#### Volume 88, №6

**NONISOTHERMAL FLOW OF A REACTIVE FLUID WITH SIMULTANEOUS IMPREGNATION OF A POROUS LAYER**

Consideration is given to the nonisothermal filling of a plane cavity with a Newtonian chemically reactive fluid with
simultaneous impregnation of a porous layer. Flow in the plane cavity is described by noninertial Navier–Stokes
equations, and in the porous layer, by the Darcy equation; fl ow in the region adjacent to the boundary between
the fluid and the porous layer is defi ned using the Brinkman equation. The viscosity is taken to be dependent on
temperature and on the extent to which the chemical reaction proceeds. A single-temperature model is used as the
energy equation. Temperature fi elds in the region of a channel and in the porous layer are interrelated by conjugate
fourth-kind boundary conditions. An example of determining the maximum allowable molding time is shown.

**Author:**
A. V. Baranov

**Keywords:**
Newtonian fluid, heat transfer, shear flow, impregnation, molding

**Page:**
1311

**NONSTATIONARY MASS TRANSFER NEAR THE SURFACE OF A CYLINDRICAL BODY**

The problem of nonstationary diffusion of the target component to a phase that is external relative to the surface of
a cylindrical body has been formulated and solved analytically. From the found solution the dependences have been
obtained for calculating the instantaneous mass transfer coeffi cient and the phase-contact-time mean mass transfer
coeffi cient, on the basis of which the process of extraction of technological pollutants from fi brous materials has
been analyzed.

**Author:**
S. P. Rudobashta, M. K. Kosheleva, and É. M. Kartashov

**Keywords:**
mass transfer coefficient, diffusion, extraction, fibers

**Page:**
1320

**PRESSURE FIELD IN THE PROCESS OF RADIAL FILTRATION IN A NONUNIFORM ORTHOTROPIC STRATUM IN THE ASYMPTOTIC APPROXIMATION **

Simple analytical formulas for defi nition of the pressure fi eld, formed in the process of continuous withdrawal of a
fluid from a nonuniform anisotropic stratum, in the zero and fi rst approximations on the assumption that the fl uid flow
in the stratum is one-dimensional and linear were derived on the basis of the modifi ed asymptotic method exact on
average. The results of calculations of the pressure fi elds in such stratums by the formulas obtained are presented.

**Author:**
A. I. Filippov, O. V. Akhmetova, and M. R. Gubaidullin

**Keywords:**
pressure field, filtration, asymptotic method, nonuniform orthotropic stratum

**Page:**
1329

**ON NONSTATIONARY PROCESSES OF HEAT TRANSFER IN A BED OF FINELY DISPERSED CAPSULES IN THE PRESENCE OF PHASE TRANSITION**

Within the framework of the two-temperature model, the authors have investigated the dynamics of charging and

discharging of a bed of fi nely dispersed spherical capsules. Generalized dependences have been obtained for

calculating the times of charging and discharging of a heat accumulator.

**Author:**
Yu. S. Teplitskii and A. R. Roslik

**Keywords:**
heat accumulator, enthalpy method, two-temperature model, charging, discharging, paraffin

**Page:**
1341

**CRITERION OF OCCURRENCE OF FILTRATION CONVECTION OF A MIXTURE WITH ACCOUNT OF EQUILIBRIUM AND NONEQUILIBRIUM ADSORPTION**

Convective stability of a binary mixture in a porous medium has been studied with account taken of equilibrium
and nonequilibrium adsorption. The regularities of the infl uence of the parameters of equilibrium adsorption and of
kinetic coeffi cients in the case of nonequilibrium adsorption on the conditions of occurrence of convection have been
established. A comparison of the results with the case of the absence of adsorption has been presented.

**Author:**
M. M. Ramazanov and N. S. Bulgakova

**Keywords:**
filtration convection, adsorption of the components, porous medium

**Page:**
1351

**FRONTAL REGIME OF HEAT AND MASS TRANSFER IN A GEOTHERMAL BED**

Based on an earlier proposed mathematical model, the conditions for the existence of a frontal regime of steam
extraction from a high-temperature bed have been derived. It is shown that unlike the familiar one-dimensional case,
in the radial-symmetrical model considered the radius of the region occupied by steam tends to a limiting value,
that is, the front of boiling that separates the regions of water and steam practically comes to a stop after a time.
A formula has been derived pointing clearly to the dependence of the indicated limiting value of the front radius on
the water and steam parameters as well as on the characteristics of the geothermal bed. It is shown that for the steam
to occupy a considerable region around the well when the bed is in service, it is necessary that the initial state of
water be close to that of steam generation. Otherwise the front of boiling in the considered regime of heat and mass
transfer extends from the well only a little.

**Author:**
A. B. Alkhasov, M. M. Ramazanov, and D. A. Alkhasova

**Keywords:**
steam generation in a bed, heat and mass transfer, fl ow regimes, radial model, analytical solution

**Page:**
1358

**EVAPORATION AND CONDENSATION OF MOISTURE IN A MOLE-PLOWED SOIL**

Consideration is given to temperature waves, traveling in a soil from its surface, with account for phase transitions
of moisture and for the influence exerted by mole passages made by a special technology. It is pointed out that
evaporation and condensation, rather than a fl ux of soil air, introduce noticeable corrections into the distribution
of the soil layer temperature. An analysis of the problem and evaluating solutions are given and a technique of
calculation of the moisture condensed in mole passages and in the rooty layer of soil is suggested. Weather data
for Yuzhno-Sukhokumsk are used. The results are applicable to the climatic conditions of the Prikaspiiskaya (NearCaspian)
semidesert.

**Author:**
M. G. Alishaev

**Keywords:**
air, moisture content, evaporation, condensation, mole passage, soil, filtration, temperature, traveling wave.

**Page:**
1366

**MATHEMATICAL MODEL OF A THERMOSTATING COATING WITH A THERMOELECTRIC MODULE**

On the basis of a variational formulation of the problem of stationary heat conduction in a heterogeneous solid,
a mathematical model of a fragment of a fl at heat-insulating layer containing a thermoelectric module has been
constructed. This model has been used to establish conditions under which, when fulfi lled, the heat-insulating layer
can serve as a thermostating coating for an object with a given fi xed temperature under convective-radiative heat
exchange on the outer surface of the fragment under consideration. The results of the qualitative analysis of the
proposed model are presented.

**Author:**
V. S. Zarubin, G. N. Kuvyrkin, and I. Yu. Savel′eva

**Keywords:**
heat insulation, thermostating Peltier effect, thermoelectric module

**Page:**
1373

**INFLUENCE OF MICROWAVES ON THE THERMAL CONDITIONS OF A "POLYMER–SEMICONDUCTOR–COMPOSITE" SYSTEM**

A numerical analysis of the influence of microwaves on the thermal conditions of elements of electronic equipment
(EE) has been carried out. Investigations have shown that the temperature fi eld of the ″polymer–semiconductor–
composite″ system under the action of microwaves is nonuniform. It has been established that under rather typical
operating conditions with increasing electric fi eld intensity there is a considerable increase (from 362 to 387 K) in
the maximum temperature of the modeled object. Such a strong infl uence of microwaves on the thermal conditions of
the ″polymer–semiconductor–composite″ system is comparable to the increase in the ambient temperature by 20 K
or the increase in the heat release of the internal source by 30%.

**Author:**
V. G. Kuznetsov and E. V. Kravchenko

**Keywords:**
radio emission, microwave heating, unstable thermal conditions, computational modeling, finite difference method

**Page:**
1381

**METHOD OF BOUNDARY CHARACTERISTICS**

A new integral method based on the system of identical equalities of 2n-multiple integrals of the desired temperature
function and the corresponding boundary characteristics is presented. This method was used for the approximate
solution of problems of a semi-bounded space and a lengthy plate with fi rst-kind boundary conditions. The results
obtained show that the integral method of boundary characteristics surpasses the analogous integral methods by
several orders of magnitude in accuracy and convergence of approximate solutions. The solutions constructed with
this method are exact in essence because the errors in determining parameters in a wide range of their values
comprise hundredths and ten-thousands of a percent

**Author:**
V. A. Kot

**Keywords:**
heat-condition equation, boundary characteristics, disturbance front, heat-balance integral, identical equality, integral method

**Page:**
1390

**ENGINEERING APPROACH TO THE DETERMINATION OF THE RADIATION FIELD OF A POLYETHYLENETEREPHTHALATE (PET) MEDIUM UNDER RADIANT HEATING**

An engineering approach to the determination of the radiation fi eld of the PET medium under radiant heating is
proposed. Instead of the reverse counting procedure for determining the radiation intensity in the negative direction,
we make a correction that has a superposition character and can be determined through the refl ection coeffi cient at
the boundary and the already determined radiation fi eld in the positive direction inverted in the coordinate direction.
The structure of the given approach provides a reasonable balance between the adequacy of calculations and the
computational resource consumption and permits estimating quickly the necessary machine time expenditures.

**Author:**
D. É. Sidorov, A. E. Kolosov, O. V. Pogorelyi, and A. A. Gur′eva

**Keywords:**
polyethyleneterephthalate (PET), radiant heating, semitransparent medium, radiation field, numerical calculation.

**Page:**
1409

**SIMULATION OF CONVECTIVE HEAT EXCHANGE IN THE ELECTRICALLY CONDUCTING LIQUID IN A SPHERICAL CAVITY. ALGORITHM OF SOLUTION**

An algorithm is proposed for calculating the convective heat exchange in a spherical cavity modeling the liquid
core of the Earth with account for the internal heat sources and the Joule dissipation in the electrically conducting
liquid in it.

**Author:**
S. V. Solov′ev

**Keywords:**
convective heat exchange, magnetic hydrodynamics, Joule dissipation, spherical cavity

**Page:**
1416

**SIMULATION OF THE KINETICS OF GROWTH OF IRON NANOPARTICLES IN THE PROCESS OF CHEMICAL VAPOR DEPOSITION OF HYDROCARBONS WITH INJECTION OF FERROCENE FOR THE SYNTHESIS OF CARBON-NANOTUBE ARRAYS**

A kinetic model of growth of iron nanoparticles in the process of synthesis of carbon-nanotube arrays in an injectiontype
reactor of chemical vapor deposition, in which iron nanoparticles are formed as a result of the coalescence
of iron atoms representing products of the thermal decomposition of a mixture of ferrocene with xylene, has been
developed. It is shown that the formation of iron nanoparticles in the indicated reactor is very nonequilibrium in
character. The parametric dependences of the monodisperse distributions of iron nanoparticles by their diameter,
number density, and volume fraction on the fl ow rate of nitrogen, the temperature of the high-temperature region
in the reactor, and the concentration of ferrocene in xylene have been obtained. The calculations performed have
shown that the diameter of the iron nanoparticles formed increases monotonically with increase in the temperature
of the chemical vapor deposition of hydrocarbons and the concentration of ferrocene in xylene and, quite the reverse,
decreases monotonically with increase in the rate of the nitrogen fl ow. The calculated and experimental diameters
of the iron nanoparticles formed at mass fractions of ferrocene in xylene of 0.5–10% were compared. The model
proposed can be used for calculating the synthesis of carbon nanotubes in a chemical-vapor-deposition reactor
of the injection type.

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

**Keywords:**
chemical vapor deposition, injection-type CVD reactor, carbon nanotubes, iron nanoparticles, coalescence, nanotube array, heterogeneous catalysis, transition metals, metallorganic materials, ferrocene, hydrocarbons, xylene

**Page:**
1432

**ISOTHERMAL DEPOSITION OF DROPLETS AND NANOPARTICLES FROM THE INCIDENT GAS JET ONTO A SUBSTRATE**

By computational-hydrodynamics methods the authors have investigated the fi eld of the gas velocity in the fl ow
developed after the turn of the gas jet near the substrate. Consideration has been given to the problem on deposition
of charged micron-size droplets from radial fl ow above the substrate by the action of the external electrostatic fi eld.
A study has been made of the infl uence of Brownian diffusion on the nanoparticle deposition from the laminar radial
fl ow above the substrate. The authors have introduced similarity numbers for these problems and have determined
their infl uence on the effi ciency of deposition.

**Author:**
Yu. A. Stankevich and S. P. Fisenko

**Keywords:**
computational gasdynamics, laminar fl ow, electrostatic deposition, Brownian diffusion

**Page:**
1442

**SYNTHESIS OF CARBON NANOSTRUCTURES ON NICKEL NANOPOWDERS PRODUCED BY THE METHOD OF ELECTRIC EXPLOSION OF CONDUCTORS**

The authors present the results of experiments on the synthesis of carbon nanostructures by the method of thermal
chemical gas-phase deposition with the use of nickel nanopowders produced by the method of electric explosion
of conductors and utilized as the catalysts. To study the process of origination and growth of individual carbon
nanostructures, the authors conducted experiments not only on nanopowders, but also on separated clusters.
Experiments were conducted at different temperatures (200–700^{o}C) and pressures (100–400 mbar) to determine
optimum conditions and the lower temperature boundary for carbon-nanostructure synthesis. The experiments have
shown that the lower boundary of synthesis for nanopowders is a temperature of 325^{o}C. For the separated powders,
as for the nanopowders, stable growth of carbon nanostructures was observed at 350^{o}C, but at pressures lower
than 300 mbar. Unlike the carbon nanostructures produced on nanopowders, carbon nanostructures on separated
powders exhibit a strong dependence of their origination and growth on temperature and pressure. Results of the
Raman spectroscopy and of the x-ray structural analysis have shown that carbon nanostructures grown at 325^{o}C
and 300 mbar have the highest purity.

**Author:**
G. Partizan, B. Z. Mansurov, B. S. Medyanova, B. A. Aliev, and Xin Jiang

**Keywords:**
carbon nanostructure, nanopowders, nickel, thermal chemical deposition, gas phase

**Page:**
1451

**CONTROL OF THE SYNTHESIS OF SUBMICRON TITANIUM DIOXIDE PARTICLES IN A CONTINUOUS PLASMA-CHEMICAL REACTOR**

A simulation of the formation and growth of titanium dioxide particles in the working zone of a plasma-chemical
reactor has been performed. The possibility of use of the premixing of reagents (titanium tetrachloride and oxygen)
outside the reactor for increasing the yield of the fi nal product was investigated. Calculations of the formation
and growth of titanium dioxide particles were performed for different values of parameters of the physical and
mathematical model of the process.

**Author:**
S. M. Aul′chenko and E. V. Kartaev

**Keywords:**
titanium dioxide, plasma-chemical reactor, quasi-gasdynamic system of equations, homogeneous and heterogeneous reactions, nucleation, coagulation

**Page:**
1459

**HEAT TRANSFER BETWEEN A PLASMA JET AND A METAL SURFACE IN A CUT CAVITY**

Investigations are presented of the formation of a plasma jet and of the current-density and heat-fl ux distributions
in the process of metal cutting along the cut cavity with direct and reverse polarities of the plasmatron connection.
The study of the specifi c features of heat transfer of the arc with the surface of the cut cavity was carried out on the
basis of the developed plasma unit which makes it possible to model the technological process of separating metal
cutting. A sectional cut model is proposed which can be used to work out and optimize the methods of determination
of cutting parameters.

**Author:**
A. N. Veremeichik, M. I. Sazonov, V. M. Khvisevich, and D. L. Tsyganova,

**Keywords:**
metal cutting, plasmatron, electric arc

**Page:**
1466

**PLASMACHEMICAL PROCESSING OF MEDICOBIOLOGICAL WASTES**

The process of processing medicinal wastes by plasma methods has been investigated. Thermodynamic calculations of
the processing of wastes have been performed using bones of animal origin as an example. Experimental investigations
were carried out in a plasma chamber furnace equipped with an electric arc plasmatron of power 30 kW

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

**Keywords:**
medicobiologic wastes, plasma methods, thermodynamic calculations, plasma chamber furnace

**Page:**
1471

**IONIZATION OF AIR IN A RANQUE–HILSCH VORTEX TUBE AND THE METHOD OF OBTAINING UNI- AND BIPOLAR IONIZATION**

Results of investigations on determining the principles of ionization in a Ranque–Hilsch vortex tube have been
given. The existing principles of ionization and the possibilities for them to occur in a Ranque–Hilsch vortex tube
have been considered. Conclusions based on an analysis of ionization methods have been drawn. With the aim of
establishing processes occurring in the vortex tube, the authors have developed a procedure, have identifi ed the goal
and objectives of testing, have created a test bench, and have conducted experimental investigations on the physical
prototype of a vortex tube. Testing results have been given in the form of plots. An analysis of the results has been
made, and conclusions have been drawn. On the basis of the conducted investigations, the authors have proposed
a novel method of ionization of air and control over the parameters of uni- and bipolar ionization. A diagram of the
device developed for air ionization has been presented.

**Author:**
K. V. Lebedinskii, N. E. Kurnosov, A. A. Nikolotov, and D. P. Alekseev

**Keywords:**
ionization, vortex tube, balloelectric effect, magnetic field.

**Page:**
1476

**SIMULATION OF NON-NEWTONIAN EMULSION FLOWS IN MICROCHANNELS**

Simulation of emulsion flows in differently shaped microchannels to reproduce the choking of such flows as a result
of the effect of dynamic blocking has been made. A model of a highly concentrated emulsion as a structure of tightly
packed deformed droplets surrounded by elastic shells is considered. The motion of liquid was determined by the
method of the lattice Boltzmann equations together with the immersed boundary method. The infl uence of the nonNewtonian
properties and of elastic turbulence of the indicated emulsion, as well as of the elasticity of the shells of
its droplets and of the interaction of these shells on the emulsion motion in a microchannel, has been investigated.
It is shown that the flow of this emulsion can be slowed down substantially only due to the mutual attraction of the
shells of its droplets.

**Author:**
I. V. Malanichev and F. G. Akhmadiev

**Keywords:**
emulsion, effect of dynamic blocking, computational hydrodynamics, method of the lattice Boltzmann equations, method of immersed boundary

**Page:**
1483

**HYDRODYNAMIC ASPECTS OF THE TOMS EFFECT**

The physicomathematical model of migration of polymers in a liquid turbulent fl ow in a pipe is based on a comparison
of forces transverse to the motion of the mainstream fl ow: the Saffman, Magnus, and turbophoresis forces. It has
been shown that the polymer particles are grouped near a certain boundary within the limits of the boundary layer.
On this basis, the authors have made assumptions on the mechanism of suppression of turbulent pulsations and
decrease in the viscous friction near the wall, which makes up the Toms effect. The proposed model satisfi es, at least,
qualitatively, various actually observed manifestations of the effect.

**Author:**
S. A. Strel′nikova, G. V. Tkachenko, and B. A. Uryukov

**Keywords:**
turbulent flow in pipelines, polymer additives, Toms effect, Magnus effect, Saffman force

**Page:**
1491

**TURBULENT BOUNDARY LAYER ON A FINELY PERFORATED SURFACE UNDER CONDITIONS OF AIR INJECTION AT THE EXPENSE OF EXTERNAL FLOW RESOURCES**

The characteristics of an incompressible turbulent boundary layer on a fl at plate with air blown in though a fi nely
perforated surface from an external confi ned fl ow through an input device, located on the "idle" side of the plate, have
been investigated experimentally and numerically. A stable decrease in the local values of the coeffi cient of surface
friction along the plate length that attains 85% at the end of the perforated portion is shown. The experimental and
calculated data obtained point to the possibility of modeling, under earth conditions, the process of controlling a
turbulent boundary layer with air injection by using the resources of an external confi ned fl ow.

**Author:**
V. I. Kornilov, A. V. Boiko, and I. N. Kavun

**Keywords:**
turbulent boundary layer, flat plate, finely perforated surface, blowing-in (injection), input device, friction

**Page:**
1500

**MAGNETOHYDRODYNAMIC PHENOMENA AND HEAT TRANSFER NEAR A ROTATING DISK**

We propose an approach that permits constructing an analytical solution of the problem of flow and heat transfer in
a viscous compressible conducting medium near an infi nite dielectric disk rotating in a homogeneous magnetic field.
The influence of the magnetic fi eld on the process of heat transfer near the disk surface has been investigated. It has
been shown that Joule energy dissipation prevails over viscous dissipation at moderate magnetic fi elds.

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

**Keywords:**
rotating disk, boundary layer, conducting gas, flow and heat transfer

**Page:**
1513

**INFLUENCE OF THE GEOMETRIC PARAMETER ON THE REGIMES OF NATURAL CONVECTION AND THERMAL SURFACE RADIATION IN A CLOSED PARALLELEPIPED**

We have performed a numerical analysis of the stationary regimes of thermogravitational convection and thermal
surface radiation in a closed differentially heated parallelepiped. The mathematical model formulated in dimensionless
natural velocity–pressure–temperature variables was realized numerically in the control volume approach. Analysis
of the radiative heat exchange was carried out on the basis of the surface radiation approach with the use of
the balance method in the Polyak variant. We have obtained three-dimensional temperature and velocity fi elds, as
well as dependences for the mean Nusselt number refl ecting the infl uence of the geometric parameter, the Rayleigh
number, and the reduced emissive factor of the walls on the fl ow structure and the heat transfer.

**Author:**
S. G. Martyushev, I. V. Miroshnichenko, and M. A. Sheremetb,

**Keywords:**
natural convection, thermal surface radiation, diathermal medium, parallelepiped, control volume approach

**Page:**
1522

**PRESSURE DISTRIBUTION IN THE ANNULUS BETWEEN ROTATING COAXIAL CYLINDERS AT LARGE SHEAR STRESSES**

Results of an experimental study of the excess pressure distribution in the annulus between the inner rotating and the
outer immovable coaxial cylinders at large shear stresses are reported.

**Author:**
V. D. Tyutyuma

**Keywords:**
isentropic model of momentum transfer, equations of motion, viscous compressible medium, fl ow in the annulus between rotating cylinders, pressure distribution

**Page:**
1530

**COMMENTS ON THE PAPER "UNSTEADY RADIATIVE-CONVECTIVE BOUNDARY-LAYER FLOW OF A CASSON FLUID WITH VARIABLE THERMAL CONDUCTIVITY" BY M. GNANESWARA REDDY**

The comments on the recently published paper by M. Gnaneswara Reddy are presented. It is shown that the similarity
transformations made in the paper are not correct.

**Author:**
P. M. Patil

**Keywords:**
similarity solution, unsteady boundary layer, Casson fluid, variable thermal conductivity, thermal radiation, stretching surface

**Page:**
1534

**ELECTROMAGNETIC EFFECTS ON WAVE PROPAGATION IN AN ISOTROPIC MICROPOLAR PLATE**

The generalized theory of thermoelasticity is applied to study the propagation of plane harmonic waves in an infi nitely
long, isotropic, micropolar plate in the presence of a uniform magnetic fi eld. The present analysis also includes the
thermal relaxation time, electric displacement current, and the coupling of heat transfer and microrotation of the
material. To determine the effect of the presence of thermal as well as magnetic fi elds on the phase velocity, two
potential functions are used, and more general dispersive relations are obtained for symmetric and antisymmetric
modes. The results for the cases of coupled thermoelasticity, magnetoelasticity, micropolar thermoelasticity, and
classical micropolar elasticity as special cases are derived. The changes in the phase velocity and attenuation
coeffi cient with the wave number are shown graphically.

**Author:**
S. Shaw and B. Mukhopadhyay

**Keywords:**
thermoelasticity, micropolar plate, plane harmonic waves, micropolar thermoelasticity, magnetoelasticity, symmetric mode, antisymmetric mode

**Page:**
1537

**ERRORS IN DETERMINING THE THERMOPHYSICAL CHARACTERISTICS OF HETEROGENEOUS HIGH-ENERGY MATERIALS BY THE LASER-PULSE METHOD**

An analysis has been carried out with respect to the errors incurred in the determination of the thermophysical
characteristics of the high-energy heterogeneous material "aluminum–ammonium perchlorate–butyl rubber" and
associated with the radiation transfer of energy in the heated layer under conditions corresponding to the realization
of the laser-pulse method in the course of action of a fi nite-length collimated laser pulse on the material surface. The
infl uence of the radiation absorption process on the magnitude of this error has been established

**Author:**
M. D. Kats and I. M. Kats

**Keywords:**
heterogeneous material, thermophysical characteristics, laser-pulse method, systematic errors, numerical solution, coefficient of radiation absorption

**Page:**
1548

**NANOMATERIALS IN PROTON EXCHANGE FUEL CELLS**

The present paper considers the state of the art of investigations on the use of nanomaterials in the technology
of preparing proton exchange fuel cells. This technology has great prospects for use in transport facilities, as well
as in stationary and portable electronic devices. The unique properties of nanostructures permit creating new
effective catalysts, polymer membranes, and hydrogen storage systems — key elements of the above technology,
which upgrades markedly the effi ciency of energy conversion in devices created on its basis and decreases
their cost.

**Author:**
G. Ya. Gerasimov

**Keywords:**
fuel cells, proton exchange membranes, nanomaterials, carbon nanostructures, electrochemical reaction, catalysts, hydrogen storage systems

**Page:**
1554

**ANALYTICAL ESTIMATION OF VELOCITY AND TEMPERATURE FIELDS IN A CIRCULAR PIPE ON THE BASIS OF STOCHASTIC EQUATIONS AND EQUIVALENCE OF MEASURES**

A stream of nonisothermalNewtonian liquid in a circular smooth pipe is considered on the basis of systems of
stochastic equations and of the physical law of equivalence of measures between laminar and turbulent motions.
Analytical expressions were previously obtained for isothermal fl ows for the fi rst and second critical Reynolds
numbers, critical point, indices of velocity profi les, second-order correlation moments, correlation functions, and
spectral functions depending on the parameters of initial turbulence. Analytical expressions, obtained with the use
of the earlier derived formulas for the critical Reynolds numbers and the critical points, are presented for the indices
of velocity and temperature profi les as functions of the initial turbulence parameters as well as of the Eckert and
Prandtl numbers.

**Author:**
A.V. Dmitrenko

**Keywords:**
equivalence of measures, stochastic equations, turbulence

**Page:**
1569

**OPTIMIZATION OF THE SLOT SUCTION OF AIR FROM A CIRCULAR VORTEX CELL ON A THICK NACA0022 AIRFOIL WITH A MAXIMUM LIFT–DRAG RATIO**

On the basis of multiblock computational technologies and the Menter model of shear-stress transfer modifi ed with
account of the curvature of streamlines, the optimum position of a slot for air suction on the leeward side of the
contour of a vortex cell built in a thick NACA0022 airfoil was determined for the purpose of increasing its lift–drag
ratio to a maximum value in a nondisturbed air fl ow at a Mach number of 0.05 and an angle of attack of 7^{o}
.

**Author:**
S. A. Isaev, E. I. Kalinin, A. G. Sudakov, and V. B. Kharchenko

**Keywords:**
lift-drag ratio, thick airfoil, vortex cell, slot suction, turbulence

**Page:**
1577