#### Volume 88, №3

**PRIGOGINE THEOREM FOR THE PROCESS OF ROLLING OF A VISCOPLASTIC STRIP**

Consideration is given to slow plane isothermal flow of a viscoplastic strip in rolling. Tangential stresses are assigned at the boundary of contact of the strip with the roll and at the boundaries between the flow region and the back and head rigid ends of the strip. A defi nition is provided for possible perturbations of the velocities of travel for special stationary flows of a viscoplastic strip in rolling. Minimum entropy production is proved for special stationary flows
with respect to possible perturbations of velocities of travel (Prigogine theorem).

**Author:**
V. D. Solovei

**Keywords:**
slow flow of a viscoplastic strip in rolling, stationary fl ows, possible perturbations of velocities of travel, entropy-production minimum

**Page:**
561

**AEROSOL CLOUD PROPAGATION IN A CLOSED SPACE**

This paper presents the results of an experimental-theoretical investigation of the evolution of a cloud of aerosol particles in a closed space obtained by the shock-wave method. It has been shown that the prevailing propagation
mechanism of aerosol particles of diameter 1–7.5 μm is convective diffusion. For the considered class of aerosols, the effective value of the convective diffusion coeffi cient in a closed space has been determined.

**Author:**
O. B. Kudryashova, N. V. Korovina, A. A. Pavlenko,a,c V. A. Arkhipov, V. D. Gol′din, and E. V. Muravlev

**Keywords:**
aerosol particles, shock-wave method, aerosol cloud propagation, closed space, diffusion, gravity sedimentation, particle concentration, mathematical modeling, experimental investigation

**Page:**
568

**BINARY SCHEMES OF VAPOR BUBBLE GROWTH**

A problem on spherically symmetric growth of a vapor bubble in an infi nite volume of a uniformly superheated liquid
is considered. A description of the limiting schemes of bubble growth is presented. A binary inertial-thermal bubble
growth scheme characterized by such specifi c features as the "three quarters" growth law and the effect of "pressure
blocking" in a vapor phase is considered.

**Author:**
Yu. B. Zudin

**Keywords:**
spherically symmetric growth, limiting schemes of growth, binary scheme of growth, "three quarters" growth law, "pressure blocking" effect

**Page:**
575

**NUMERICAL DESCRIPTION OF ACOUSTIC VIBRATIONS OF A VAPOR–GAS–DROPLET MIXTURE IN A CLOSED CHANNEL BASED ON A ONE-VELOCITY, ONE-TEMPERATURE MODEL**

The paper describes a mathematical model and the results of numerical calculations of resonance acoustic vibrations
of a vapor–gas–droplet mixture in a closed volume under the action of periodic acoustic waves generated by a
harmonically vibrating piston. The numerical method of solving the equations of the model is based on MacCormack′s
scheme. The model of equilibrium phase transitions used in the numerical scheme has allowed a chart of regimes of
the vapor–gas–droplet mixture vibrations to be constructed depending on the initial vapor content. In accordance
with the piston vibration amplitude, the limit of the critical vapor content below which vapor condensation is
impossible has been found.

**Author:**
R. I. Bayanov and A. L. Tukmakov

**Keywords:**
resonance acoustic vibrations, MacCormack′s numerical scheme, phase transitions, vapor–gas–droplet mixture

**Page:**
587

**PREDICTION OF THERMOPHYSICAL AND THERMOMECHANICAL CHARACTERISTICS OF POROUS CARBON–CERAMIC COMPOSITE MATERIALS OF THE HEAT SHIELD OF AEROSPACE CRAFT**

A procedure for predicting thermophysical and thermomechanical characteristics of porous carbon–ceramic
composite materials of the heat shield of aerospace craft as functions of the type of reinforcement, porosity
of the structure, and the characteristics of the material′s components has been developed. Results of mathematical
modeling of the temperature and stressed-strained states of representative volume elements for determining the
characteristics of a carbon–ceramic composite material with account taken of its anisotropy have been given.

**Author:**
S. V. Reznik, P. V. Prosuntsov, and K. V. Mikhailovskii

**Keywords:**
heat shield, carbon–ceramic composite material, microstructure, thermal conductivity, linear thermal expansion coefficient

**Page:**
594

**ON THE LIMITING CASES RELATED TO FLOW PAST A ZHUKOVSKII SHEET PILE**

Within the framework of the Darcy′s theory of plane steady fi ltration of an incompressible liquid, two limiting schemes
are considered that model filtration flows under a Zhukovskii sheet pile through a large mass of ground underlain by
an impermeable base or by a permeable water-bearing pressure horizon. For purposes of analyzing these schemes,
mixed boundary-layer problems of the theory of analytical functions are formulated that are solved with the aid of the
Polubarinova-Kochina method. Based on these models, algorithms have been developed for calculating a saturation
zone in those cases where, while considering the motion of water, one has to take into account the exposure of flow
pattern to the combined effect of such important factors as backwater from the side of the impermeable base or of
the underlying well permeable water-bearing bed, evaporation or infi ltration on the free groundwater surface, as
well as the ground capillarity.

**Author:**
É. N. Bereslavskii

**Keywords:**
filtration, Zhukovskii sheet pile, groundwater, pressure underground horizon, water confi ning layer, evaporation, infi ltration, free surface, ground capillarity, complex fl ow velocity, conformal mappings, PolubarinovaKochina method

**Page:**
602

**THERMAL ACID TREATMENT OF THE NEAR-WELL ZONE OF THE OIL POOL**

The problem of thermal acid treatment of the near-well zone of the oil pool has been investigated. We present a
mathematical model describing the thermohydrodynamic processes proceeding in the above zone upon its thermal
acid treatment with account for the chemical kinetics of these processes. The influence of the temperature on the
above processes has been investigated.

**Author:**
V. F. Burnashev, É. K. Irmatov, and B. Kh. Khuzhaerov

**Keywords:**
acid, insoluble mineral particles, near-well zone, porosity, permeability, thermal acid treatment, filtration, chemical kinetics

**Page:**
610

**DIRECTIONAL DIAGRAMS OF THE PARTICLE DRIFT IN A STANDING WAVE WITH ACCOUNT OF THE BASSET FORCE**

A study is made of the threshold parametric values at which the direction of the particle drift in a standing wave is
reversed, with account taken of the Basset force at different Reynolds and Strouhal numbers. The dependences of
the threshold value squared of the entrainment coeffi cient on the relative density of the particle with account and
without account of the Basset force are found. The infl uence of the Basset force on the threshold value of the density
parameter is investigated. It is shown that account taken of the Basset force exerts a particularly strong infl uence on
the threshold curves for nondense particles. The threshold values of density of the particle and of the coeffi cient of
its entrainment decrease as the Strouhal number increases.

**Author:**
D. A. Gubaidullin, P. P. Osipov, and A. N. Zakirov

**Keywords:**
particle drift, forces in acoustic wave fields, Basset force

**Page:**
621

**A CONTRIBUTION TO THE THEORY OF SPREADING OF LIQUID-CONTAINING EJECTIONS OVER A HORIZONTAL SURFACE**

Based on the shallow water theory, the problem on radial spreading of incompressible liquid over a horizontal
surface with account for the presence of vegetation has been studied. Some exact as well as approximate analytical
solutions have been obtained that describe various cases, stages, and possible regimes of the process of spreading.
A comparison of the results obtained with experimental data is made

**Author:**
V. Sh. Shagapov and S. A. Gil′manov

**Keywords:**
shallow water, spreading, fl ora (vegetation), pool, self-similar solution, inertialess regime

**Page:**
630

**INTENSIFICATION OF THE EFFECT EXERTED BY BUBBLES ON A BODY IMMERSED IN A LIQUID DUE TO THE RADIAL BUBBLE OSCILLATIONS**

It is shown that radial oscillations of bubbles can signifi cantly intensify the effect exerted by them on a body immersed
in a liquid

**Author:**
N. S. Khabeev

**Keywords:**
bubble, oscillations, acoustic field, hydromassage

**Page:**
645

**GODUNOV METHOD FOR CALCULATING FLOWS OF A ONE-VELOCITY VISCOUS HEAT-CONDUCTING MEDIUM**

For a hyperbolic model of a one-velocity viscous heat-conducting mixture, a modified Godunov method with approximate Riemann solvers is developed. Using this method, we studied wave processes in frothing and bubble
media. It is shown that the flow picture is signifi cantly influenced by heat transfer processes, which are manifested to a greater extent for bubble liquids.

**Author:**
V. S. Surov

**Keywords:**
one-velocity multicomponent viscous heat-conducting heterogeneous medium, hyperbolic systems of nondivergent form, modifi ed Godunov method, approximate Riemann solvers, numerical simulation

**Page:**
652

**INCREASING THE INTENSITY OF GAS OSCILLATIONS IN AN ACOUSTICAL RESONATOR**

A method is considered for increasing the intensity of gas oscillations in an acoustical resonator by choosing the design of the piston, with the power and amplitude of the actuator oscillations remaining unchanged. Numerical
calculations for various confi gurations of the piston unit have been carried out.

**Author:**
D. A. Tukmakov

**Keywords:**
viscous compressible heat-conducting gas acoustical resonator, generation of oscillations by a harmonically moving piston, explicit scheme

**Page:**
661

**NUMERICAL INVESTIGATION OF LAMINAR HEAT TRANSFER OF NANOFLUID-COOLED MINI-RECTANGULAR FIN HEAT SINKS**

The single- and two-phase models in three-dimensional analysis are applied to study laminar convective heat transfer
of nanofluids in a minichannel heat sink. The nanofluids with suspending TiO^{2} nanoparticles of average diameter
21 nm are prepared by ultrasound with a constant nanoparticle concentration of 0.4 vol.% without using surfactants.
Experiments are carried out to verify the predicted results. It is shown that the results obtained from the two-phase
model are more precise in comparison with the experimental results than those from the single-phase model. The
predicted heat transfer coefficients for nanofl uids are higher than those for water

**Author:**
Paisarn Naphon and Lursukd Nakharintr

**Keywords:**
nanofl uids, convective heat transfer, single- and two-phase models

**Page:**
666

**STUDY OF THE HEAT-TRANSFER PROCESSES OF TUBULAR ELEMENTS OF GROUND HEAT EXCHANGERS**

In this paper, consideration is given to the efficiency of utilization of the low-potential heat of the ground. Also,
the advantages and distinctive features of polyethylene tubes used in vertical tubular elements of heat pumps are
described. This paper gives the results of investigation of the heat transfer of tubular elements of ground heat
exchangers. The dependences of the temperature distributions in the ground in the vicinity of a tube and the change
in the temperature with time in dry and moist grounds are determined.

**Author:**
K. Kusaiynov, N. N. Shuyushbayeva, K. M. Shaimerdenova, Zh. G. Nurgalieva, and N. N. Omarov

**Keywords:**
heat exchanger, polyethylene tube, temperature distribution, ground, moist ground

**Page:**
676

**MATHEMATICAL MODEL AND CALCULATION OF HEAT TRANSFER COEFFICIENTS OF ROUGH TURBULENT-FLOW-CARRYING CHANNELS**

Semiempirical approaches to the determination of the average coeffi cients of heat transfer from rough surfaces of channels are considered. The expressions obtained on the basis of the boundary-layer models of Prandtl, Deissler, Hanratty, and von Kármán are given. The possibility of calculating the parameters of these expressions with account for the channel surface roughness is shown. A comparison of the results of calculations of Nusselt numbers for rough
channels from the obtained formulas with calculations by the familiar formulas and with corresponding experimental data is made. A generalizing expression for rough channels has been obtained.

**Author:**
A. G. Laptev and M. M. Basharov

**Keywords:**
heat transfer, roughness, hydraulic resistance, boundary layer, turbulence

**Page:**
681

**ANALYTICAL SOLUTIONS OF HEAT-CONDUCTION PROBLEMS WITH TIME-VARYING HEAT-TRANSFER COEFFICIENTS**

The problem on heat conduction of an infi nite plate with a heat-transfer coeffi cient changing linearly with time for third-kind boundary conditions was solved analytically based on determination of the front of a temperature
disturbance in this plate and introduction of additional boundary conditions. On the basis of the solution obtained, graphs of the distribution of isotherms in the indicated plate and the velocities of their movement along a spatial
variable in it were constructed. As a result of the solution of the inverse problem on the heat conduction of the infinite plate with the use of the results of numerical calculation of the change in its temperature at any point on the indicated
spatial coordinate, the Predvoditelev number was identifi ed with an accuracy of 2%, which made it possible to determine the time dependence of the heat-transfer coeffi cient of the plate.

**Author:**
V. A. Kudinov, A. V. Eremin, and E. V. Stefanyuk

**Keywords:**
heat-transfer coeffi cient, temperature-disturbance front, inverse heat-conduction problem, isotherms

**Page:**
688

**SUBSTANTIATION OF THE STRUCTURAL-LAYOUT SCHEME OF THE MIRROR-SPACE-ANTENNA REFLECTOR WITH A HIGH SHAPE STABILITY AND A LOW DENSITY PER UNIT LENGTH**

Problems of designing space-antenna reflectors from composite materials for promising telecommunication satellites are considered. Selection of designs is based on the numerical modeling of heat-transfer and mechanics processes
corresponding to orbital-fl ight conditions

**Author:**
S. V. Reznik, P. V. Prosuntsov, and A. V. Azarov

**Keywords:**
spacecraft, mirror antennas, reflectors, composite materials.

**Page:**
699

**ON THE MINIMIZATION OF HEAT LOSSES THROUGH THE EXTERIOR WALL OF A BUILDING WITH A WINDOW OPENING**

We propose a method for finding the conditions of minimizing heat losses through an enclosure structure with a window opening with account for the continuous action of climatic factors. An example of calculations is given.

**Author:**
A. I. Nakorchevskii

**Keywords:**
window casing, enclosure, window opening, multiple glass unit, wind, solar radiation, heat flow, heat transfer, heat losses

**Page:**
706

**INFLUENCE OF CLIMATIC FACTORS ON THE HEAT TRANSFER THROUGH VENTILATED TWO-CHAMBER WINDOWS**

A method for calculating the heat transfer through ventilated two-chamber windows with account for the continuous action of climatic factors is proposed. An example of calculations is given

**Author:**
A. I. Nakorchevskii and A. N. Nedbailo

**Keywords:**
multiple glass unit chamber, enclosure, heat loss, heat resistance

**Page:**
716

**MICROWAVE ELECTROMAGNETIC METHOD OF MELTING THE PARAFFIN PLUG IN AN OPEN COAXIAL SYSTEM**

The formation of the temperature profi le in an open coaxial system with a paraffin plug interacting with a microwave electromagnetic field has been investigated experimentally. It has been shown that the temperature distribution in the
pipes is nonuniform, corresponding to the standing electromagnetic wave formed in the interelectrode space by the refl ection of electromagnetic waves from the oil pool and the coaxial line inhomogeneities. The presence of paraffin
in the interpipe space accelerates the process of melting throughout the coaxial system.

**Author:**
M. A. Fatykhov and L. M. Fatykhov

**Keywords:**
microwave electromagnetic method of melting, paraffi n plug, open coaxial line, temperature, internal pipe, interpipe space, standing wave, experiment

**Page:**
724

**ISOTHERMAL GASEOUS DETONATION MODEL**

We propose an isothermal gaseous detonation model taking into account the initial pressure of the explosive mixture that permits describing in a simplifi ed form both the self-sustaining and the supercompressed and undercompressed
detonation regimes. The exactness of this model has been estimated on the basis of a comparative analysis with the results of equilibrium calculations of the gas-dynamic parameters at the front of detonation waves

**Author:**
E. S. Prokhorov

**Keywords:**
detonation waves, detonation products, isothermal process, modeling

**Page:**
730

**EFFECT OF THE CONCENTRATION OF A COMBUSTIBLE GAS ON THE LIMITING CRITICAL CONDITIONS OF ITS CATALYTIC OXIDATION**

For the case of the cold, relative to a gas mixture, walls of an apparatus and radiation heat transfer, an investigation is made of the dependence of the limiting minimum gas mixture temperatures above which catalytic self-ignition and
fi ring of a low-concentration combustible gas on a catalyst particle are possible. The proposed method is based on obtaining the desired dependences in a parametric form. An analysis of the degeneration of critical temperatures and
of ignition and extinction diameters is carried out.

**Author:**
V. V. Kalinchak, A. S. Chernenko and V. V. Kalugin

**Keywords:**
catalyst particle, self-ignition, fi ring, thermal hysteresis, critical conditions, degeneration, radiation heat transfer

**Page:**
737

**THERMAL NATURE OF CONCENTRATION LIMITS OF COMBUSTION**

An explanation is proposed for the concentration limits of slow combustion of gas mixtures due to the diffusional–thermal instability of a fl ame and the leading role of the thermal effect of mixture combustion. Basic to this
explanation are the following experimental facts obtained for a wide class of mixtures: the concentration limits of slow combustion of a mixture and of its detonation are closely coinciding and depend strongly on the stoichiometric
composition of mixture; there is an approximate symmetry relation between the upper and lower combustion limits. It is shown that the fl ame temperature of gas mixtures depends on their stoichiometric composition and that as their
stoichiometric relation deviates from unity, the state of mixture combustion approaches the stability threshold beyond which a stationary fl ame cannot exist.

**Author:**
K. O. Sabdenov and T. M. Baitasov

**Keywords:**
combustion, fl ame, concentration limit, thermal effect, stoichiometric relation, diffusional–thermal instability

**Page:**
743

**RESULTS OF LABORATORY AND INDUSTRIAL TESTS OF PERIODIC-TYPE GAS GENERATORS**

Results of laboratory and industrial tests of periodic-type gas generators burning various solid biofuels have been presented. The tests were carried out with the aim of obtaining producer gas which could totally or partly replace
natural gas in power equipment burning gaseous fuel. The energy and environmental characteristics of a boiler unit burning a mixture of producer gas and natural gas have been assessed.

**Author:**
I. N. Karp, K. E. P′yanykh, T. A. Antoshchuk, and A. A. Lysenko

**Keywords:**
producer gas, natural gas, biofuel, gas generator, gasifi cation

**Page:**
749

**ON THE RELATIONSHIP BETWEEN PHYSICAL PROPERTIES OF ELEMENTARY SUBSTANCES AND THEIR CHARACTERISTIC TEMPERATURE**

It has been shown that the physical properties of elementary substances (s elements of groups I and II of the Mendeleev periodic table) are linearly dependent on their characteristic temperature.

**Author:**
V. Ya. Khentov and V. M. Gasanov

**Keywords:**
chemical elements, physical properties, correlation, characteristic temperature

**Page:**
756

**ON THE CORRECTNESS OF INTERPRETING DATA ON DETERMINING THE CAPILLARY PRESSURE IN ROCKS BY THE CENTRIFUGATION METHOD**

We have analyzed the common errors made in interpreting centrifugation data with the aim of determining the capillary pressure in rock samples. We propose a method for increasing the reliability of processed data based on
the separation of the data set by determining the limiting rotational velocity of the centrifuge corresponding to the attainment of the maximum value of the capillary pressure in the rotating core sample. It has been established that
in using the standard centrifugation method it is physically impossible to attain capillary pressures exceeding 1atm. We have improved this method by increasing the initial pressure in the core holder of the centrifuge.

**Author:**
A. M. Svalov

**Keywords:**
capillary pressure, rocks, centrifugation method

**Page:**
760

**A NOVEL CORRELATIONAL APPROACH TO ESTIMATING NATURAL GAS VISCOSITY**

A new correlation to estimating natural gas viscosity in wide temperature, composition, and pressure ranges is presented on the basis of 1748 data for eleven different mixtures taken from the literature. In comparison with other
commonly used correlations, the average error of the new correlation is found to be 3.56%.

**Author:**
Ali Akbar Amooey

**Keywords:**
viscosity, natural gas, correlation

**Page:**
769

**OBTAINING CARBON DENDRITES FROM THE PRODUCTS OF CONVERSION OF POLYMER MATERIALS**

In the work we give the results of an experiment during which carbon dendrite structures were formed in the plasma of an atmospheric-pressure gas discharge by using depolymerization products of polymer materials.

**Author:**
M. P. Danilaev, E. A. Bogoslov, O. G. Morozov, R. Nasybullin, D. M. Pashin, and Yu. E. Pol′skii

**Keywords:**
polystyrene, styrene, microwave field, depolymerization, carbon dendrites, plasma chemistry

**Page:**
774

**SYNTHESIS AND CHARACTERIZATION OF POLYMER+InP COMPOSITES**

Results of investigating the spectral properties of InP-based polymer composites are given. It is shown that the effects observed in the IR and UV absorption spectra are due to the radiation of the supermolecular structure and to
the degree of crystallinity of the polymeric matrix

**Author:**
Sh. Sh. Rashidova, M. A. Guseinova, and S. M. Rzaeva

**Keywords:**
high-density polyethylene, indium phosphide, semiconductor fi llers, composite films, optical absorption spectra

**Page:**
781

**AMPLITUDE-FREQUENCY ANALYSIS OF SIGNALS OF ACOUSTIC EMISSION FROM GRANITE FRACTURED AT ELEVATED TEMPERATURES**

The problem of stability of underground structures serving to store radioactive waste, to gasify carbon, and to utilize
geothermal energy is associated with the action of elevated temperatures and pressures. The acoustic-emission
method makes it possible to monitor the accumulation of microcracks arising in stress fi elds of both thermal and
mechanical origin. In this report, the authors give results of a laboratory investigation into the acoustic emission from
granite subjected to impact fracture at temperatures of up to 600^{o}C. An amplitude-frequency analysis of acousticemission
signals has enabled the authors to evaluate the dimension of the arising microcracks and to determine their
character (intergranular or intragranular). It has been shown that intergranular faults on the boundaries between
identical minerals predominate at room temperature (purely mechanical action); at a temperature of 300^{o}
C (impact
plus thermoelastic stresses), there also appear cracks on the quartz–feldspar boundaries; fi nally, at temperatures
of 500–600^{o}
C, it is intragranular faults that predominate in feldspar. The dimensions of the above three types of
microcracks are approximately 2, 0.8, and 0.3 mm respectively

**Author:**
I. P. Shcherbakov and A. E. Chmel′

**Keywords:**
granite, impact fracture, thermal action, acoustic emission, microcracks

**Page:**
786