#### Volume 89, № 6

**USE OF IDENTIFICATION EQUATIONS FOR A MODEL OF THE BLACK-BOX TYPE IN THE CASE OF ITS INSTABILITY**

A chemical-engineering system represented in the form of a black box with an input and an output is considered. The heat and mass transfer in this system was defi ned with the use of ordinary differential equations with constant coeffi cients of defi nite order. A method of use of "unstable" equations for the description of practical problems is proposed. The term instability was taken to mean that a differential operator has eigenvalues with a positive real part. The coeffi cients of an equation were determined on the basis of an analysis of the curve of response of the system

to a disturbance in the form of a step. A concrete example of realization of the algorithm proposed is considered.

**Author:**
A. I. Moshinskii, A. V. Markova, L. N. Rubtsova V. V. Sorokin, and P. G. Ganin

**Keywords:**
heat and mass transfer, mathematical simulation, startup curve, identifi cation of a model, unstable behavior

**Page:**
1349

**ON A THERMODYNAMIC MECHANISM OF DISSIPATION OF MECHANICAL ENERGY IN POROUS ELASTOMERS AS APPLIED TO THE PROBLEM OF HEATING OF AUTOMOBILE TIRES**

It has been shown that in the case of cyclic mechanical loads on a porous elastomer there are regimes in which irreversible processes of heat transfer between the gas and the elastomer are responsible for the appearance of a

nonzero heat fl ux averaged over the period and directed from the gas into the condensed phase; this heat fl ux is compensated for with the dissipation of mechanical energy from the loading source. A possible infl uence of this

mechanism of dissipation on the heating of automobile tires is assessed. Possible methods of recording of this effect

are discussed.

**Author:**
P. S. Grinchuk and A. I. Shnip

**Keywords:**
porous elastomer, cyclic load, mechanical-energy dissipation, heating of tires.

**Page:**
1358

**RATE OF DISSIPATION OF THE ENERGY OF LOW-FREQUENCY MECHANICAL DISTURBANCES IN A TIRE**

An expression for the rate of dissipation of the energy of low-frequency mechanical disturbances in a tire, accounting for the tired wheel radius, velocity of motion, and loading, has been derived. After processing experimental data on heating the tread rubber of an oversize tire by the proposed method, it has been revealed that about 30% of the

energy of deformations appearing in motion of a loaded tire is converted into heat, and the coeffi cient of heat transfer

between the tire and air has been derived

**Author:**
P. S. Grinchuk and S. P. Fisenko

**Keywords:**
frequency, steady-state temperature, dimensional analysis, heat transfer coeffi cient, stand test.

**Page:**
1365

**HEAT EXCHANGE WITH AIR AND TEMPERATURE PROFILE OF A MOVING OVERSIZE TIRE**

A one-dimensional mathematical model of heat transfer in a tire with account for the deformation energy dissipation and heat exchange of a moving tire with air has been developed. The mean temperature profi les are calculated and transition to a stationary thermal regime is considered. The infl uence of the rate of energy dissipation and of effective thermal conductivity of rubber on the temperature fi eld is investigated quantitatively.

**Author:**
P. S. Grinchuk and S. P. Fisenko

**Keywords:**
local density of the rate of energy dissipation, heat transfer coeffi cient, explicit scheme, effective radius

**Page:**
1369

**MATHEMATICAL MODELING OF CHEMICAL VAPOR DEPOSITION OF MATERIAL ON A CURVILINEAR SURFACE**

In this work, a mathematical model has been constructed that describes the process of chemical vapor deposition of material on a curvilinear plate. On the boundary where the deposition occurs, account is taken of convective heat transfer, heat transfer by radiation, and heat and mass transfer during the attachment of the substance to the surface.

A numerical algorithm is proposed for fi nding the temperature profi le at any instant of time; results and an analysis

of numerical calculation are given for different materials.

**Author:**
G. N. Kuvyrkin, A. V. Zhuravskii, and I. Yu. Savel′eva

**Keywords:**
chemical vapor deposition, curvilinear surface, numerical modeling

**Page:**
1374

**MODELING OF METHODS TO CONTROL HEAT-CONSUMPTION EFFICIENCY**

In this work, consideration has been given to thermophysical processes in automated heat consumption control systems (AHCCSs) of buildings, fl ow diagrams of these systems, and mathematical models describing the thermophysical processes during the systems′ operation; an analysis of adequacy of the mathematical models has been presented.

A comparison has been made of the operating effi ciency of the systems and the methods to control the effi ciency. It has been determined that the operating effi ciency of an AHCCS depends on its diagram and the temperature chart of central quality control (CQC) and also on the temperature of a low-grade heat source for the system with a heat

pump.

**Author:**
E. A. Tsynaeva and A. A. Tsynaeva

**Keywords:**
heat and mass transfer, thermophysical processes, heat consumption, effi ciency, automated control systems

**Page:**
1380

**ON THERMOPHYSICAL PROPERTIES OF RUBBERS AND THEIR COMPONENTS**

Results of investigation of the thermophysical properties of commercial carbon of different grades used in the production of tires, and also of rubber mixtures, including those containing karelite, have been presented. A thermal analysis (thermogravimetry, differential thermal analysis) was made of samples of rubber mixtures and powdered fi llers, which has enabled the author to establish the distinctive features of thermal stability of materials. The obtained results are important for a better understanding of the problem of critical overheating of supergiant tires, solution of

the problem of selecting the optimum compositions of rubber mixtures, and updating the technologies of production

and utilization of rubber products

**Author:**
S. M. Danilova-Tret′yak

**Keywords:**
thermal conductivity, specifi c heat, rubber, commercial carbon, karelite

**Page:**
1388

**HEAT ABSORPTION BY A GROUNDMASS DUE TO THE ACTION OF SOLAR RADIATION**

A procedure for the calculation of the heat-absorption ability of the ground, as far as solar radiation is concerned, has been proposed. An example of the calculation has been presented.

**Author:**
A. I. Nakorchevskii

**Keywords:**
groundmass, solar radiation, heat fl ux, heat transfer

**Page:**
1394

**MINIMAX ANALYSIS OF ECONOMIC AND ENERGY EFFICIENCIES OF HEAT-SUPPLY PIPELINES**

A minimax problem of minimization of fi nancial expenses and energy expenditure in a heat-supply system of buildings has been formulated and solved. The optimum parameters of a pipeline, i.e., the pipe radius and the thickness of the heat-insulating material, have been found.

**Author:**
K. O. Sabdenov

**Keywords:**
heat supply of buildings, pipeline, energy and economic effi ciencies

**Page:**
1401

**ASYMPTOTIC REPRESENTATION OF THE FILTRATION-WAVE FIELD IN THE LAYER OF AN INHOMOGENEOUS MEDIUM IN THE FORM OF A PLANE WAVE**

The fi ltration-wave process in the central layer of a three-layer anisotropic medium is described as an equivalent plane wave with a modifi ed asymptotic method accurate in the mean. The initial problem is parametrized and broken down into simpler problems for the coeffi cients of expansion in an asymptotic parameter. The zero expansion coeffi cient describes the sought plane wave, whereas the fi rst coeffi cient ensures refi nement of the

wave-front geometry. The exact solution of the parametrized problem is obtained on the basis of the Fourier sine transformation. The correctness of the developed method is confi rmed by comparing the obtained asymptotic

solutions and the coeffi cients of Maclaurin-series expansion of the exact solution of the parametrized problem in a formal parameter.

**Author:**
A. I. Filippov, O. V. Akhmetova, and A. A. Koval′skii

**Keywords:**
wave equation, asymptotic method, wave pressure fi eld, exact solution, fi ltration, anisotropic medium

**Page:**
1410

**ASYMPTOTIC REPRESENTATION OF THE TEMPERATURE FIELD IN INJECTION STAGES DURING THE CYCLIC ACIDIZING OF THE FORMATION**

The authors have obtained an asymptotic solution to the problem on the temperature fi eld appearing during the injection of a chemically active solvent into a layered inhomogeneous orthotropic formation with account taken of temperature disturbances due to the preceding technological processes. This makes it possible to use the obtained solution for calculations under the conditions of multiple cyclic action. The sources of temperature disturbances are the liberation of heat due to the chemical reaction and the change in the temperature of the acid solution

injected into the formation. Therefore, the obtained solution also covers the range of thermal-acidizing processes. The implemented method of construction of the solution is an extension of an asymptotic method accurate in the mean, which has been proposed by the authors as applied to the problems with nonzero initial conditions. The results of calculations of space–time temperature distributions under the conditions of hydrochloric acid treatment of carbonaceous formations have been given.

**Author:**
A. I. Filippov, O. V. Akhmetova, A. A. Koval′skii and I. F. Kabirov

**Keywords:**
temperature fi eld, injection of acid, carbonate formation, asymptotic method

**Page:**
1426

**ON THERMAL FLUIDIZATION OF A GRANULAR BED HEATED FROM ABOVE**

The thermal fl uidization of quartz sand particles under the action of a constant-power heat source on the upper boundary of a granular bed has been investigated.

**Author:**
E. A. Pitsukha, Yu. S. Teplitskii, and A. R. Roslik

**Keywords:**
fi xed granular bed, bubbling (fl uidized) bed, fl uidization, nonisothermal gas fi ltration, surface of strong discontinuity

**Page:**
1441

**DETERMINATION OF THE PARAMETERS OF THE HOLE BOTTOM ZONE OF A VERTICAL WELL FROM THE RESULTS OF THERMODYNAMIC INVESTIGATIONS**

A computational algorithm for estimating the parameters of the hole bottom zone from the results of measuring pressure and temperature at the bottom hole of a vertical well is suggested. The ambiguity of determining the permeability and of the hole bottom zone radius depending on the original information is shown.

**Author:**
M. Kh. Khairullin M. N. Shamsiev B. R. Gadilshina P. E. Morozov A. I. Abdullin and E. R. Badertdinova

**Keywords:**
inverse problem, thermohydrodynamic investigations, hole bottom zone, skin factor

**Page:**
1449

**ON MOTION OF BIOFUEL PARTICLES IN A FLUIDIZED BED**

The migration of macroparticles in a fl uidized bed of a fi nely divided quartz sand has been studied experimentally. The mechanism underlying the infl uence of the mixing of fl uidized bed particles on the character of macroparticle motion is described. The dependence of the depth of macroparticle immersion on the physical and operational

parameters has been obtained

**Author:**
É. K. Buchilko, A. Zh. Greben′kov, V. A. Borodulya, E. A. Pitsukha, and Yu. S. Teplitskii

**Keywords:**
biofuel, macroparticle, fl uidized bed, gas bubble, migration, Archimedes force, associated mass

**Page:**
1454

**THREE-DIMENSIONAL SIMULATION OF A VIBROFLUIDIZED BED WITH THE USE OF A TWO-FLUID MODEL OF GRANULAR GAS**

We present the results of three-dimensional calculations of the degree of expansion of a vibrofl uidized bed that were obtained with the aid of the twoPhaseEulerFoam solver of a freely accessible OpenFOAM package and the data of experiments on vibrobubbling of relatively large dolomite particles. Satisfactory agreement is obtained between the

results of numerical calculations and experimental data.

**Author:**
E. S. Kamenetskii, N. S. Orlova, A. M. Tagirov, and M. V. Volika,

**Keywords:**
three-dimensional simulation, two-fl uid model, vibrofl uidized bed, granular gas, monodisperse particles, dolomite

**Page:**
1459

**INFLUENCE OF PRESSURE ON STABLE FILM BOILING OF SUBCOOLED LIQUID**

Film boiling of subcooled liquids is an integral part of the hardening process. Understanding of the mechanisms underlying fi lm boiling is important for modeling processes in atomic power engineering and cryogenic technology.

Stationary processes of fi lm boiling of subcooled liquids under conditions of their free motion near cylindrical heaters, just as subcooled liquid turbulent fl ow past high-temperature surfaces, represent quite a different type of

process. In cooling metal spheres heated to a high temperature by a subcooled water, a special regime of fi lm boiling is observed (microbubble boiling) distinguished by high intensity of heat transfer. Such a regime has not been revealed up to now for nonaqueous liquids. The paper presents new experimental data on heat transfer regimes in cooling nickel spheres in subcooled isopropanol and perfl uorohexane at pressures of up to 1 MPa. It

has been established that stable fi lm boiling is the main regime of heat transfer that accounts for the larger part

of the total time of cooling. The regimes of highly intensive fi lm boiling heat transfer were not observed in the

entire range of operational parameters even in the case of extreme subcoolings of liquid below their saturation

temperature (to 170 K). The intensity of heat transfer in stable fi lm boiling increases noticeably with subcooling

of a chilling liquid.

**Author:**
A. R. Zabirov, V. V. Yagov, O. N. Kaban′kov M. A. Leksin, and P. K. Kanin

**Keywords:**
fi lm boiling, subcooled liquid, cooling, microbubble boiling, stable regime, heat transfer coeffi cient

**Page:**
1466

**INFLUENCE OF SUPERHYDROPHOBIC PROPERTIES ON DEICING**

Nowadays the creation of anti-icing, or deicing, surfaces is one of the most important problems, as such surfaces are widely used in aeronautics, wind turbines, and telecommunication antennas. In this paper, we focus mainly on

reducing the ice adhesion forces and easy ice removal, once ice has formed. Removal of a liquid from a surface can be provided by modifi cation of the surface wettability by means of applying superhydrophobic coatings. Such coatings are water-resistant, i.e., are characterized by low water adhesion forces. To study the impact of superhydrophobic coatings, tests were performed on the surface of a wing in a wind tunnel. By spraying Tefl on and polyphenylene sulfi de (PPS) on the wing, we obtained a superhydrophobic fi lm. This fi lm has a structure that provides superhydrophobic

properties, so that the wetting angle is above 140o . A comparison of the resulting surface with a clean Tefl on one shows that adhesion of the Tefl on + PPS mixture to an aluminum surface is fi ve times higher. We also investigate the degree of ice formation on the surfaces of simple and superhydrophobic aircraft wings at a temperature of –18o

C. It was shown that ice was formed on a simple wing within 40 s and on a superhydrophobic wing within 25 s. When the

simple wing with a mass of 23 g was inserted into the wind tunnel, its mass reached 50 g, and for a superhydrophobic

wing with a mass of 26 g the latter reached 42 g. The sample of the airfoil wing we prepared has a low adhesion,

which helps in easy ice removal

**Author:**
M. Nazhipkyzy, Z. A. Mansurov, A. Amirfazli, A. Esbosin,a T. S. Temirgaliyeva, B. T. Lesbayev, E. T. Aliyev, and N. G. Prikhodko

**Keywords:**
superhydrophobic properties, deicing, wettability, airfoil

**Page:**
1476

**PYROLYSIS OF RUBBER IN A SCREW REACTOR**

On the basis of an analysis of thermal methods described in the literature and from the results of experimental

investigations of steam conversion, the authors have developed and created a facility for thermal processing of

rubber waste. Rubber crumb was used as the raw material; the temperature in the reactor was 500o

C; nitrogen,

steam, and a mixture of light hydrocarbons (noncondensable part of pyrolysis products) represented the working

medium. The pyrolysis yielded 36–38% of a solid fraction, 54–56% of a liquid hydrocarbon fraction, and 6–9% of

noncondensable gases. Changes in the composition of the gas mixture have been determined at different stages of

processing. Gas chromatography of pyrolysis gases has shown that the basic gases produced by pyrolysis are H2

and hydrocarbons C2H4, C3H6, C3H8, C4H8, C2H6, C3H6O2, and C4H10, and a small amount of H2S, CO, and CO2.

Noncondensable gases will be used as a fuel to heat the reactor and to implement the process.

**Author:**
A. V. Lozhechnik and V. V. Savchin

**Keywords:**
rubber waste, screw reactor, utilization technology

**Page:**
1482

**PARAMETRIC INVESTIGATION OF THE ISOTHERMAL KINETICS OF GROWTH OF GRAPHENE ON A NICKEL CATALYST IN THE PROCESS OF CHEMICAL VAPOR DEPOSITION OF HYDROCARBONS**

A kinetic model of isothermal synthesis of multilayer graphene on the surface of a nickel foil in the process of chemical

vapor deposition, on it, of hydrocarbons supplied in the pulsed regime is considered. The dependences of the number

of graphene layers formed and the time of their growth on the temperature of the process, the concentration of

acetylene, and the thickness of the nickel foil were calculated. The regime parameters of the process of chemical

vapor deposition, at which single-layer graphene and bi-layer graphene are formed, were determined. The dynamics

of growth of graphene domains at chemical-vapor-deposition parameters changing in wide ranges was investigated.

It is shown that the time dependences of the rates of growth of single-layer graphene and bi-layer graphene are

nonlinear in character and that they are determined by the kinetics of nucleation and growth of graphene and the

diffusion fl ow of carbon atoms in the nickel foil.

**Author:**
S. I. Futko, B. G. Shulitskii, V. A. Labunov, and E. M. Ermolaevaa

**Keywords:**
graphene, single-layer graphene, bi-layer graphene, carbon allotropes, chemical vapor deposition, nickel catalyst, isothermal kinetics, synthesis of graphene, heterogeneous catalysis, transition metals, hydrocarbons

**Page:**
0019

**CONTROL OF THE PERIODIC TURBULENT FLOW OVER A SEMICIRCULAR AIRFOIL WITH THE USE OF THE SLOT SUCTION OF THE AIR FROM A CIRCULAR VORTEX CELL AT SMALL ANGLES OF ATTACK**

It is shown that, in the case where, into the back wall of a semicircular airfoil with an angle of attack of 5o

, a vortex

cell of diameter 0.2 in fractions of the airfoil chord is built in and the mean-mass rate of slot suction of the air

from this cell is larger than 0.15 of the incident-fl ow velocity, the pattern of the turbulent fl ow over the airfoil is

transformed, and, at an optimum suction rate of 0.75, the lift coeffi cient of the airfoil reaches a maximum value of

the order of 1.7 at an aerodynamic effi ciency of 10.

**Author:**
S. I. Isaev, P. A. Baranov, A. G. Sudakov and A. E. Usachev

**Keywords:**
control of fl ow, aerodynamic effi ciency, thick airfoil, vortex cell, slot suction, turbulence, MSST, VP2/3 package

**Page:**
1500

**INFLUENCE OF THERMAL PROCESSES ON THE EFFICIENCY OF THE ENERGY SEPARATION IN A RANQUE VORTEX TUBE**

**Author:**
V. D. Tyutyuma

**Keywords:**
Ranque–Hilsch effect, vortex, swirling fl ow, velocity fi eld, thermodynamic parameters

**Page:**
1505

**COMPARISON OF THE RESULTS OF MODELING THE FLAME PROPAGATION IN A HYBRID GAS SUSPENSION WITH EXPERIMENTAL DATA**

This article considers the laminary combustion of a hybrid gas suspension consisting of a gaseous combustible, an oxidizer, and an inert gas, as well as particles capable of interacting with the gas-phase oxidizer. The mathematical

model takes into account the thermal expansion of the gas and its related relative motion of particles. The problem has been solved numerically in dimensionless variables. The dependences of the steady velocity of the fl ame front on the initial concentration of the combustible in the gas phase at various values of the parameters of the dispersed

phase are presented. A comparison has been made between experimental and calculated data for a gas suspension

consisting of a gaseous oxidizer, an inert gas, and reactive particles.

**Author:**
A. A. Dement′ev, K. M. Moiseeva, Y. Yu. Krainov, and D. Yu. Paleev

**Keywords:**
gas suspension, laminar fl ame, reactive particles, inert particles, rate of combustion, processes in the gas phase, mathematical modeling

**Page:**
1514

**EXPERIMENTAL STUDY OF THE INFLUENCE OF THE STRUCTURE OF LOCAL ENERGY SOURCES ON THE CONDITIONS AND CHARACTERISTICS OF THE IGNITION OF LIQUID FUELS**

Experimental studies have been made of the laws of ignition of a group of typical liquid fuels (kerosene, diesel fuel, mazut) by single particles of metals and porous particles of metal oxides heated to high temperatures. We have

established the dependences of numerical values of ignition delay times of liquid fuels on the temperature of porous

particles formed by welding and of monolithic steel particles in the form of disks. The experimental results show that

the delay times of ignition of the typical distillate fuels — kerosene and diesel fuel — by "hot" particles formed by

welding metals are shorter than for the ignition of the same fuels by monolithic steel particles of adequate sizes. The

ignition delay times of the highly viscous fuel — mazut — are independent of the particle porosity

**Author:**
A. V. Zakharevich and M. S. Zygin

**Keywords:**
ignition, liquid fuel, metal oxide particle, ignition delay time

**Page:**
1522

**INVESTIGATION OF THE CONJUGATE HEAT AND MASS TRANSFER AT IGNITION AND SUBSEQUENT NONSTATIONARY EROSION COMBUSTION OF POWDERS UNDER CONDITIONS CLOSE TO THOSE OF FIRING A SHOT**

The laws of combustion of powders under conditions close to those of fi ring an artillery shot have been investigated.

A solid-state local heat ignition model was used, and the process of powder combustion was simulated on the basis

of the notions of the Belyaev–Zel′dovich thermal combustion theory. The complete formulation of the combustion

problem includes the nonstationary processes of heat propagation and chemical transformation in the k-phase,

as well as the quasi-stationary processes in the chemically reacting two-stage turbulent boundary layer near the

combustion surface related to the characteristics of the averaged nonstationary fl ow by the boundary conditions

at the outer boundary of the boundary layer. The features of the joint solution of the equations of the thermal

combustion theory and the equations of internal ballistics have been analyzed. The questions on the convergence of

the conjugate problem have been considered. The infl uence of various factors on the rate of combustion of powder

has been investigated. The investigations conducted enabled us to formulate an approximate method for calculating

the nonstationary and erosion rates of combustion of artillery powders at a shot on the basis of the Lenouard–

Robillard–Karakozov approach.

**Author:**
I. G. Rusyak and A. M. Lipanov

**Keywords:**
ignition, combustion, nonstationary, turbulence, erosion, heat and mass transfer, conjugate problem, computing method, internal ballistics, artillery shot

**Page:**
1527

**CONDITIONS AND CHARACTERISTICS OF THE IGNITION OF A TYPICAL VEGETABLE COMBUSTIBLE MATERIAL BY A LOCAL ENERGY SOURCE**

This paper presents the results of experimental studies of the ignition of a typical vegetable combustible material

(dry grass) by a single particle heated to high temperatures. The ignition conditions correspond to the rather typical

conditions of the action on a vegetable combustible. The dependence of the ignition delay time of dry grass on the

initial temperature of the particle has been obtained, and the limiting temperatures of combustion initiation have

been determined. A hypothesis on the mechanism of heat transfer in a heated bed of the material during the induction

period has been formulated.

**Author:**
N. V. Baranovskii and A. V. Zakharevich

**Keywords:**
ignition, vegetable fuel, heated particles, ignition delay time

**Page:**
1538

**A CONVERTER FOR PRODUCING A HYDROGEN-CONTAINING SYNTHESIS GAS**

A computational thermodynamic and experimental investigation of the characteristics of a model of a converter

for producing a hydrogen-containing synthesis gas from a hydrocarbon fuel (kerosene) with its separate delivery to

thermal-oxidative and steam conversions has been carried out. It is shown that the optimum conditions of converter

operation correspond to the oxidant excess coeffi cient in the converter′s combustion chamber α > 0.5 at a temperature

of the heat-transmitting wall (made from a heat-resistant KhN78T alloy (ÉI 435)) of 1200 K in the case of using a

nickel corrugated tape catalyst. The content of hydrogen in the synthesis gas attains in this case 60 vol.%, and there

is no release of carbon (soot) in the conversion products as well as no need for water cooling of the converter walls.

**Author:**
Yu. P. Malkov, O. N. Molchanov, B. K. Britov, and I. A. Fedorov

**Keywords:**
converter, reactor, catalyst, hydrogen-containing synthesis gas, hydrocarbon fuel, thermal-oxidative and steam conversions

**Page:**
1545

**INVESTIGATION OF THE DUST STRUCTURES IN A STRATIFIED NEON COLUMN**

Dust plasma in a stratifi ed positive column of a stationary neon discharge has been investigated. To create stationary

strata, 5–7% of air was added to neon. The discharge current was 2–7 mA. The size of macroparticles from aluminum

oxide was varied over the range of 10–80 μm. The plasma diagnostics was carried out by the probe method.

The temperature and concentration of particles were determined by the volt-ampere characteristic. To investigate

the dust structures, optical measurements were made. From the temperature and density of charged particles, the

thickness of the volume charge layer surrounding the dust particle was determined and its value was compared with

the value obtained as a result of optical measurement data processing. The dependence of the volume charge layer

thickness on the dust particle potential has been calculated.

**Author:**
A. M. Astaf′ev, S. A. Gutsev, and N. B. Kosykh

**Keywords:**
low-pressure neon plasma, Langmuir probes, orbital motion, volt-ampere characteristic, electron temperature, particle number density, volume charge layer, dust structures

**Page:**
1554

**CALCULATION OF THE DYNAMIC CHARACTERISTICS OF AN ELECTRIC ARC SUBJECTED TO FORCED EXTINCTION**

Models and methods of calculating the currents in a free-burning arc and in an arc in an arc chute with magnetic

blow and the voltages across them in the process of their extinction are considered. A comparison of calculation and

experimental data has been performed.

**Author:**
S. A. Nekrasov

**Keywords:**
arc, discharge, extinction of arc, magnetic blow-out, arcing

**Page:**
1565

**A HEURISTIC APPROACH TO THE DETERMINATION OF THE EFFECTIVE THERMAL CONDUCTIVITY COEFFICIENTS OF BIPERIODIC COMPOSITE MEDIA**

A heuristic approach to determining the effective thermal conductivity coeffi cients of unidirectionally reinforced

biperiodic composite media is suggested allowing one to substantially refi ne the calculated values of the effective

coeffi cients of transverse thermal conductivity of the indicated compositions by using the simplest partitioning of

a periodicity cell into thin layers (subelements) with subsequent application of the simplest formulas of averaging

by simple and inverse mixture rules. A comparison of the calculated values of these coeffi cients with familiar

experimental data is made. The good agreement of the prediction with experiment allows an assumption that the

method developed can be used for practical calculations of the thermophysical characteristics of fi brous media with

biperiodic structure. At the present time the accuracy of more complex structural models of the thermal conductivity

of unidirectionally reinforced composites lacks a strict experimental justifi cation.

**Author:**
A. P. Yankovskii

**Keywords:**
thermal conductivity, composites, unidirectional reinforcement, structural theory, biperiodic medium

**Page:**
1574

**THERMAL-FORCE DEFORMATION OF A PHYSICALLY NONLINEAR THREE-LAYER STEPPED ROD**

Consideration has been given to the thermal-force deformation of a three-layer plastoelastic rod with a stepped

thickness of one supporting layer. The physical equations of state are consistent with the Il′yushin theory of small

plastoelastic deformations. To describe the kinematics of a rod bundle nonsymmetric across the thickness, the authors

adopted the broken-normal hypotheses. A system of equilibrium equations has been derived, and its general iterative

solution in displacements has been obtained. A numerical parametric analysis of the rod′s stress–strain state has

been made.

**Author:**
É. I. Starovoitov, D. V. Leonenko, and D. V. Tarlakovskii

**Keywords:**
temperature, physical nonlinearity, deformation, three-layer rod, stepped thickness

**Page:**
1582

**LAMINAR MAGNETOHYDRODYNAMIC BOUNDARY LAYER ON A DISK IN THE PRESENCE OF EXTERNAL ROTATING FLOW AND SUCTION**

The rotation of a conducting viscous medium near a dielectric disk in a homogeneous magnetic fi eld in the presence

of an external fl ow and a suction is considered. On the basis of the Dorodnitsyn transformation, an analytical solution

of the system of boundary-layer and heat-conduction equations has been obtained. It is shown that the direction of

the radial fl ow in the boundary layer of the disk can be changed by changing the ratio between the angular velocities

of the external fl ow and the disk and the ratio between the temperatures in the external fl ow and on the disk as well

as by varying the hydrodynamic Prandtl number. The infl uence of the magnetic fi eld on the intensity of circulation of

the viscous medium was investigated.

**Author:**
V. D. Borisevich and E. P. Potanin

**Keywords:**
rotating disk, magnetic fi eld, suction, boundary layer, conducting gas

**Page:**
1591