#### Volume 91, №6

**NUMERICAL-ANALYTICAL SOLUTION OF THE NONLINEAR COEFFICIENT INVERSE HEAT CONDUCTION PROBLEM**

An approach to identifi cation of thermophysical characteristics on the basis of numerical-analytical solution of a nonlinear coeffi cient inverse heat conduction problem is considered. The proposed approach is based on reduction of the differential heat conduction equation, which models measuring operations, to the corresponding integrofunctional equation with the use of the method of integral transformation and on its numerical solution by iteration method. To raise the stability of numerical solution and eliminate the noises in the measuring apparatuses that
distort the measured values of the temperature fi eld, an approximation by the least square method and preliminary
smoothing of experimental temperature data by spline-functions are made. The results of numerical experiments
carried out on model problems are given, from which it follows that as to the accuracy of calculation the indicated
approach is superior to the well-known numerical methods, retaining the possibility of constructing identifi able
characteristics as arbitrary functions of temperature

**Author:**
O. S. Dmitriev and A. A. Zhivenkova

**Keywords:**
inverse heat conduction problem, integro-functional equation, iteration method, thermophysical characteristics

**Page:**
1353

**COMPUTATIONAL AND EXPERIMENTAL INVESTIGATION OF MECHANICAL AND THERMAL CONTACTS OF CERAMIC BLADES WITH THE METAL DISK IN GAS TURBINE ENGINES**

Models of thermal and mechanical contacts of ceramic and metal parts in lock joints of turbines of aircraft gas turbine
engines have been developed which take account of the character of operating loads in them. Experimental data
on the strength and thermal conductance of a ceramics–metal contact joint have been presented. The investigations
were carried out with ceramic specimens based on hot-pressed silicon nitride and silicon carbide reinforced with
diamond particles

**Author:**
S. V. Reznik, D. V. Sapronov, and P. V. Prosuntsov

**Keywords:**
aircraft gas turbine engines, lock joints of turbines, structural ceramics, contact interaction, contact heat transfer

**Page:**
1365

**DIRECT (CLASSICAL) METHOD OF CALCULATION OF THE TEMPERATURE FIELD IN A HOLLOW MULTILAYER CYLINDER**

A structural scheme of construction of a solution to a mixed problem for the heat-conduction equation in the case
of a hollow multilayer cylinder under the conditions of ideal thermal contact between the layers is proposed and
substantiated. The presence of connective heat exchange with the environment is assumed, i.e., boundary conditions
of the third kind are observed. Coeffi cients of the heat-conduction equation are considered to be piecewisecontinuous as far as the space coordinate is concerned. The scheme is based on the: reduction method, concept of
quasi derivatives, modcern theory of systems of linear differential equations, Fourier method, and modifi ed method
of eigenfunctions. A numerical example of calculation of the temperature fi eld in an actual hollow four-layer pipeline
under external-fi re conditions is given

**Author:**
R. M. Tatsii and O. Yu. Pazen

**Keywords:**
reduction, quasi derivative, Bessel function, Cauchy matrix, method of eigenfunctions

**Page:**
1373

**EXPERIMENTAL MODELING OF THE METHOD OF AIR COOLING IN THE PROCESS OF GAS MIXTURE SEPARATION**

A variant of the scheme of fractional separation of a gas mixture with the use of air-cooled settling tanks is suggested. Experimental verifi cation of the use of the proposed scheme for fractional separation of a gas mixture consisting of uranium hexafl uoride and hydrogen fl uoride is carried out on a specially designed rig that simulates the technological process. The results of the experimental verifi cation show the fundamental possibility of using the proposed scheme for fractional separation of a mixture of uranium hexafl uoride and hydrogen fl uoride

**Author:**
A. A. Kartavykh and A. Yu. Krainov

**Keywords:**
desublimation, hydrogen fl uoride, uranium hexafl uoride, separation of gas mixture, experimental measurements

**Page:**
1385

**PARABOLIC PROFILE IN HEAT-CONDUCTION PROBLEMS. 1. SEMI-BOUNDED SPACE WITH A SURFACE OF CONSTANT TEMPERATURE**

A new approach to the construction of constitutive integral relations, involving the introduction into consideration
of local functions for a heat fl ow or a temperature determined directly from the differential heat-conduction
equation, is proposed. With the use of this approach, new integral relations: the temperature-momentum integral
of single modifi cation, the temperature-momentum integral of double modifi cation, the heat-fl ow integral, and the
temperature-function integral, have been obtained. On the basis of these integrals as well as the integral method
of heat balance and the refi ned integral method, different variants of the hybrid integral method realized with
the use of manifold integral relations were investigated. In addition to the Langford norm, new error norms were
introduced into consideration. The parabolic solutions obtained possess much better qualities compared to those of
the analogous known solutions

**Author:**
V. A. Kot

**Keywords:**
temperature-disturbance front, integral method of heat balance, temperature-momentum integral, heat fl ow integral, temperature-function integral, hybrid integral method

**Page:**
1391

**STRUCTURAL-TECHNOLOGICAL METHODS FOR REDUCTION OF THERMAL STRESS IN GRINDING**

A study has been made of temperature fi elds occurring in a workpiece in the process of its fl at grinding. The author
has obtained relations making it possible to calculate the rate of heating and cooling of the machined workpiece at
any point of it with account of the machining regime and of the intensity of the heat fl ux and the time of its action, and
also the dependence of the stresses in the workpiece on the time of action of the heat source and its temperature. It
has been established that by changing the structural parameters of the cutting surface of the wheel and the relation
between the velocity of motion of the workpiece, the velocity of motion of the wheel, and the grinding depth, one can
control the time of action of the heat fl ux on the workpiece and reduce thermal stress of the process

**Author:**
T. N. Ivanova

**Keywords:**
thermal stress, fl at grinding, residual stress

**Page:**
1413

**INVESTIGATION OF THERMAL STRESSES IN A MONOBLOCK STOPPER AT DIFFERENT VALUES OF THE LINEAR EXPANSION COEFFICIENT**

An algorithm for investigation of the dynamics of temperature fi elds and thermal stresses in bodies of intricate
geometric shape has been developed on the basis of the fi nite-element method. With the example of a monoblock
stopper, the authors have modeled the process of heat transfer and the dynamics of thermal stresses, and also studied
thermal stresses at different values of the linear expansion coeffi cient. The maximum value of the linear expansion
coeffi cient whose excess terminates in the failure of the monoblock stopper has been determined under specifi ed
heat-transfer conditions.

**Author:**
N. D. Morozkin and V. I. Tkachev

**Keywords:**
temperature fi eld, thermal stresses, heat transfer, linear expansion coeffi cient, fi nite-element method

**Page:**
1419

**FORMATION OF THE TEMPERATURE FIELD OF DIELECTRIC FILMS AND OF A BASE IN THE FIELD OF A CONTINUOUS ION BEAM**

The infl uence of the temperature dependence of the thermal conductivity and heat transfer coeffi cients, as well
as of the emissivity of a dielectric fi lm and of an insulating base on formation of a stationary temperature fi eld of
the dielectric–base system exposed to irradiation by a continuous ion beam in air, has been studied theoretically.
Analytical expressions have been obtained for the temperature fi elds of a sample and base, as well as a system of
interrelated nonlinear algebraic equations for characteristic temperatures. With the aid of numerical solution of a
system of nonlinear algebraic equations, the dependences of the temperature of the irradiated surface of the sample–
base system and of the rear side of this system on the incident ion beam parameters have been found. It has been
established that these dependences are nonlinear. It has been found that heating of a sample, including its irradiated
surface, decreases substantially with increase in the thermal conductivity of the base

**Author:**
T. Kh. Salikhov and A. A. Abdurakhmonov

**Keywords:**
temperature fi eld, radiation physics, dielectrics

**Page:**
1425

**ON THE HYSTERESIS OF AERODYNAMIC CHARACTERISTICS OF A CYLINDER WITH A "FLUID FLARE" IMMERSED IN A SUPERSONIC THREE-DIMENSIONAL FLOW**

By using the model of an ideal inviscid perfect gas, the aerodynamic characteristics of a cylinder immersed in a stationary three-dimensional supersonic fl ow in the case of strong axisymmetrical blowing of air from the lateral surface into the shock layer ("fl uid fl are") are investigated. The aim of the present work is to compare the dependences of the aerodynamic characteristics of the cylinder with a ″fl uid fl are″ on the angle of attack on increase of the latter from zero to 10^{o}
(straight motion) and on its further decrease from 10o
to zero (backward motion).

**Author:**
F. M. Pakhomov

**Keywords:**
supersonic fl ow past a body, angle of attack, inviscid model of fl ow, cylinder with a blunted end face, blowing of a gas astern ("fl uid fl are″)

**Page:**
1431

**INFLUENCE OF THE GAS SATURATION OF A LIQUID ON THE PECULIARITIES OF UNSTEADY FLOWS IN INTRICATE PIPELINES**

Consideration has been given to liquid fl ows in a simple pipeline and in an intricate branched pipeline system with
local hydraulic resistances in the presence of gas release to form a fi ne-bubble two-phase suspension. On the basis
of a numerical method of characteristics, the authors have proposed an algorithm for calculation of such fl ows.
Peculiarities of transient hydrodynamic processes have been established which are due to the effects of gas release
on the startup of the system and it reaching a stationary regime of fl ow. With the example of feed lines of a system
of bipropellant low-thrust control rocket engines, the infl uence of gas release on the system′s operation in a pulsed
regime has been shown.

**Author:**
V. I. Timoshenko and Yu. V. Knyshenko

**Keywords:**
gas-saturated liquid, velocity of sound, method of characteristics, intricate pipeline system, transient processes

**Page:**
1434

**INFLUENCE OF GAS-DYNAMICAL NONSTATIONARITY ON LOCAL HEAT TRANSFER IN THE GAS–AIR PASSAGES OF PISTON INTERNAL-COMBUSTION ENGINES**

The results of experimental investigation of the effect exerted by gas-dynamical nonstationarity on the intensity of heat transfer in the intake and discharge manifolds of piston internal-combustion engines are presented. Experimental setups, instrumentation, and experimental procedures are described. Combined dependences of the change in the instantaneous fl ow velocity and in the local coeffi cient of heat transfer in the gas–air passages on the engine crank angle are analyzed. It is shown that the gas-dynamical nonstationarity reduces the local heat transfer intensity in

the gas–air passages of piston internal-combustion engines 1.3–2.5 times depending on the gas fl ow velocity (on the mode of engine operation). A method is suggested to account for the gas-dynamical nonstationarity by applying a correction coeffi cient of heat transfer mobility to the classical equations used for calculating the local heat transfer coeffi cient.

**Author:**
L. V. Plotnikov and B. P. Zhilkin

**Keywords:**
local heat transfer, gas-dynamical nonstationarity, gas fl ows, intake manifold, discharge manifold, gas exchange processes, piston internal-combustion engine.

**Page:**
1444

**HYDRODYNAMICS OF A NONSTATIONARY FLOW IN A MICROCYLINDER BEGINNING SUDDEN ROTATION**

Results of a theoretical investigation of an acceleration liquid fl ow in a microcylinder beginning sudden rotation are
presented. The problem on this fl ow was solved analytically with the use of the Laplace transform and the method of
groups of symmetries as well as numerically using the method of Boltzmann lattices. The nonstationary fl ow-velocity
profi les obtained analytically were compared with the results of a numerical solution. It is shown that the fl ow in the
microcylinder develops by the asymptotic law and that the time of stabilization of this fl ow increases with increase
in the Knudsen number. An analytical expression for the friction coeffi cient of the indicated fl ow has been obtained.

**Author:**
A. A. Avramenko, N. P. Dmitrenko, A. B. Kravchuk, Yu. Yu. Kovetskaya, and A. I. Tyrinov

**Keywords:**
acceleration fl ow, microcylinder, friction coeffi cient, velocity profi le, rotation moment

**Page:**
1452

**CRISIS OF THE LAMINAR FLOW OF A NON-NEWTONIAN LIQUID IN A PIPE**

The laminar-turbulent transition of fl ows of Newtonian (viscous) and non-Newtonian liquids in pipes was investigated
on the basis of the combined analysis of the generalized equation of the fi rst and second laws of thermodynamics
for a simple system and the Darcy–Weisbach equation. It is shown that a reason for the crises of the laminar fl ows
of such liquids in pipes is the disturbance of the balance between the positive entropy production and the negative
entropy fl ow in them. An analysis of calculation and experimental data on the disturbance of the laminar fl ow of
a non-Newtonian liquid in a pipe and the transformation of this fl ow into a turbulent fl ow has shown that the crises
of a laminar fl ow of an elastoviscoplastic liquid in a pipe happens at a larger critical Reynolds number compared to
that of a laminar fl ow of a viscoplastic liquid at one and the same values of the Hedstrom parameter

**Author:**
A. G. Potapov

**Keywords:**
laminar-turbulent transition, Newtonian and non-Newtonian liquids, entropy production, entropy fl ow

**Page:**
1462

**TWO-STAGE PROCESSING OF A MATERIAL WITH PREDOMINANT COMBUSTIBLE MATTER**

The authors have presented an improved technology for processing of organic substances, which is based on
an analysis of various methods described in the literature and results of experimental investigations of thermal
conversion and plasma-assisted pyrolysis, conducted at the A. V. Luikov Heat and Mass Transfer Institute of the
National Academy of Sciences of Belarus. The proposed technology includes two stages the fi rst of which is pyrolysis
with a temperature of 400 to 550o
C. The combustible matter of the material decomposes with the resulting formation
of volatile hydrocarbons and solid coke-ash residue with a high content of carbon and a developed surface. Thus,
after the pyrolytic stage step, the hydrocarbon part of the substance goes into a gas phase, and the coke-ash residue
is dispersed. The second stage is high-temperature (1100–1400o
C) processing of the products of the fi rst stage by the
mechanism of partial oxidation. Additional oxygen is fed to convert carbon into CO. As a result, all the hydrocarbons
are converted into a syngas which consists of CO and H2. This gas has a high calorifi c value and can be utilized as
a fuel in an electric generator. The inorganic matter can be vitrifi ed and is suitable for safe burial.

**Author:**
A. I. Leonchik, V. V. Savchin, G. V. Dolgolenko, D. S. Skomorokhov, I. V. Khvedchin, and N. M. Kurbanov

**Keywords:**
pyrolysis, plasma gasifi cation, processing of rubber, processing of wood

**Page:**
1468

**INFLUENCE OF THE PHYSICAL PROPERTIES OF MIXED BIOFUELS ON THE SPRAY CHARACTERISTICS**

An analysis has been made of the infl uence of the physical properties of mixed biofuels on the characteristics of
spraying by centrifugal atomizers. It has been shown that the characteristics of the jet downstream of devices
effectively atomizing oil fuels can signifi cantly degrade in using biofuels. To avoid collapse of the fuel bubble, it
is necessary to calculate the form of the fuel sheet. We have constructed the boundary curves in coordinates fuel
Reynolds number–Laplace number characterizing the transition from the ″tulip″ form of disintegration of the sheet
to its atomization and enabling one to determine the boundaries of the spraying region for any atomizer. The swirl of
the air surrounding the atomizer in the same direction as the twist of the fuel sheet markedly upgrades the spraying
characteristics of strongly bound fuels. The determining infl uence on the form of the sheet is exerted thereby by the
value of the tangential air fl ow velocity, and the value of the axial velocity is immaterial

**Author:**
A. Yu. Vasil′ev, A. I. Maiorova, A. A. Sviridenko, and O. G. Chelebyan

**Keywords:**
atomization, biofuel, centrifugal atomizer, combustion chamber

**Page:**
1475

**HEATING A GRANULAR BED BY A TUBULAR HEAT EXCHANGER**

Modeling of the process of thermal fl uidization of a ventilated granular bed by means of a heat exchanger in the form
of horizontal tubes positioned inside the bed is carried out.

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

**Keywords:**
granular bed, bubbling bed, tubular heat exchanger, thermal fl uidization, superheated vapor

**Page:**
1486

**CONDITIONS FOR EXPLOSIVE DISINTEGRATION OF INHOMOGENEOUS WATER DROPLETS ON HIGH-TEMPERATURE HEATING**

Experimental investigations of the characteristic stages of the processes of heating, evaporation, and explosive disintegration of inhomogeneous water droplets (with a commensurate graphite inclusion) in a high-temperature (600–1200 K) gaseous medium are carried out. Three methods of heating droplets differing in the dominating mechanism of heat transfer are used: heating in a muffl e tube furnace (thermal radiation), in a stream of heated air (radiative-convective heat transfer), and in a stream of high-temperature combustion products of a typical liquid fuel (radiative-convective heat transfer). Characteristic values of each heat fl ux component ate determined for the conditions of experiments, as well as their dependences on temperature. It is shown that the highest values of the radiative heat fl ux (determining one from the viewpoint of the origination of the effect of explosive fragmentation of droplets) correspond to the schemes of heating in a stream of combustion products and in a tubular muffl e furnace. The threshold values of the gaseous media temperatures at which a stable explosive disintegration of evaporating inhomogeneous droplets is realized (T_{g} > 850 K for conditions of heating in a stream of heated air, T_{g} > 800 K for the tubular muffl e furnace, and T_{g} > 600 K for a stream of combustion products) have been obtained experimentally.
With the use of thermocouple measurements the assumption on accumulation of the energy of thermal radiation near
the liquid–solid particle interface and on the resulting formation of an additional source of liquid fi lm heating has
been confi rmed, which leads to the overheating of the liquid and to explosive disintegration of the droplet.

**Author:**
O. V. Vysokomornaya, M. V. Piskunov, G. V. Kuznetsov, and P. A. Strizhak

**Keywords:**
inhomogeneous droplet, graphite particle, explosive fragmentation, disintegration, intense vaporization, heat flux.

**Page:**
1496

**GRAVITY SEDIMENTATION-INDUCED DEFORMATION OF A DROPLET UNDER CONDITIONS OF BLOWING-OVER BY AN INCOMING AIR STREAM**

The results are presented of experimental investigation of the loss of the viscous droplet shape stability in the course
of gravity sedimentation of droplet under conditions of blowing-over by an incoming stream at low Weber numbers
(We < 7). A new scheme of a setup for studying the droplet deformation by aerodynamic forces is suggested, with the
aid of which a qualitative picture of droplet deformation and an empirical dependence of the degree of deformation
on the Weber number have been obtained in the range of Reynolds numbers Re = 490–2070.

**Author:**
A. Antonnikova, V. A. Arkhipov, S. A. Basalaev K. G. Perfi l′eva, A. S. Usanina, and G. R. Shrager

**Keywords:**
droplet, blowing-over fl ow, deformation degree, Weber number, Bond number, Reynolds number, experimental investigation.

**Page:**
1505

**ESTABLISHMENT OF TEMPERATURE IN RADIATIVELY COOLED DISPERSE FLOW IN THE PRESENCE OF EXTERNAL THERMAL RADIATION**

The problem of establishing the temperature profi le in a radiatively cooling-down disperse fl ow in the presence
of external thermal radiation is considered. A comparison of the obtained analytical estimates of the speed of
establishment of an equilibrium profi le with the results of numerical solution is made. The amplitude of the wave
phenomena accompanying the establishment of temperature has been calculated.

**Author:**
A. A. Safronov, A. A. Koroteev, and N. I. Filatov

**Keywords:**
radiative cooling, disperse fl ow, discrete medium, nonlinear dynamics, wave processes

**Page:**
1514

**TWO-PHASE FLOW IN A PLANT FOR PRODUCTION OF CAVITATION DIAMONDS**

Consideration is given to the regimes of water fl ow in a hydrodynamic-fl ow plant with cavitation and hydraulic
shock. Calculations are carried out by the CFX hydrodynamic unit of the general physical computational system
ANSYS and are compared with experimentally measured values of pressure; fl ow velocities are also computed. It is
shown that the hydraulic shock ensures a growth of the order of 5 atm in the external pressure on a vapor bubble. The
possibility of the nanodiamond forming in fl ows of carbon-containing fl uids in such regimes is discussed.

**Author:**
A. Yu. Dnestrovskii, N. V. Dushenko, and S. A. Voropaev

**Keywords:**
cavitation, ANSYS, nanodiamonds, two-phase fl ows

**Page:**
1521

**ON THE THEORY OF INJECTION OF A COLD GAS INTO A SNOW MASS ACCOMPANIED BY HYDRATE FORMATION**

The problem on the formation of a gas hydrate in a snow mass, whose pores in the initial state are saturated with
a gas, in the process of injection of the same gas into this mass was considered. Self-similar solutions defi ning the
distributions of the main parameters of the snow mass (its temperature, pressure, and phase saturation) have been
constructed. It is shown that, depending on the initial thermobaric state of the snow–gas system and the intensity of
injection of the gas into the snow mass, in its fi ltration region there can arise three characteristic zones: a near zone
in which the snow turned completely into the hydrate state and which, consequently, is saturated with the gas and the
hydrate, an intermediate zone in which the gas, the snow, and the hydrate are at phase equilibrium, and a far zone
fi lled with the gas and snow. It was established that the extension of the three-dimensional zone of hydrate formation
in a snow mass decreases with increase in its initial snow saturation, an intermediate hydrate-formation zone of
larger length arises in a snow mass with a higher permeability, and this zone is heated more intensively in a snow
mass with a lower initial temperature in which, for this reason, the snow fraction at the near boundary is increased.

**Author:**
V. Sh. Shagapov, A. S. Chiglintseva, A. A. Rusinov, and M. K. Khasanov

**Keywords:**
cold gas, snow mass, self-similar solution, hydrate formation, three-dimensional region, Leibenzon linearization

**Page:**
1527

**INFLUENCE OF THE RELAXATION DEFORMATION OF ROCKS ON THE CHARACTERISTICS OF NONISOTHERMAL FILTRATION OF LIVE CRUDE IN THE STRATUM**

Consideration is given to the thermohydrogasdynamic problem on studying the infl uence of the relaxation
deformation of rocks on the dynamic characteristics of fi ltration processes occurring in an oil stratum with account
of the temperature conditions in it. It has been shown that in nonstationary nonisothermal fi ltration, the infl uence of
the relaxation deformation of rocks on the characteristics of fi ltration in the oil stratum is diminished.

**Author:**
B. Z. Kazymov

**Keywords:**
deformation, relaxation, convection, pressure, porosity, oil saturation, production rate.

**Page:**
1539

**METAL–FULLERENE FILMS AND COATINGS. PRODUCTION AND SOME PROPERTIES**

The structure of fi lms and coatings obtained by condensation of metal (Cu, Al, Ni, Ti) atoms and C60-fullerene
molecules from combined fl ows of these atoms and molecules in a vacuum and the electrical and frictional properties
of the indicated fi lms and coatings were investigated. It was established that the introduction of fullerenes into metal
fi lms and coatings substantially changes their structure and the electrical and frictional characteristics (by several
times in some cases) even if the content of C60 in them comprises 1.0 wt.%. It is shown that fullerenes can be used to
advantage for control of the structure and properties of materials.

**Author:**
E. M. Shpilevsky, S. A. Filatov, G. Shilagardi, P. Tuvshintur,b and D. Ulam-Orgikh

**Keywords:**
fi lms, coatings, fullerene, metal–fullerene complex, friction coeffi cient, wear, electrical resistance

**Page:**
1543

**SIMULATION OF THE INTERNAL STRUCTURE OF A TANDEM-TYPE PLASMATRON**

Numerical simulation of a tandem-type plasmatron intended for supersonic plasma spraying of metallic and ceramic
materials at atmospheric pressure has been carried out. The calculation results are compared with experimental
data. The internal gas dynamics of the plasmatron and the interaction of a plasma stream with spray particles are
presented in the form of distributions of the main thermal and kinetic characteristics of stream.

**Author:**
A. Essiptchouk and L. Charakhovski

**Keywords:**
high-velocity plasma spraying, cold spraying, plasma powder spraying, computer simulation

**Page:**
1550

**CALCULATION OF THE SPACE CHARGE LAYER THICKNESS WITH ACCOUNT FOR THE DIPOLE MOMENT OF WATER MOLECULES IN KCl AND NaCl SOLUTIONS**

The problem of the electric double layer in electrolytes is considered. The Poisson equation is integrated with
account for the screening of electrodes by salt ions and water molecules. The space charge layer has been calculated.
The volt–ampere characteristics in NaCl and KCl solutions are presented. A method for determining the temperature
of ions from the volt–ampere characteristic of the electrolyte solution is proposed.

**Author:**
S. A. Varzin and S. A. Gutsev

**Keywords:**
electrolyte, ions, volt–ampere characteristic, space charge layer, distribution function, temperature, concentration.

**Page:**
1558

**INVESTIGATION OF PASSIVE SYSTEMS FOR THERMAL CONTROL OF SPACECRAFT**

Physical and mathematical simulation of the heat exchange in a multilayer heat-insulating coating found in an
experimental module have been performed. On the basis of the results obtained, requirements on the quality of
such coatings and the conditions of their testing have been developed. A mathematical formulation of the inverse
problem on the heat conduction in the indicated coating is presented. From the solution of this problem, with the
use of the results of testing of such a coating, temperature dependences of its thermophysical parameters have been
constructed

**Author:**
S. A. Budnik, A. N. Nenarokomov, and D. M. Titov

**Keywords:**
thermophysical properties, vacuum heat shield insulation, inverse problem on heat conduction.

**Page:**
1565

**DETERMINATION OF THE TEMPERATURE DEPENDENCE OF THE ISOBARIC VOLUMETRIC EXPANSION COEFFICIENT FOR CERTAIN MOLECULAR CRYSTALS OF NITRO COMPOUNDS**

This paper presents the form of the equations of state of molecular crystals of nitro compounds constructed on the
basis of dividing Helmholtz free energy into an intramolecular and an intermolecular components. This division
enabled us to determine the form of the Grüneisen equation for molecular crystals, the volume dependence of
the Grüneisen coeffi cient, and the temperature dependence on the volumetric expansion coeffi cient. Comparative
analysis of the calculated and experimental values of volumes of elementary cells of triaminotrinitrobenzene crystals
depending on the temperature has shown their fair agreement

**Author:**
Yu. M. Kovalev

**Keywords:**
equation of state, molecular crystal, Helmholtz energy, Planck constant, Boltzmann constant, Debye approximation, Einstein approximation

**Page:**
1573

**LIMITING STATES OF A MICROLAYERED PLATE IN BRITTLE AND DUCTILE FRACTURE DUE TO THE CHANGE IN THE TEMPERATURE FIELD**

Schemes of ductile and brittle fracture of a microlayered plate with cuts upon the change in its temperature fi eld have
been presented. The infl uence of the microinhomogeneity of the plate′s material on its thermal conductivity, elasticity,
and heat capacity, and also on the value of stresses in it has been investigated

**Author:**
Yu. M. Pleskachevskii and Yu. A. Chigareva

**Keywords:**
plasticity, cuts, fracture, stress-intensity factors, orthotropism.

**Page:**
1583

**IMPROVEMENT OF THE REFLECTIVITY OF FLAT COATINGS**

Consideration is given to the possibility of improving the refl ectivity of a fl at refl ecting surface using the nonabsorbing
coating of assigned thickness applied to it

**Author:**
S. R. Kasimova

**Keywords:**
electromagnetic wave, refl ection surface

**Page:**
1592

**FORMULATION OF THE J-INTEGRAL FOR THE BIOT ELASTIC POROUS MEDIUM MODEL**

This paper considers the thermodynamically substantiated derivation of the scalar and vector forms of the J-integral
for the Biot elastic porous medium model representing a permeable deformable matrix saturated with a fl uid, which is
described as a double continuum and whose behavior is determined by coupled equations of elasticity and fi ltration
theory

**Author:**
M. M. Ramazanov, B. V. Kritskii, and E. B. Savenkov

**Keywords:**
fracture mechanics, J-integral, porosity and elasticity, Biot equations.

**Page:**
1595

**ADSORPTION AND DIFFUSION OF HYDROGEN ON LOW-INDEX (110) AND (111) SURFACES OF ALUMINUM**

By the density-functional method, the authors have considered the energetics of adsorption and diffusion of a
hydrogen molecule into atomically thin aluminum plates with body-centered tetragonal and rhombohedral crystallite
structures bounded by the (110) and (111) surfaces, and also geometric confi gurations of surface aluminum hydrides.
It has been shown that physical adsorption of H2 molecules on the Al(110) and Al(111) surfaces is a weak exothermic
process. Polarization and deformation due to the physical adsorption lead to a certain increase in the H–H
interatomic spacing (0.734 Å).
The diffusion of the hydrogen atoms into body-centered tetragonal and rhombohedral plates tends to increase
the system's energy. It has been found that hydrogen diffuses most easily through the Al(110) surface; in atomic
diffusion through the subsurface layer, the energy grows up to 1.1 eV. A stable energy state is attained due to the
formation of a tetrahedral hydrogen complex.

**Author:**
A. L. Zaitsev and T. N. Genarov

**Keywords:**
adsorption of hydrogen, diffusion of hydrogen, aluminum hydride, low-index aluminum surface, ab initio solution

**Page:**
1603

**MODELING OF THE PROCESS OF HYDROLYSIS OF SODIUM BOROHYDRIDE IN A CIRCULATING REACTOR**

The authors have presented a mathematical model of heat- and mass-transfer processes in a circulating-type reactor

implementing the hydrolysis of sodium borohydride in the hydrogen generator. The model was used to analyze two

methods of control of the generator output and can be applied to scaling and optimization of structures of generators

of this type.

**Author:**
S. I. Shabunya, V. I. Kalinin, V. G. Minkina, and V. V. Martynenko

**Keywords:**
hydrogen generator, circulation scheme, mathematical model, sodium borohydride.

**Page:**
1617