#### Volume 95, №2

**CALCULATION OF HEAT EXCHANGE FOR VARIABLE-HEAT-CAPACITY FLOWS**

The authors have obtained minimum conditions for the irreversibility and the contact surface of double-fl ow
heat exchange with a prescribed total heat load with various constraints imposed on the set of permissible fl ow
temperatures. Consideration has been given to fl ows with a constant heat capacity and to fl ows with a temperaturedependent heat capacity and, in particular, changing their phase state, that are of arbitrary high heat capacity at the
boiling/condensation point. It has been shown that the obtained relations yield the existence of realizability limits
of the process and relations have been derived to calculate them. For variable-heat-capacity fl ows, the entropy
production in their mixing has been obtained

**Author:**
A. M. Tsirlin , L. G. Gagarina

**Keywords:**
double-fl ow heat exchange, irreversibility, contact surface, heat load, entropy production

**Page:**
283

**PALEOTEMPERATURES OF THE EARTH′S SURFACE. 1. DETERMINATION OF THE AVERAGE ANNUAL TEMPERATURE OF THE EARTH AND HEMISPHERES**

The author has presented functional dependences to determine the distribution of the average annual temperature
and annual insolation alog an Earth latitude

**Author:**
I. I. Smul′skii

**Keywords:**
midlatitude temperature, annual insolation, paleoclimate

**Page:**
291

**PALEOTEMPERATURES OF THE EARTH′S SURFACE. 2. DETERMINATION OF THE MIDLATITUDE NEAR-SURFACE HEAT-CAPACITY OF THE EARTH**

Two methods have been proposed for calculating the midlatitude near-surface heat-capacity of the Earth: 1) using
the latitude variation of the Earth temperature, and 2) using the insolation of the Earth in the modern epoch and its
variation with time. Using the obtained values of this heat capacity, profi les have been determined for the midlatitude paleotemperatures of the Earth in three extreme epochs in the past 50 thousand years, and the evolution of the
paleotemperature in the past 200 thousand years has been calculated.

**Author:**
I. I. Smul′skii

**Keywords:**
midlatitude temperature, insolation, heat capacity, paleotemperature, paleoclimate.

**Page:**
299

**ACCUMULATION OF ISOTOPE MIXTURE COMPONENTS IN A SEPARATION CASCADE**

Numerical investigations have been conducted into the process of separating a multicomponent isotope mixture
in a cascade. Regular patterns have been established for the effects of the cascade parameters on the component
concentration value in the cascade gas content. Conditions have been identifi ed under which the maximum quantity
of the target component is accumulated in the cascade. The investigation results can be used for further study of
unsteady processes of accumulating isotope mixture components in a separation cascade.

**Author:**
A. A. Ushakov , A. A. Orlov , V. P. Sovach

**Keywords:**
multicomponent isotope mixture, isotope separation, isotope enrichment, fi ne purifi cation of substances, computer modeling of separation processes

**Page:**
309

**CORRECTION OF SIGNALS IN A MICROBOLOMETRIC ARRAY RAISING THE VALIDITY OF MEASURING OBJECTS′ TEMPERATURE. PART 2**

Consideration has been given to methods of accounting for the effects of deviation of the temperature of the array
sensitive elements from the values registered during the conduct of calibration and also from the effective thermal
emissivity of the controlled bodies and the heat radiation of the ambient environment refl ected from them on the
calculated values of the temperature fi eld being formed.

**Author:**
V. A. Firago

**Keywords:**
thermal imaging signals, radiation, temperature fi elds, measurements

**Page:**
316

**NUMERICAL SIMULATION OF THERMOELECTRONIC THERMAL PROTECTION IN THE CASE OF HIGH ENTHALPY FLOW PAST A MULTILAYER SHELL**

A mathematical model of the process of unsteady conjugate heat transfer of a thermionic thermal protection
system during supersonic air fl ow around a spherically-blunted cone is investigated. Estimates of the effect of
evaporation (emission) of electrons from the emitter surface on lowering the temperature of the composite shell of
the thermoelectronic thermal protection are made. The infl uence of different angles of attack on heat transfer modes
in the system of multielement thermionic thermal protection has been studied. Qualitative agreement of calculated
results with the known data has been found.

**Author:**
K. N. Efimov , V. A. Ovchinnikov , A. S. Yakimov

**Keywords:**
thermoelectronic thermal protection, emitter, collector, heat transfer, cooler

**Page:**
327

**SIMULATION OF THE CONVECTIVE HEAT TRANSFER IN A SPHERICAL ELECTROCONDUCTIVE LIQUID LAYER WITH HEAT SUPPLY AND HEAT REMOVAL**

Results of a numerical simulation of the nonstationary heat transfer in the layer of an electrically conducting liquid
between two concentric spheres are presented, the infl uence of the internal heat sources in this layer on the structure
of the liquid fl ow, the temperature and magnetic induction fi elds, and the distribution of Nusselt numbers in it was
investigated

**Author:**
S. V. Solov′ev

**Keywords:**
mathematical simulation, nonstationary heat transfer, magnetic hydrodynamics, spherical liquid layer, internal heat sources

**Page:**
343

**INFRARED DRYING OF A PLATE IN A CONTINUOUS ELECTROMAGNETIC FIELD**

Absorption of electromagnetic energy by a plate in an infrared frequency range is considered. A linear problem
(constancy of process parameters) of infrared heating of the plate under conditions of convective heat and mass
transfer of its surface with an external gas medium is formulated and solved analytically both for the general process
of drying and for drying in the fi rst period. In formulating the heat conduction problem, it is assumed that the internal
heat source caused by the absorption of radiant energy is distributed exponentially over the plate thickness and that
phase transformations during moisture evaporation occur near the plate surface. The drying intensity is described
on the basis of the analytical solution of the linear (constancy of mass conductivity) problem of mass conductivity
(diffusion of moisture) for the plate under the boundary condition of mass transfer of the third kind. Solutions of
the problems of heating are obtained in relation to local and body volume-averaged temperatures. They are used
as the basis for numerical simulation of the process of heating a plate with account for its drying: the infl uence of
the drying intensity and radiant fl ux density on the plate heating dynamics is shown. As applied to the fi rst period of
drying, it is shown that the particular solution obtained in this case for the problem makes it possible to calculate the
drying intensity, as well as the local and volume-averaged temperatures of the plate under the conditions of infrared
energy supply. The article presents the procedure of determining the drying intensity in the fi rst period with the use
of the Antoine equation for calculating the saturated vapor pressure near the plate surface from the plate surface
temperature determined from the solution obtained

**Author:**
S. P. Rudobashta , É. M. Kartashov , G. A. Zueva

**Keywords:**
drying, infrared (IR) heating, convective heat and mass transfer, analytical solution

**Page:**
357

**WAVE HEAT TRANSFER IN ANISOTROPIC HALF-SPACE UNDER THE ACTION OF A POINT EXPONENTIAL-TYPE HEAT SOURCE BASED ON THE WAVE PARABOLIC-TYPE EQUATION**

Based on the generalized law of wave heat transfer, a wave equation of parabolic type is obtained, for which the
problem of heating an anisotropic half-space under the action of a point nonstationary source of thermal energy of
exponential character is posed and solved analytically. The anisotropic half-space has anisotropy of heat transfer in
planes parallel to the plane bounding the body, whereas the body is isotropic in the direction of the axis perpendicular
to these planes. Therefore, the isotherms moving in time have the form of elliptical paraboloids, at the fronts of which
the fi rst-kind discontinuous changes are observed in both temperatures and heat fl uxes, which is a consequence of
the wave nature of heat transfer. Numerical results are obtained and analyzed

**Author:**
V. F. Formalev , É. M. Kartashov , S. A. Kolesnik

**Keywords:**
wave heat transfer, anisotropy, relaxation time, parabolic-type wave equation, principal axes and components of the thermal conductivity tensor, nonstationary temperature field

**Page:**
366

**TOWARD THE SOLUTION OF INVERSE THERMAL CONDUCTIVITY AND THERMAL ELASTICITY PROBLEMS**

The article describes a method of solving inverse problems, which is based on the joint application of the
A. N. Tikhonov regularization principle and of the method of infl uence functions that play an important role in
obtaining stable solutions of ill-posed problems and in facilitating the computational process due to the preliminarily
determined infl uence functions. The method is the result of development of the methodology previously developed
by the authors for solving inverse problems, which is based on the various methods of regularizing solutions
to multiparameter ill-posed problems of fi eld theory, as well on the experience in identifying the parameters of
mathematical models of various levels. The results of identifi cation of heat transfer at the boundary of a body
by displacements measured with an error characterized by a random variable distributed by the normal law are
presented. The proposed method makes it possible to use experimental information obtained from several sensors.
It is applicable to the study of heterogeneous media and combines the simplicity of programming with the ability of
parallelizing the computational process, which meets modern requirements for methods and algorithms of solving
direct and inverse problems.

**Author:**
Yu. M. Matsevityi , E. A. Strel′nikova , V. O. Povgorodnii , N. A. Safonov , V. V. Ganchin

**Keywords:**
inverse problem, thermal stresses, regularization, infl uence functions, identifi cation, stabilizing functional

**Page:**
374

**RATIONAL THERMODYNAMIC PARAMETERS OF MULTISTAGE POWER CYCLES APPROPRIATE FOR LOW-TO-MODERATE GEOTHERMAL RESOURCES**

The geofl uid temperatures of the most promising geothermal areas of Ukraine are estimated to be less than approximately 130^{o}C. This paper presents the results of a theoretical design study on the thermodynamic cycle parameters of a geothermal power station that would utilize these geothermal resources, and these results are similar to ones given elsewhere. Various confi gurations of the organic Rankine cycle (ORC) are considered. Thermal schemes of 3-stage geothermal power installations are studied. The effectiveness of geothermal power stations with various working fl uids at each stage is investigated. The results of a numerical study of the thermal 3-stage geothermal installation schemes show that at a geothermal liquid temperature of 130^{o}C the possible total specifi c
power output of a turbine is 20.7–20.8 kW per kg/s of a geofl uid flow. The combined 3-stage cascaded system with
a bottoming cycle can generate about 15% more power than a simple single-stage binary plant at the same brine
inlet conditions

**Author:**
A. Redko , O. Redko , N. Kulikova , S. Pavlovskyi , R. DiPippo

**Keywords:**
geothermal power, organic Rankine cycle, 3-stage cycle, thermal effi ciency, utilization effi ciency, geothermal areas of Ukraine

**Page:**
380

**ANALYSIS OF THERMAL PERFORMANCE, EFFICIENCY, AND EFFECTIVENESS OF A STRAIGHT POROUS FIN WITH VARIABLE THERMAL CONDUCTIVITY**

Radiating extended surfaces are generally used to reinforce heat transfer between a primary surface and its
environment. Specifi cally, if great temperature contrasts are taken into account, variable thermal conductivity
materially affects the performance of the system. Thus the present numerical study is concerned with the thermal
performance of a straight porous fi n under the infl uence of temperature-dependent thermal conductivity, magnetic
fi eld, and radiation. The heat transfer model, which includes the Darcy law for simulating fl ow with solid–fl uid
interactions in a porous medium, the Rosseland approximation for heat transfer through radiation, the Maxwell
equations for the magnetic fi eld effect, and linearly varying temperature-dependent thermal conductivity, results in a
highly nonlinear ordinary differential equation solved with using the fi nite-difference scheme with suitable boundary
conditions. The obtained solutions are interpreted physically by considering the impact of relevant nondimensional
parameters on the thermal performance, effi ciency, and effectiveness of the system. It follows from the analysis that
the temperature-dependent thermal conductivity improves these characteristics

**Author:**
Babitha , K. R. Madhura

**Keywords:**
straight porous fi n, temperature-dependent thermal conductivity, magnetic fi eld, fi nite-difference method, Rosseland approximation

**Page:**
392

**LABORATORY MODELING OF THE PROCESSES OF SOUND EXCITATION BY SELF-OSCILLATING REGIMES IN FLOWS IN HEAT-EXCHANGE-SYSTEMS' PIPELINES**

The authors have performed laboratory modeling of noise-emission processes in turbulent fl ows of the heattransfer agent in shutoff and control valves of a pipeline. Experiments were conducted on an aeroacoustic bench
consisting of a model of the fl ow chamber of shutoff and control valves (parallelepiped), inlet and outlet tubes, an
exhaust fan, and a baffl e chamber. Parallel measurements of velocity fi elds were performed by the PIV method,
and of acoustic characteristics, with a microphone. The experiments were conducted with different widths of the
gaps between the tubes in the fl ow-chamber model. At certain values of the gaps, tone sounding was recorded
at frequencies of 340 and 680 Hz by the microphone, which, as subsequently shown by results of the velocityfi eld measurements, is a consequence of the self-oscillating fl ow regime occurring with a periodic separation of
vortices whose scale is comparable with the gap width in the fl ow chamber

**Author:**
D. A. Sergeev , A. A. Kandaurov , A. V. Stulenkov , A. S. Suvorov

**Keywords:**
self-oscillations, fl ows in pipelines, sound, laboratory modeling

**Page:**
402

**FLOW DYNAMICS AND ACOUSTICS OF THE GAS JET EMANATING FROM A CONICAL NOZZLE INTO AN IMMERSED SPACE**

The subsonic and supersonic gas jets emanating from a conical nozzle into an immersed space were investigated.
The infl uence of the difference between the total pressure at the inlet of the nozzle and the static pressure in the
surrounding medium on the structure of such a jet and its fl ow dynamics and acoustics were determined and the
noise level in the far fi eld of the jet was calculated. The results of numerical simulation of the outfl ow of a gas from
a conical nozzle into an immersed space were compared with the corresponding experimental and calculation data
available in the literature. The methods developed for numerical simulation of the fl ow dynamics and acoustics
of gas jets can be used for solving different research and engineering problems as well as for development of new
computational algorithms

**Author:**
K. N. Volkov , V. N. Emel'yanov , P. S. Chernyshov

**Keywords:**
computational gas dynamics and aeroacoustics, supersonic underexpanded jet, noise, conical nozzle

**Page:**
409

**INVESTIGATION INTO THE PROCESS OF INTERACTION OF THE LIQUID AND THE GAS IN A JET-FILM CONTACT DEVICE**

With the aim of increasing the capacity of commercial cooling towers and enhancing heat-transfer processes, the
authors have developed a structure of a jet-fi lm contact device. An experimental setup was assembled that permits
investigating the hydrogasdynamics of a liquid in the operating region of the device. Results of investigation into
the infl uence of the fl ow rate of the liquid and the gas on the hydraulic resistance of the contact device have been
presented. A mathematical dependence has been obtained for calculating the pressure difference of a dry packing of
the jet-fi lm contact device on the velocity factor. It has been established that with increase in the water concentration,
the hydraulic resistance changes only slightly, which is a great advantage among the existing structures. The heat
output of a cooling tower has been determined; the criterion of energy effi ciency has been considered which takes
account of the expenditure of energy to pump air. The high energy effi ciency of a jet-fi lm contact device compared to
various types of water-cooling devices has been proved

**Author:**
A. V. Dmitriev , M. M. Farakhov , A. I. Khafi zova , O. S. Dmitrieva , I. N. Madyshev , A. D. Gilyazov , A. A. Akhmitshin

**Keywords:**
contact device, mass transfer, hydraulic resistance, energy efficiency

**Page:**
421

**MATHEMATICAL SIMULATION OF HEAT TRANSFER AND CHEMICAL REACTION IN A SWIRLING FLOW OF EQUILIBRIUM-DISSOCIATING GAS**

Results of investigations of the heat transfer in the swirling turbulent fl ow of dinitrogen tetroxide in a cylindrical channel are presented. The equilibrium stage of the dissociation reaction N_{2}O_{4} ⇄ 2NO_{2 } was considered. It was established that the mass fraction of N_{2}O_{4} in its swirling fl ow is smaller than that in the analogous forward fl ow
at one and the same distance from the input cross section of the channel. In the case where the fl ow of dinitrogen
tetroxide is strongly swirled, its intense heating in the zone of reverse fl ows near the channel inlet causes it to
dissociate. It is shown that an increase in the swirling of a gas fl ow intensifi es the heat transfer in it with increase in
its Nusselt number

**Author:**
O. V. Matvienko , P. S. Martynov

**Keywords:**
heat transfer, chemical reaction, dissociation, boundary layer, swirling fl ow, computational fl uid dynamics

**Page:**
428

**EXIT DEVICES WITH RESONATORS-THRUST AMPLIFIERS FOR JET ENGINES**

The authors have presented results of investigations into the exit devices of jet engines with resonators-thrust
amplifi ers. The infl uence of the size of a resonator cavity, and also of the temperature and the gas constant on the
effi ciency of buildup of the thrust of the exit device with a resonator has been determined. A study has been made of
the possibilities of augmenting the effective thrust of the jet engine with a resonator exit device. The possibility of
creating exit devices of increased size with the effect of amplifi cation of the thrust of the exit device with resonators
of various types has been analyzed

**Author:**
V. I. Bogdanov , D. S. Khantalin

**Keywords:**
exit device, resonator-thrust amplifi er, weight-size characteristics, added mass, gas constant

**Page:**
441

**HIGH-VELOCITY PENETRATION INTO A METAL BARRIER BY A VISCOELASTIC ROD**

A model has been proposed for a high-velocity interaction of a viscoelastic rod with a barrier resulting in ejecting a
plug in a target. We have obtained an approximate analytical solution of a problem, in which the deformation of the
striker and the target is considered jointly, and a relation that associates the barrier penetration time with the plug
mass, the critical shear strength of the target, and the striker parameters in the case when the plug after-penetration
velocity is equal to zero

**Author:**
A. Yu. Algabachiev , N. N. Kholin

**Keywords:**
viscoelastic rod, plug ejection, barrier, cumulative jet, space debris, destruction, longitudinal oscillations, shock wave

**Page:**
452

**MODELING AERODYNAMIC CHARACTERISTICS OF A WIND ENERGY INSTALLATION WITH ROTATING CYLINDER BLADES ON THE BASIS OF THE ANSYS SUITE**

Modeling has been carried out for the aerodynamics of air fl ow past the windwheel with three cylinder blades rotating
around their axis using the Ansys suite. A system of equations in approximation of a realizable k–ε turbulence model was
solved by the method of fi nite volumes using the approach of multiple (imbeddable) systems of coordinates. Patterns
have been constructed for vortex zones near cylinder blades. Analysis is given of the aerodynamic characteristics of
fl ow past rotating cylinders under the conditions of the operation of a wind turbine using the Magnus eff ect depending
on the velocity of cylinders′ rotation and the Reynolds number. Dependences have been obtained for the drag force of
the windwheel, the lift force of the cylinder, and also the force moment on the velocity of approach fl ow

**Author:**
N. K. Tanasheva , A. R. Bakhtybekova , K. M. Shaimerdenova , S. E. Sakipova , N. N. Shuyushbayeva

**Keywords:**
windwheel, rotating cylinder blades, aerodynamics, drag force, lift force, Magnus eff ect, modeling, ANSYS.

**Page:**
457

**ON CALCULATION OF FLOWS OF HETEROGENEOUS MEDIA BY THE MULTIDIMENSIONAL NODAL METHOD OF CHARACTERISTICS**

A description is given of a nodal method of characteristics, designed for integrating hyperbolic systems, based on
splitting the initial system of equations into a number of one-dimensional subsystems, with the one-dimensional
nodal method of characteristics being used for their calculation. The calculating formulas of the method are
cited. A number of fl at and three-dimensional test problems have been calculated using this method. The results of
calculations have been compared with the existing self-similar solutions

**Author:**
V. S. Surov

**Keywords:**
heterogeneous media, multidimensional nodal method of characteristics

**Page:**
464

**MODELING THE CAPILLARY INFLOW OF A LIQUID TO DRY SPOTS ABOVE VAPOR BUBBLES AS A FACTOR OF INCREASING THE CRITICAL HEAT-FLUX DENSITY DURING THE BOILING ON A POROUS SURFACE**

The authors propose a calculation model for the process of infl ow of a liquid from a microfi lm to dry spots above
vapor bubbles, which occurs in nucleate boiling and is due to the action of capillary forces (Laplace head) in
a porous coating on the heating surface. In comparing the value of the heat fl ux from the heating surface to the
interface in the zone of intense evaporation of the liquid and the value of the heat fl ux to evaporate the liquid sucked
through a porous substrate to a dry spot, it turns out that these values are comparable, which explains the effect
of rise in the critical density of the heat fl ux on porous surfaces compared to "smooth" surfaces. A comparison of
the results of quantifi cation of this effect with the proposed model and the experimental data obtained during the
boiling of water on a porous surface that was formed by nanoparticles precipitated from a nanolfl uid has shown
their mutual agreement

**Author:**
E. D. Fedorovich , A. N. Kovalenko , S. S. Makukhin

**Keywords:**
nucleate boiling, active nucleation site, vapor bubble, microfi lm, dry spot, critical heat-fl ux density, porous coating, capillary-infl ow effect

**Page:**
473

**STRUCTURAL INHOMOGENEITY AND EFFECTS OF SEPARATION BY SIZE AND DENSITY IN GRAVITY FLOW OF GRANULAR MATERIALS**

The authors have substantiated the expediency of representing the effect of separation of particles as a result of the
conjugation of phenomena that are caused by the inhomogeneity of a granular medium and the spatial structural
heterogeneity of a shear fl ow. With the general separation-dynamics model taking account of separation, convection,
and mixing fl ows, regions of relative values of particle size and density have been determined, in which the dominance
of the separation fl ows due to the local and spatial inhomogeneity of the granular-medium's rapid gravity fl ow is
noted. It has been established that the boundary of the regions of dominance of separation fl ows with a fundamentally
different physical nature which is determined by hydrodynamics and diffusion kinetics is near the equilibrium line of
inhomogeneous-particle masses.

**Author:**
V. N. Dolgunin, A. N. Kudi, A. G. Tarakanov

**Keywords:**
granular material, rapid gravity fl ow, structural inhomogeneity, separation by size and density, segregation, migration, quasi-diffusion

**Page:**
484

**ESTIMATION OF THE PARAMETERS OF THE POROUS STRUCTURE OF POWDER MATERIALS**

Based on the globular model with the use of the values of porosity and particle size, a method is presented for
calculating the structure parameters of porous monofractional powder composite materials for fi lters. A formula
for determining the average (hydraulic) radius of the capillaries of permeable materials has been obtained, which
is more accurate than the Kozeny formula. The results of calculating the average radius of capillaries and of the
permeability of porous powder materials by the proposed dependences are presented, which are in better agreement
with experimental data than calculations by the Kozeny formula

**Author:**
Yu. N. Kryuchkov

**Keywords:**
model, fi lter, structure, coordination number, average radius of capillaries, packing density, porosity, particle size, specifi c surface, coeffi cient of capillary tortuosity, permeability

**Page:**
495

**SIMULATION OF HYDRAULIC DIFFUSION PROCESSES AND FILTRATION OF OIL IN A POROUS BED**

The problems of analysis and solution of the equation of hydraulic diffusion for the oil bed as an isotropic porous
medium with different boundary conditions are considered. A collection of analytical solutions and the possibilities of
using them to construct a pressure recovery curve for estimating the coeffi cients of hydraulic diffusion and permeability
of the bed are given. The one-dimensional solutions of these equations are compared with experimental data obtained
on an operating setup, and their satisfactory convergence is demonstrated. The solutions obtained can be used to solve
various problems of oil fi ltration in an isotropic porous medium. The structure formation of the non-Newtonian oil due
to asphalt-resinous substances and their infl uence on the fi ltration rate of oil and its rheological properties have been
investigated. New rheological equations for non-Newtonian oil fi ltration in a porous medium have been suggested

**Author:**
G. I. Kelbaliev , S. R. Rasulov , D. B. Tagiev

**Keywords:**
oil, hydraulic diffusion, fi ltration, porous medium, permeability, viscosity, rheology, structure formation, shear stress

**Page:**
499

**HYBRID LBGK-FD MODEL FOR STUDYING TURBULENT NATURAL CONVECTION**

A hybrid mesomacroscopic approach has been developed for modeling developed turbulent thermogravitational fl ows in closed rectangular differentially heated regions. Within the framework of the formulated approach, it is proposed to use the mesoscopic lattice Boltzmann equations to describe gas-dynamical processes, and the macroscopic energy equation solved by the fi nite difference method for thermodynamic ones. To approximate the Boltzmann equation, simultaneous relaxation and a two-dimensional nine-speed scheme were used. Mathematical simulation was carried out at the Rayleigh number Ra = 10^{10} and the Prandtl number Pr = 0.71. The infl uence of the order of approximation
of the energy equation on the local heat transfer characteristics has been analyzed. It is found that an increase in the
number of computational nodes leads to the smoothing of pulsations in the fl ow. In this case, the results of numerical
simulation agree satisfactorily with the "reference" data obtained by other researchers.

**Author:**
A. É. Nee

**Keywords:**
turbulence, hybrid method of lattice Boltzmann equations, method of fi nite differences, natural convection

**Page:**
508

**NUMERICAL SIMULATION OF A FORCED CONVECTION LAMINAR FLUID FLOW WITH REGARD FOR THE THERMODIFFUSION OF NANOPARTICLES IN IT**

The forced convection of the nanofl uid representing a water with aluminum oxide particles, fl owing in the laminar
regime in a circular channel with a heat fl ow of constant density at the channel wall, was numerically investigated
by the homogeneous and heterogeneous models of the fl uid fl ow with regard for the transport of nanoparticles in it
due to their diffusion or thermodiffusion. An increase in the thermodiffusion of nanoparticles in a laminar fl uid fl ow
with increase in their concentration in it was demonstrated. The results of calculations performed by the indicated
two models are in good agreement with the corresponding experimental data. However, the homogeneous model
as a whole approximates experimental data more closely. It is shown that, in the case where the concentration of
nanoparticles in a fl uid is high (6%), the infl uence of their thermal diffusion on the heat transfer and the pressure
drop in the laminar fl uid fl ow in a channel does not exceed 2%

**Author:**
D. V. Guzei , A. V. Minakov , V. Ya. Rudyak

**Keywords:**
forced convection, numerical simulation, nanofl uid, thermal diffusion, two-component model, experiment

**Page:**
516

**REFRACTIVE AND ELECTROPHYSICAL PROPERTIES OF DISPERSED SOLUTIONS OF FULLERENE C60 IN BINARY SOLVENTS**

An experimental study has been made of the infl uence of the concentration of a solvent and a solute on the clusterization of fullerene C_{60} molecules in a C_{60}/xylol/hexane solution by refractometry methods. By the methods of dynamic light scattering and transmission electron microscopy, it has been established that when a nonequilibrium method of preparation of a fullerene C60 solution in binary mixtures (xylol + hexane) is employed negatively charged clusters of diameters ~60–70 nm are formed in the solution. It has been established that the high aggregative stability of the solution of fullerene with a concentration of C_{60} of ~0.036 g/L is determined by the relatively high values of the
electrokinetic ζ potential of nanoclusters (ζ = –26.6–28.2 mV).

**Author:**
U. K. Makhmanov

**Keywords:**
fullerene C60, mixtures of solvents, refractive index, electrokinetic potential, microscopy

**Page:**
527

**PREPARATION OF HYBRID NANOFLUIDS, THEIR THERMOPHYSICAL PROPERTIES, AND STABILITY PARAMETERS**

A review of methods of preparation of hybrid nanofl uids produced with the use of particles of metals, nonmetals, and

their oxides as well as results of recent investigations on the thermophysical properties of these nanofl uids and their

stability are presented.

**Author:**
Okafor Anthony Amaechi , Mgbemena Chinedum Ogonna

**Keywords:**
hybrid nanofl uid, preparation, characterization, properties, stability

**Page:**
533

**THERMODYNAMIC PROPERTIES OF A LIQUID MIXTURE OF CYCLOHEXANE WITH DECALIN AT TEMPERATURES 298.15–433.15 K AND PRESSURES UP TO 100 MPa**

An experimental study of the density and speed of sound for a liquid mixture of decalin with cyclohexane in the range
of temperatures 298.15–433.15 K and pressures up to 100 MPa has been carried out. The parameters of the Redlich–
Kister equations for an excess volume in a wide range of temperatures and pressures and for excess isobaric heat
capacity at atmospheric pressure have been obtained. The values of density, speed of sound, isobaric and isochoric
heat capacities, isobaric expansion coeffi cient, isotropic and isothermal compressibility coeffi cients, as well as of
the corresponding excess properties in the range of temperatures 298.15–433.15 K and pressures 0.1–100.1 MPa
have been calculated.

**Author:**
A. P. Shchemelev , V. S. Samuilov , N. V. Golubeva , O. G. Poddubskii

**Keywords:**
decalin, cyclohexane, mixture, density, speed of sound, thermodynamic properties

**Page:**
539

**INFLUENCE OF THE CONDUCTIVITY OF RESONATOR WALLS ON THE CHARACTERISTICS OF A MICROWAVE GENERATOR WITH A VIRTUAL CATHODE: NUMERICAL EXPERIMENTS**

Using PIC simulation, the authors have carried out an investigation into the generation characteristics of a
microwave generator with a virtual cathode as functions of the conductivity of the material of resonator walls.
The dependence of the peak power of microwave generation in the resonator on the value of conductivity has been
obtained which shows a decrease in the power with conductivity. No substantial change in the generation spectrum
with variation of the conductivity has been found.

**Author:**
A. E. Dubinov , V. P. Tarakanov

**Keywords:**
microwave generator with a virtual cathode, resonator, conductivity

**Page:**
553