**HEAT CONDUCTION AND HEAT TRANSFER IN TECHNOLOGICAL PROCESSES**

**
A METHOD FOR SOLVING A CONJUGATE PROBLEM OF HEAT TRANSFER. **

PART 1

A. S. Yakimov

UDC 536.241:519.47

Based on the integral Laplace transform, the method of quasi-linearization, and the locally one-dimensional scheme

of splitting into spatial variables, an approximate analytical solution of a conjugate problem of heat transfer in the

three-dimensional formulation has been obtained.

Keywords: heat conduction equation, conjugate heat transfer, integral Laplace transform, analytical solution.

PAGE 479

**A METHOD FOR SOLVING A CONJUGATE PROBLEM OF HEAT TRANSFER. **

PART 2

A. S. Yakimov

UDC 536.241:519.47

An analytical solution of the spatial conjugate problem of heat transfer with constant thermophysical coeffi cients

has been obtained. Conditions for the single-valued solvability of the nonlinear boundary-value problem have been

found, and the rate of convergence of iteration process has been estimated. The results of test checkings of the

analytical solution from Part 1 of the present article are given, and the assessment of the accuracy of formulas when

compared with the well-known numerical method and analytical solution is presented.

Keywords: heat conduction equation, conjugate heat transfer, convergence, accuracy, analytical solution.

PAGE 492

**INVESTIGATION OF THE COOLING OF TWO-LAYER CORRUGATED POLYMERIC PIPES**

V. T. Voznyuk, A. Ya. Karvatskii, and I. O. Mikulenok

UDC 678.027.3-036.5

Physical and mathematical models of the one-side and two-side cooling of two-layer corrugated polymeric pipes

in the process of their production by coextrusion are considered. The models proposed allow one to determine the

rational regimes of work of the coolers used in a line for production of such pipes, providing a required output of this

line. Results of a mathematical simulation of the one-side and two-side cooling of the indicated pipes are presented.

The results of calculations were compared with the corresponding experimental data.

Keywords: polymer, two-layer corrugated pipes, two-side cooling, mathematical simulation, experiment.

PAGE 505

**ACTION OF CLIMATE CONDITIONS ON HEAT TRANSFER THROUGH THE FENCING CONSTRUCTIONS OF BUILDINGS**

**
AND USE OF EXCESS HEAT FOR THEIR HEATING**

A. I. Nakorchevskii

UDC 536.2+662.997

The problem of heat transfer through the fencing constructions of buildings was numerically solved with account for

a set of climate factors. A partial solution of the problem on the use of excess heat produced by the Sun for heating

of buildings is proposed.

Keywords: wind, building, climate, fencing construction, solar radiation, heat fl ow, heat transfer.

PAGE 511

**HEAT TRANSFER UNDER HEATING OF A LOCAL REGION OF A LARGE ****PRODUCTION AREA BY GAS INFRARED RADIATORS**

G. V. Kuznetsov,^{a} N. I. Kurilenko,^{b} V. I. Maksimov,^{a}

UDC 536.33:536.244

G. Ya. Mamontov,c and T. A. Nagornovaa

This paper presents the results of a computational modeling of the processes of heat transfer in a region having the

size of a local working zone and heated due to the energy input from gas infrared radiators. The regimes of turbulent

natural conjugate convection with one boundary open for air have been investigated. The plane nonstationary

problem has been solved from the viewpoint of the Navier–Stokes model for the gas and the heat conduction for solid

walls.

Keywords: conjugate heat transfer, radiation heating source, computational modeling, turbulent natural convection,

gas infrared radiators.

PAGE 519

**POSSIBILITY OF INCREASING THE FIRE-SUPPRESSION EFFICIENCY ****OF THE FOAM IN AUTOMATIC EXTINGUISHING INSTALLATIONS**

I. V. Kachanov,^{a} V. V. Veremenyuk,^{a} I. V. Karpenchuk,^{b}

^{b}

UDC 614.843.8

The mechanics of movement of a liquid in the diffuser of the injector of an automatic extinguishing installation

with preaeration of the fi re-fi ghting substance was theoretically investigated. An integral solution of the equation

for movement of the preaerated fi re-fi ghting gas-liquid mixture in the indicated diffuser has been obtained. A

mathematical model of two-phase liquid fl ow in this diffuser, which allows one to calculate the distribution of the

average pressure in the diffuser along its length and to determine the loss in this pressure, has been developed. This

model can be used for designing the output region of a hydraulic system with a hydrodynamic drag providing the

operation of its injector in a defi nite regime.

Keywords: automatic extinguishing installation, foam, diffuser, injector, gas saturation.

PAGE 525

**
NANOSTRUCTURES ****IGNITABILITY OF ETHANOL CONTAINING CARBON NANOPARTICLES**

O. G. Penyazkov,a M. A. Silenkov,b and S. V. Shushkova

UDC 62-631.42+662.757

The formation of solid nanoparticles under the action of the electric discharge plasma on ethanol has been realized.

Comparison tests of the initial and modifi ed ethanol have been carried out on a facility with moving-apart electrodes,

in which a drop of the tested fuel is atomized by an electric discharge. It has been shown that the modifi ed ethanol

features a higher rate of ignition than the initial ethanol.

Keywords: ethanol, electric discharge treatment, carbon nanoparticles, fuel ignition.

PAGE 534

**ON MIXING OF GASES IN A LAMINAR CHEMICAL-VAPOR-DEPOSITION REACTOR**

P. S. Grinchuk, M. V. Kiyashko, Yu. A. Stankevich, and S. P. Fisenko

UDC 536.423

Experimental results on the dynamics of fi lling and displacement of the gases from a fl ow reactor by a mixture of

oxygen and nitrogen at different wall temperatures have been given. It has been established that when the wall

temperature is high, the processes of fi lling and displacement are much more rapid at all fl ow rates. A similarity

parameter of the problem, which is equal to the ratio of the characteristic times of convective and diffusion processes,

has been introduced. An analytical representation in the form of a Pade approximant has been obtained for the

characteristic mixing time.

Keywords: diffusion coeffi cient, thermal diffusivity of a mixture, fi lling of the reactor, displacement from the reactor,

nonisothermal regime.

PAGE 540

**INCORPORATION OF GAS MOLECULES INTO NANOSIZED PARTICLES**

V. V. Levdanskii,^{a} J. Smolik,^{b} V. Zdimal,^{b} and P. Moravec^{b}

UDC 541.182

The infl uence of size effects on the incorporation of gas molecules into nanosized aerosol particles has been

investigated theoretically.

Keywords: size effects, adsorption, desorption, absorption.

PAGE 547

**HYDROGASDYNAMICS IN TECHNOLOGICAL PROCESSES THERMAL CRISIS OF A VORTICITY SOURCE WITH A COMPRESSION SHOCK**

A. N. Kucherov

UDC 533.6+535.211

A study is made of the thermal crisis of a vorticity source fl owing out into a rarefi ed space with the supersonic-tosubsonic

transition in the compression shock followed by the deceleration of the subsonic fl ow in a submerged space.

Consideration is given to a perfect gas with a constant heat capacity and with negligible thickness of the shock and

thickness of the energy-release region. Dependences of the fl ow parameters on the parameter of mechanical-energy

loss, the circulation, the coordinate of the energy-release region, and on the energy-supply parameter are studied.

Keywords: vorticity source, compression shock, perfect gas, circulation, fl ow rate, energy supply, Mach number,

thermal crisis.

PAGE 551

**COMPLEX POLE METHOD FOR INTERPRETING RESULTS ****OF NONSTATIONARY HYDRODYNAMIC TESTS OF WELLS**

O. Yu. Dinariev and A. B. Starostin

UDC 532.546

The problem of interpreting results of nonstationary hydrodynamic tests of a vertical well in the presence of an

inhomogeneity zone in its vicinity has been considered. It has been shown that the Fourier transform of the seam

pressure has complex poles determined by the inhomogeneity parameters. Numerical examples demonstrating the

distribution of poles in a complex plane and their contribution to the inverse Laplace transform of the seam pressure

are given. In practical applications, the experimental data on the pole parameters can be used to estimate the

characteristics of the seam inhomogeneity near the well.

Keywords: hydrodynamic tests of wells, seam pressure, Fourier transform, complex poles.

PAGE 559

**NUMERICAL INVESTIGATION OF DROPLET MOTION IN ROTATING ****VISCOUS LIQUID FLOW**

V. A. Arkhipov,^{a,b} A. S. Tkachenko,^{c} and A. S. Usaninad,^{e}

UDC 539.529.6

The results of numerical investigation of the motion of a single droplet in a twisted fl ow of immiscible viscous liquid

are presented. The motion trajectories of a droplet depending on its size, angular velocity of liquid rotation, and

the physical parameters of the liquid and droplet have been determined. The values of the Reynolds, Bond, and

Weber numbers along the droplet trajectory have been calculated. The effect of the Coriolis forces on the trajectory,

velocity, and acceleration of the droplet in fl ow have been analyzed. The effect of the acceleration components of the

droplet on the parameters of its motion is estimated. The numerical results are compared with experimental data.

Keywords: droplet, viscous liquid, twisted fl ow, numerical investigation.

PAGE 567

**EXPERIMENTAL STUDY OF SPARK-DISCHARGE INITIATION OF DETONATION**

K. V. Korytchenko,^{a} V. I. Golota,^{b} D. V. Kudin,^{b} and S. V. Rodionov^{b}

UDC 621.43.95, 662.215.4

The mechanisms of action on a high-current spark discharge that make it possible to reduce the total expenditure of

electric energy on initiating detonation have been proposed. The action is based on the control of a discharge current

with the aid of an external circuit and on the addition of easily ionizable admixtures to a fuel-oxygen mixture. Results

of experimental investigations into the spark-discharge initiation of detonation with the action on the discharge

process have been presented; the results were obtained in mixtures of hydrogen with oxygen and of commercial

propane-butane with oxygen at atmospheric pressure.

Keywords: spark discharge, discharge current, initiation of detonation, fuel-oxygen mixture.

PAGE 577

**PRANDTL–MAYER FLOW FOR A MULTICOMPONENT MIXTURE**

V. S. Surov

UDC 532.529.5

For the multivelocity model of a heterogeneous medium, which takes into account the properties of a mixture as a

whole, the solution of the Prandtl–Mayer self-similar problem is obtained.

Keywords: multicomponent multivelocity medium, hyperbolic systems of partial differential equations, self-similar

solution.

PAGE 587

**SELF-SIMILAR RUNNING WAVES IN MULTICOMPONENT VISCOUS HEAT-CONDUCTING MEDIA**

V. S. Surov

UDC 532.529.5

Within the framework of one- and multivelocity models of a multicomponent medium that take into account the

viscous and heat-conducting properties of a mixture, self-similar solutions of the type of running waves are analyzed.

Keywords: multicomponent viscous heat-conducting mixtures, one- and multivelocity media, hyperbolic systems of

partial differential equations, self-similar solutions.

PAGE 593

**MATHEMATICAL MODELS OF MOMENTUM TRANSFER IN THE BOUNDARY LAYER**

A. G. Laptev and T. M. Farakhov

UDC 533.517.4

Consideration has been given to the processes of momentum transfer in the laminar and turbulent boundary layers

on a plate and in a tube. Original models for calculation of the tangential stress, friction factors, boundary-layer

thickness, and coeffi cients of momentum transfer in the boundary layers on a plate and in a tube have been obtained

under different conditions of motion of the gas medium. Examples of calculation of the indicated characteristics have

been given; the results obtained have been compared to the existing experimental data. The obtained equations and

methods of determination of the characteristics of the boundary layer can be used in designing industrial heat- and

mass-exchange apparatuses of various structures and other equipment.

Keywords: momentum transfer, laminar and turbulent regimes, boundary layer.

PAGE 604

**HEAT AND MASS TRANSFER IN DISPERSED AND POROUS MEDIA ****NONLINEAR OSCILLATIONS OF THE GAS SUSPENSION AND SOLID PHASE DRIFT IN AN ACOUSTICAL FLOW RESONATOR**

V. G. Tonkonog and D. A. Tukmakov

UDC 519

We have investigated the oscillations and separation of the gas suspension moving in an acoustical resonator

representing an open plane channel, in which the direction of medium oscillations is perpendicular to the fl ow

direction. Computational modeling of the processes in the above resonator has been carried out. The drift conditions

for the solid phase in a dispersed fl ow under the action of nonlinear acoustic fi elds have been determined. The results

of calculations of the gas suspension dynamics and the distribution of the solid fraction density depending on the

carrier phase velocity for various instants of time are presented.

Keywords: two-velocity two-temperature gas suspension model, Navier−Stokes equations, MacCormack scheme,

acoustical resonator, nodes and antinodes of standing wave of the velocity fi eld, drift of aerosol particles, acoustic

separation.

PAGE 614

**HEAT TRANSFER KINETICS AND EXPERIMENTAL METHODS ****FOR CALCULATING THE MATERIAL TEMPERATURE**

**
IN THE DRYING PROCESS**

A. I. Ol′shanskii

UDC 66.047.37

This paper presents methods for calculating the integral-average temperature of the material for the period of

decreasing drying rate on the basis of generalized variables of the process.

Keywords: integral-average temperature, temperature coeffi cient of drying, Rehbinder number, generalized drying

time, relative temperature, relative moisture content.

PAGE 622

**SHAPE AND VOLUME OF LIQUID MENISCUS AT THE SURFACE OF A SPECIMEN**

E. M. Lobanov

UDC 532.546

The change in the liquid meniscus at the surface of a specimen (rectangular or cylindrical) being lifted from water

and immersed into it is considered. An equation for the meniscus surface is given, and the boundary conditions of

its existence are determined. The solution of this equation describes the shape of the meniscus at all stages of its

displacement from the vertical surface of a specimen to its upper and lower planes. The solution agrees with the

data of observations. Dependences of the profi le area and volume of a meniscus on its height have been obtained.

The relationship between the meniscus parameters at the instant of its collapse and the contact angle is given. The

meniscus parameters for a standard cylindrical specimen have been estimated. A typical curve of the change in the

meniscus weight depending on its height is given. It can be employed for assessing the contact angle on a rough

surface of a specimen.

Keywords: hydrodynamic modeling, capillary phenomena, solutions of nonlinear equations, estimation of parameters.

PAGE 634

**PRODUCTION OF MODERN FUNCTIONAL MATERIALS BASED ****ON RENEWABLE VEGETABLE RESOURCES**

D. V. Onishchenko and V. P. Reva

UDC 541.136+546.34+541.18.053

An energy-saving technology for production of variously structured carbon modifi cations from a renewable vegetable

raw material, i.e., the waste of agricultural crops and peat moss, has been developed. Promising functional materials

— refractory compounds (tungsten and titanium carbides) and oil sorbents possessing a combination of high

operating characteristics — have been formed on the basis of the synthesized carbon modifi cations.

Keywords: renewable raw material, pyrolysis, mechanochemical synthesis, mechanoactivation, structure of carbon

modifi cations, titanium carbide, tungsten carbide, cold isostatic pressing, high-temperature sintering, oil sorbents.

PAGE 645

**PLASMA PLANT FOR PROCESSING OF WASTES: DESIGN VARIANTS AND TECHNOLOGICAL APPLICATION**

A. L. Mossé,^{a} G. É. Savchenko,^{b} V. A. Vlasov,^{c}

A. G. Karengin,^{c} A. A. Karengin,^{c} and A. V. Levashov^{b}

UDC 533.9 (075.8)

Stationary and mobile compact plasma plants have been developed for processing of different liquid wastes, such as

petroleum and coal slimes and discharge organic liquids.

Keywords: plasma, high-frequency fl are plasma generator, reactor, wastes, combustible compound, reclamation.

PAGE 661

**KINETIC THEORY OF TRANSFER PROCESSES**

**
HYDROGENATION OF GRAPHENE IN A HYDROGEN ATMOSPHERE UNDER THE ACTION OF AN ELECTRON BEAM**

** **

G. Ya. Gerasimov

UDC 537.533.9

This paper considers the problems of hydrogenation of graphene in a hydrogen atmosphere from the kinetic point

of view with the use of methods of electron-beam lithography. A kinetic model of the radiation-chemical processes

in a gas has been constructed. On the basis of the analysis of the available experimental data, the rate constant

of hydrogenation has been determined. The infl uence of various parameters of the process on its rate has been

investigated.

Keywords: graphene, hydrogenation, hydrogen, electron beam, radiation-chemical processes, hydrogenation rate

constants.

PAGE 661

**MODELING HIGH-CONCENTRATION PHOSPHORUS DIFFUSION IN CRYSTALLINE SILICON**

UDC 539.219.3

O. I. Velichko,^{a} V. V. Aksenov,^{b} L. P. Anufriev,^{b} N. F. Golubev,^{b} and A. F. Komarov^{c}

Phosphorus diffusion in crystalline silicon in doping from a surface source at a temperature of 840oC and a duration

of 10 min has been modeled. Good agreement with experimental data has been obtained, which confi rms the

adequacy of the employed model of high-concentration phosphorus diffusion. This model takes account of the drift

of self-interstitials in the fi eld of internal elastic stresses.

Keywords: phosphorus, silicon, diffusion, stresses, solar cell.

PAGE 667

**TEMPERATURE DEPENDENCES OF THE EFFECTIVE DIFFUSION COEFFICIENTS OF THE COMPONENTS OF THREE-COMPONENT GAS SYSTEMS, USED IN THE SYNTHESIS OF AMMONIA**

Yu. I. Zhavrin,^{a} V. N. Kosov,^{b} I. V. Poyarkov,^{c} M. K. Asembaeva,^{a} O. V. Fedorenko,^{a} and A. T. Nysanbaeva^{a}

UDC 533.15:536.25

The temperature dependences of the effective diffusion coeffi cients of the components of three-component gas

systems, used in the synthesis of ammonia, were calculated in the temperature range 298–800 K. The results obtained

can be used as reference data.

Keywords: gas system, transfer coeffi cient, effective diffusion coeffi cient, synthesis of ammonia.

PAGE 676

**
HEAT TRANSFER IN PHASE TRANSFORMATIONS INFLUENCE OF THE AIR GAP ON THE MOTION OF THE SOLIDIFICATION FRONT OF AN INGOT IN ITS MOLD**

V. V. Dremova and O. A. Kalashnikovab

UDC 536.421

The nonstationary problem of the solidifi cation of a metal in molds with walls of different heat conductivities with

account for the air gap between the ingot and the mold has been solved by the variational method. The temperature

distribution in the liquid phase and the time dependence of the solidifi cation front have been obtained. Numerical

calculations of the motion of the solidifi cation front in a cast iron and a ceramic mold at certain instants of time have

been made.

Keywords: mold, heat conductivity of walls, liquid phase, heat resistance, solidifi cation front, heat transfer coeffi cient.

PAGE 681

**HEAT TRANSFER IN BOILING OF BINARY MIXTURES UNDER FREE-CONVECTION CONDITIONS**

I.I. Gogonin

UDC 536.423.4.535.5

A study has been made of the heat transfer in boiling of binary mixtures of refrigerant–refrigerant-type homogeneous

liquids completely soluble in each other under free-convection conditions with allowance for the effects of diffusion

and evaporation of the highly volatile component from a mixture. These effects are responsible for the complex

dependence of the heat transfer on the concentration of the mixture at a constant heat fl ux. A criterial dependence

satisfactorily describing the results of experimental investigations has been proposed.

Keywords: boiling heat transfer, binary mixture, diffusion process, evaporation of a highly volatile component.

PAGE 689

**COMPUTATIONAL INVESTIGATION OF HEAT AND MASS TRANSFER PROCESSES IN A GEL-LIKE FUEL IGNITED BY A LIMITED-CAPACITY SOURCE**

G. V. Kuznetsov and P. A. Strizhak

UDC 536.468

We have carried out a computational investigation of the interrelated processes of heat and mass transfer, exothermal

(crystallization) and endothermal (melting and evaporation) phase transitions, and chemical reactions resulting

from ignition of a gel-like condensed substance. The dependence of the main integral characteristic of the process

— the ignition delay time — on the temperature of the local heating source has been established. Limiting ignition

conditions have been revealed. The position of the zone of the leading oxidation reaction relative to the interface

between the heated particle and the fuel has been determined. A comparison has been made between the ignition

conditions of condensed substances in different aggregate states under local heating.

Keywords: heat and mass transfer, melting, evaporation, crystallization, oxidation, ignition, gel-like fuel, heated

particle.

PAGE 695

**ELECTROMAGNETO-THERMODIFFUSIVE PROBLEM FOR SHORT TIMES WITHOUT ENERGY DISSIPATION**

Sunita Deswal and Kapil Kumar Kalkal

UDC 536.2

A general solution to the fi eld equations for electromagneto-thermodiffusive elastic medium is obtained by employing

a normal mode analysis in the context of the Green and Naghdi theory of type II, when a distributed instantaneous

source is acting on the free surface of the medium. The medium deforms because of a mechanical load and application

of a magnetic fi eld, when induced magnetic and electric fi elds appear in it. The stresses, displacements, temperature,

concentration, and chemical potential for copper are calculated and presented graphically. The impact of a magnetic

fi eld and time is studied.

Keywords: energy dissipation, normal mode analysis, distributed source, electromagneto-thermodiffusion.

PAGE 705

**MOVING HEAT SOURCE RESPONSE IN A THERMOELASTIC MICROELONGATED SOLID**

S. Shaw and B. Mukhopadhyay

UDC 535.21

The present paper deals with thermoelastic interactions in a microelongated, isotropic, homogeneous medium in the

presence of a moving heat source. In this context, the generalized theory of heat conduction is considered. In order to

illustrate the results obtained, a numerical solution for aluminum epoxy-like material is obtained, and the variations

of the displacement, microelongation, normal strain, and normal stress are presented. The results may be applied for

damage characterization of materials.

Keywords: moving heat source, microelongation, microstretch, generalized heat conduction equation.

PAGE 716

**NONSTEADY FLOW OF A POWER-LAW FLUID IN A POROUS MEDIUM BETWEEN PARALLEL PLATES WITH HEAT TRANSFER, SUCTION, AND INJECTION**

Hazem Ali Attia^{1}, Mostafa A. M. Abdeen^{2}, and Alaa El-Din Abdin^{3}

UDC 665.455

The time-varying fl ow of a viscous incompressible non-Newtonian power-law fl uid through a porous medium between

two parallel horizontal porous plates under the action of a constant pressure gradient with consideration for heat

transfer is studied. Uniform suction and injection through the surfaces of the plates take place where the two plates

are kept at different, but constant temperatures, and the Joule and viscous dissipation terms are considered in the

energy equation. Numerical solutions for the governing nonlinear momentum and energy equations are obtained

using fi nite differences. The effect of the medium porosity, the parameter describing the non-Newtonian behavior, and

the velocity of suction and injection on both the velocity and temperature distributions, as well as on the dissipation

terms, is investigated.

Keywords: parallel plates fl ow, heat transfer, non-Newtonian fl uid, porous medium, numerical solution.

PAGE 723