSIPATION ON HEAT EXCHANGE AND MAGNETIC HYDRODYNAMICS OF LIQUID IN A SPHERICAL LAYER. PART I**

Results of numerical simulation of the convective heat exchange in the electrically conducting liquid fl owing between two concentric isothermal spheres are presented. The infl uence of Joule heating of this liquid and the thickness of the spherical liquid layer on the structure of the liquid fl ow, the temperature and magnetic-induction fi elds, and the distribution of Nusselt numbers in it was investigated. Equations for simulation of the heat exchange in the spherical liquid layer in the case where the gravitational acceleration is directed to its center were derived.

**Author:**
S. V. Solov'ev

**Keywords:**
convective heat exchange, Joule dissipation, magnetic hydrodynamics, spherical layer, equation for simulation of heat exchange

**Page:**
1251

**EXPERIMENTAL INVESTIGATION OF THE THERMOPHYSICAL CHARACTERISTICS OF A COATING BASED ON HOLLOW GLASS MICROSPHERES**

The thermal conductivity and effective emissivity of the industrially produced and marketable in Russia composite coating based on hollow glass microspheres have been determined.

**Author:**
O. L. Bondarev, V. V. Strazdovskii, and Yu. V. Chernov

**Keywords:**
temperature, thermal conductivity, emissivity, thermally insulating paint, microspheres

**Page:**
1266

**SIMULATION OF THE EFFECT OF BURNUP OF MATERIALS OF AN IONIZATION-CHAMBER RADIATOR BY THE MONTE CARLO METHOD**

Using the Monte Carlo method, the authors have modeled the burnup of fi ssionable material of the radiator of an ionization chamber in a neutron fl ux. A study has been made of the change in the sensitivity of the ionization chamber with time because of the burnup of fi ssionable material of the radiator for low- and high-intensity neutron fl uxes having different energies.

**Author:**
T. D. H. Le, A. A. Khrushchinskii, and S. A. Kuten'

**Keywords:**
fi ssion ionization chamber, burnup of fi ssionable material, sensitivity of the ionization chamber, Monte Carlo method

**Page:**
1274