#### Volume 94, №1

**PHYSICAL KINETICS AND SIMULATION OF THE SPREAD OF AN EPIDEMIC**

A self-consistent system of differential logistic equations has been constructed to describe the spread of an epidemic
with account for the demography and geography of a country. An original method of numerical assessment of the
number of unregistered cases in the country has been proposed.

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

**Keywords:**
number of contacts, demography, geography, time of infection, similarity parameter

**Page:**
1

**EPIDEMIC DYNAMICS KINETIC MODEL AND ITS TESTING ON THE COVID-19 EPIDEMIC SPREAD DATA**

A kinetic model has been proposed for the spread of epidemics, describing the dynamics of the variation in the
number of disease-free, infected, and recovered (SIR) cases, based on a lag logistic equation. It has been established
that this model predicts the possibility of existence of a quasi-steady-state mode of an epidemic in which the number
of infected cases is constant due to the balance of the daily increment of infections and recoveries. Conditions
have been identifi ed under which such a mode can be a source of the advance of the second epidemic wave. The
COVID-19 pandemic data were used to show the possibility of reliable forecasts based on this model of the spread
of an epidemic for a period of up to two months.

**Author:**
A. I. Shnip

**Keywords:**
prediction of epidemics, COVID-19, logistic equation, delayed argument, second wave

**Page:**
6

**ESTIMATION OF COVID-19 INFECTION GROWTH RATE BASED ON THE IMBEDDING METHOD **

An analysis is presented of universal stages in the development of the COVID-19 virus infection epidemic. It is
assumed that during a pandemic the growth rate in the number of infections in a country occurs similarly to the
process of virion replication in an infected organism. The exponent of the growth rate of the number of infection
cases refl ects not only biomedical parameters of a virus infection but also distinctive features of the social behavior
of the population of a country. The dynamics of the change in the growth rate exponents is simulated by a system
of relaxation-type ordinary differential equations. In applied mathematics, based on the imbedding method, limit
values are forecast for exponents of the growth rate of the number of cases using the currently available experimental
data. These values "forecast ahead" are subsequently approached by the actual exponents of growth in the number
of infectees. The search for unknown parameters is carried out by minimizing a specially constructed quadratic
functional accounting for all confi rmed cases of COVID-19 infection. The functional minimum is found via iterations
by solving a system of ordinary differential equations.

**Author:**
I. V. Derevich and A. A. Panova

**Keywords:**
COVID-19 epidemic, number of infectees, quarantine, social behavior, imbedding method, growth rate in the number of infectees (infection cases)

**Page:**
18

**TRANSPORT PROPERTIES OF COATINGS CONSISTING OF Al2O3 NANOPARTICLES**

The technology of obtaining coatings consisting of alumina nanoparticles and their agglomerates is presented. The
transport properties of coatings and the change of these properties with time are investigated. The dependence of the
height of capillary ascent on the quantity of deposited nanofl uid on substrates has been established. An estimate of
the change in the height of liquid rise and of the permeability of a coating with the change in the size of particles has
been made. Deterioration of the transport properties of porous coatings consisting of alumina nanoparticles with
time is investigated, and the possibility of restoring these properties is shown.

**Author:**
Yu. A. Kuzma-Kichta, N. S. Ivanov, and A. V. Lavrikov

**Keywords:**
porous coatings, alumina nanoparticles, thermal resistance, thermal stabilization, capillary structures, permeability, rise of liquid

**Page:**
30

**NUMERICAL MODELING OF FILTRATION PRESSURE FIELDS IN AN ISOLATED HOMOGENEOUS ISOTROPIC IMPERFECTLY STRIPPED SEAM**

Filtration fl ows arising on the uptake of hydrocarbons from imperfectly stripped seams-collectors are investigated. The problem on the pressure fi eld in an isolated isotropic homogeneous seam localized in the interval from H_{1d} to –H_{2d} and perforated in the range –H_{d} < z_{d} < H_{d}, fully contained in the interval of the seam, has been considered.
The problem is formulated in dimensional and dimensionless values for functions of pressure deviation from its
nonperturbed distribution normalized to the amplitude value of depression. Dimensionless relations are constructed
for the problem considered.
A fi nite-difference program is created for calculating the fi elds of pressure and velocity in a seam with imperfect
stripping when the seam boundaries do not coincide with the boundaries of the perforation interval. Graphical
dependences have been constructed for the pressure fi eld, vertical and horizontal components and velocity modulus
of the fl uid fi ltering from the periphery to the well. The level lines for the indicated fi elds are presented and, based on
their analysis, important laws governing the fl ow have been revealed. A computational experiment has shown that
at the exit into the well in the perforated part of the seam vertical fl ows are absent, and at increasing distance from
the well they differ from zero. This means that interlayer overfl ows exist even in homogeneous imperfectly stripped
seams. At the center of the symmetrically perforated bed such overfl ows are absent, since the transverse velocity
component vanishes. At the same time, infl ow from an imperfectly stripped homogeneous isotropic seam, which is
produced in the regime of assigned depression, is not uniform, and the maximum of the modulus of the horizontal
velocity component on all of the curves is attained at the boundaries of the perforation interval. It is shown that at
the center of a symmetrically perforated and imperfectly stripped seam, a minimum specifi c infl ow is observed.

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

**Keywords:**
fi ltration, imperfect stripping, two-dimensional fl ow, fi nite-difference program, pressure fi eld, velocity fi eld

**Page:**
36

**INFLUENCE OF GROUNDWATER SEEPAGE ON ARTIFICIAL FREEZING OF ROCK MASS**

Investigation of the effect of horizontal groundwater seepage in a rock mass subjected to artifi cial freezing on
the parameters of a frozen wall formed around a projected shaft is carried out. For this purpose, a mathematical
model of coupled heat and mass transfer in a watered rock mass subjected to freezing is formulated, and numerical
multiparametric simulation of the formation of frozen wall under the conditions of groundwater seepage with
variable rate has been made. A sandstone layer for the conditions of Petrikovo deposit of potash and rock salts is
predominantly considered in the work. An analysis of the results has shown that the infl uence of groundwater fl ow on
the frozen wall thickness begins at seepage rates of about 50 mm/day. In this case, the infl uence of the groundwater
fl ow on the temperature fi eld of the rock mass begins earlier, at seepage rates 10–25 mm/day. Three mechanisms of
the frozen wall dynamics on increase in the rate of groundwater seepage rate are determined: shift, deformation, and
loss of continuity. Corrections for the frozen wall thickness in the presence of groundwater fl ow for a sandstone layer
for the interval of seepage rates from 50 to 150 mm/day have also been established.

**Author:**
M. A. Semin, L. Yu. Levin, and O. S. Parshakov

**Keywords:**
frozen wall, shaft, artifi cial ground freezing, heat and mass transfer, groundwater seepage, numerical simulation

**Page:**
45

**HYDRODYNAMICS OF MOTION OF A LIQUID IN THE CONJUGATE SYSTEM "FORMATION–WELL–PIPELINE"**

A model of nonstationary motion of a liquid in the conjugate system "formation–well–pipeline" has been constructed,
and relevant coupled equations have been solved. An analytical expression for the infl uence of the change in the
pressure at the end of the pipeline on the bottomhole pressure has been obtained. Numerical calculations for different
values of parameters of the system have been carried out.

**Author:**
N. A. Agaeva

**Keywords:**
fi ltration, Laplace transformation, motion of a liquid, continuity equation, Volterra-type integral equation

**Page:**
56

**MECHANISM FOR IMPROVING THE STRENGTH OF A CEMENT MATERIAL MODIFIED BY SiO2 NANOPARTICLES AND MULTIWALL CARBON NANOTUBES**

The authors have given results of investigations into the phase transformations of a cement material modifi ed by a
complex nanodisperse admixture that consists of a superplasticizer and nanoparticles (nanosilica sol and a carbon
nanomaterial) by the method of thermogravimetric analysis; the method makes it possible to obtain quantitative
information on the change in the mass of a specimen as a result of its heating. Thermogravimetry data have been
compared with the results of ultrasound investigation and nanoindentation.

**Author:**
E. N. Polonina, V. V. Potapov, S. A. Zhdanok, and S. N. Leonovich

**Keywords:**
complex admixture, nanomaterial, strength, thermogravimetry, nanoindentation, calcium silicate hydrate gels

**Page:**
67

**NUMERICAL SIMULATION OF THE HIGH-TEMPERATURE OXIDATION OF A NANOSIZE ALUMINUM PARTICLE**

A mathematical model of high-temperature oxidation of a nanosize aluminum particle has been presented. The model
takes account of the diffusion of the oxidant and the aluminum vapor through a spherical layer of alumina around
the aluminum melt, and also of the dependence of the rate of the reaction between the oxygen and the aluminum on
temperature. Calculations of the time of burning of a nanosize aluminum particle of diameter 80 mm as a function of
the temperature and pressure of the surrounding gas and of the oxygen concentration turned out to be in agreement
with the results of experimental measurements presented in scientifi c literature. The exponents in the dependence
of the burning time of a nanosize aluminum particle on the particle diameter and the temperature and pressure of
the ambient medium have been determined; it has been shown that the exponents are dependent on temperature,
pressure, and particle diameter.

**Author:**
A. Yu. Krainov, V. A. Poryazov, K. M. Moiseeva, and D. A. Krainov

**Keywords:**
nanosize aluminum particle, burning time, mathematical modeling

**Page:**
79

**PRODUCTION OF HfTaTiNbZrC5 HIGH-ENTROPY CARBIDE MICROPOWDER IN THE PLASMA OF AN ATMOSPHERIC PRESSURE ARC DISCHARGE**

HfTaTiNbZrC5 high-entropy carbide micropowder has been synthesized using the technique of direct-current plasma arc discharge at atmospheric pressure. The synthesis was carried out in air atmosphere under conditions of the formation of a protective carbon monoxide gas layer. TiO_{2}, ZrO_{2}, Nb_{2}O_{5}, HfO_{2}, and Ta_{2}O_{5} oxide metal powders
included in the composition of high-entropy carbide with characteristic grain dimensions of 5–10 μm have been
used as raw feedstock. It has been shown that it takes at least 90–100 s for the formation of high-entropy carbide
to occur from raw feedstock under the action of arc discharge plasma. The advantage of the proposed method of
producing high-entropy carbide micropowder compared to other similar methods is the short time of synthesis of
such powder with low energy expenditure (~960 kJ/g) and the possibility of using simple equipment for synthesis.

**Author:**
A.Ya. Pak, P. S. Grinchuk, G. Ya. Mamontov, T. Yu. Yakich, and A. A. Gumovskaya

**Keywords:**
high-entropy carbide, electric-arc synthesis, vacuum-free method, atmospheric plasma

**Page:**
88

**SOLUTION OF THE STEFAN TWO-PHASE PROBLEM WITH AN INTERNAL SOURCE AND OF HEAT CONDUCTION PROBLEMS BY THE METHOD OF RAPID EXPANSIONS**

The Stefan two-phase problem with an internal source, as well as the heat conduction problem for rectangular
and curvilinear regions, has been solved by the method of rapid sine-expansion, which involves the Fourier series.
The problem of heat conduction in a body of rectangular form was solved in a general form with the Dirichlet
conditions and an internal heat source by the method of rapid expansion, and thereafter the problem for a body of
curvilinear shape. The solutions obtained were used in considering the Stefan problem with unknown curvilinear
interface. Expressions are presented for matching the input data of the problem, on satisfaction of which the solution
will be universally continuous everywhere in the region of the rectangle together with derivatives up to the sixth
order inclusive. The nonfulfi llment of these conditions leads to the discontinuity of the solution at the corner points.
The algorithms of the solution of problems in rectangular and curvilinear regions, as well as of the Stefan twophase problem, are written. The solution for the rectangular region is represented in an explicit form, whereas the
solution for the curvilinear region and the solution of the Stefan problem are reduced to a closed algebraic system
of equations of small volume

**Author:**
A. D. Chernyshov

**Keywords:**
heat conduction problem, Stefan two-phase problem, rapid sine-expansion, Fourier series

**Page:**
95

**DETERMINATION OF THE VOLUMETRIC COEFFICIENT OF MASS TRANSFER IN COOLING TOWERS WITH JET–FILM CONTACT DEVICES**

A new construction of the cooling tower sprinkler block consisting of jet–fi lm contact devices has been developed. The proposed packings are capable of increasing the surface of contact of phases at a small number of wetting points, a minimum percent of droplet entrainment by a gas fl ow, and a low hydraulic resistance. Based on the method of transfer units, generalizing the results of experimental investigations of the process of water cooling in the developed cooling tower sprinkler block, an expression has been obtained for calculating the volumetric coeffi cient of mass transfer with account for the ratio between the mass fl ow rates of air and water, as well of the wetting density. It has been established that an increase in the mean-fl ow speed of air leads to an increase in the values of the volumetric coeffi cient of mass transfer because of the increase in the degree of gas fl ow turbulence. Comparison results of calculations of the volumetric coeffi cient of mass transfer for different cooling tower sprinkler blocks are given. It has been established that at small ratios of unit loads (G_{m}/L_{m} up to 0.5) a sprinkler made of lattice elements is most effi cient. It has been proven that on increase of the ratio of init loads (G_{m}/L_{m }> 0.5), the sprinkler block consisting
of the proposed jet–fi lm contact devices has the highest cooling capability. The expression obtained for calculating
the volumetric coeffi cient of mass transfer can be used in designing and modernization of industrial, cooling towers
with jet–fi lm contact devices.

**Author:**
A. V. Dmitriev, O. S. Dmitrieva, and I. N. Madyshev

**Keywords:**
heat/mass transfer, cooling, jet–fi lm contact device, circulating water, cooling tower

**Page:**
113

**EXPERIMENTAL INVESTIGATIONS INTO THE SPEED OF THERMOELECTRIC BEVERAGE COOLERS WITH WET CONTACT**

The structure of a novel table thermoelectric cooler with wet contact, i.e., with a water-fi lled gap between the
container with a beverage and the cooler chamber, has been presented. The test bed and the procedure of tests
and their results have been described. Technical advantages of the novel cooler have been shown, in particular,
the increase in its speed, which amounted to 15 to 65%. The effect of acceleration of the cooling of the beverage
due to the activation of the second mechanism of heat exchange, i.e., natural convection, has been found and
described.

**Author:**
S. O. Filin and B. Zakrzewski

**Keywords:**
beverage cooler, cooling time, heat-exchange conditions, experimental investigations

**Page:**
118

**MATHEMATICAL SIMULATION OF THE ACTION OF OSCILLATIONS OF A BLUNT-NOSED CONIC BODY ON THE CONJUGATE HEAT AND MASS TRANSFER IN ITS COATING**

The infl uence of oscillations of a conic body with a nose blunted over a sphere on the conjugate heat and mass
transfer in its heat-resistant coating in the case where the material of the conical part of the body is subjected
to thermomechanical failure as a result of the fl ow of a high-enthalpy gas over it was investigated. Results of a
numerical investigation of the three-dimensional supersonic fl ow over such a body executing an oscillatory motion
in the pitch plane are presented.

**Author:**
K. N. Efi mov, E. L. Loboda, V. A. Ovchinnikov, and A. S. Yakimov

**Keywords:**
heat shield material, conjugate heat and mass transfer, oscillations, angle of attack, supersonic fl ow

**Page:**
127

**THERMAL EFFECTS IN THE FLOW OF A POLYMER AQUEOUS SOLUTION THROUGH A HYDROCUTTING JET-FORMING HEAD**

An experimental study of the rise in the temperature of a water–polymer jet, which occurs in hydrocutting and is
caused by the Joule–Thomson effect, has enabled the authors to propose a method to enhance the process of hydrojet
water–polymer cutting of materials.

**Author:**
A. V. Pogrebnyak, I. V. Perkun, V. G. Pogrebnyak, and V. Ya. Shimanskii

**Keywords:**
polymer solution, water–polymer cutting, Joule–Thomson effect, phase diagram, abrasive additives

**Page:**
137

**RHEOLOGY OF STRUCTURED NON-NEWTONIAN OILS IN THE GAS-LIFT RECOVERY METHOD**

Consideration has been given to the problems of rheology of non-Newtonian oils in the gas-lift method of recovery.
An analysis of the state of a non-Newtonian oil containing asphalt resinous substances has enabled the authors to
investigate structuring and its infl uence on rheological properties. The formation of adsorption fi lms on the surface
of water droplets and gas bubbles leads to obtaining stable oil emulsions. The thickness of the adsorption layer as
a function of the content of asphalt resinous substances has been calculated. Experimental investigations into the
rheology of non-Newtonian oils have been proposed and rheological models have been obtained.

**Author:**
G. I. Kelbaliyev, T. Sh. Salavatov, S. R. Rasulov, and E. V. Mamedova

**Keywords:**
rheology, non-Newtonian oils, structuring, emulsions, experiment, rheological models, rate of shear, yield stress

**Page:**
143

**INTENSIFICATION OF THE DETACHED FLOW IN A SINGLE ROW OF INCLINED OVAL TRENCH DIMPLES ON THE WALL OF A NARROW CHANNEL**

An analysis of the intensifi cation of a steady-state detached turbulent air fl ow with Re = 104
in a row of oval trench
dimples, positioned on the wall of a narrow channel and oriented at an agile of 45o
to the incident fl ow, is given.
It is shown that the anomalously high velocities of the reverse and secondary fl ows at the entrance of such a
dimple (of the order of the mean mass velocity of the fl ow in the channel), as well as the negative friction in this
part of the dimple that exceeds in absolute value the friction on the plane wall of the channel by almost fi ve times,
are due to the difference between the total pressure in the near zones of stagnation of the air fl ow at the windward
slope of the dimple and the negative pressure at the site of generation of a whirlwind-like vortex structure in the
dimple.

**Author:**
S. A. Isaev, A. I. Leont′ev, D. V. Nikushchenko A. G. Sudakov, and A. E. Usachov

**Keywords:**
inclined oval trench dimples, narrow channel, intensifi cation, detached fl ow

**Page:**
151

**SLOPE FLOWS PRODUCED BY BULK HEAT RELEASE**

The Prandtl model of slope fl ows (convection in a stratifi ed medium near an inclined surface) has been generalized to
the case of the presence of bulk heat sources/sinks oriented in parallel with the slope. Such sources exist, for example,
when the atmosphere is fi lled with an aerosol exerting its infl uence on the radiation air balance. The properties of the
analytical solutions found are nontrivial in some respects. For example, the intensity of stationary slope fl ows may
increase with decrease in the inclination angle of the lower boundary. Numerical estimates show the possibility of
generation of noticeable atmospheric slope fl ows in the presence of an aerosol that infl uences the radiation balance.

**Author:**
L. Kh. Ingel′

**Keywords:**
slope fl ows, convection, bulk heat release, analytical model, Prandtl model, atmospheric aerosol, radiation balance

**Page:**
160

**MATHEMATICAL SIMULATION AND EXPERIMENTAL INVESTIGATION OF A CONTACTLESS MEASURING SECTION IN THE PROBLEM ON HIGH-VELOCITY BALLISTIC FLIGHTS**

A method and system for contactless measurement of the velocity of fl ight of a thrown body over a measuring base in
an air atmosphere and for the actuation of a recording apparatus by the signal formed as a result of the passage of
the body through a measuring section are presented. The method proposed is based on the formation of normalized
pulses of positive polarity for the synchronization of the activation of a recording apparatus by a defi nite coordinate
of a body thrown. Results of calculation and experimental investigations of variable reluctance pickups in tests
of high-velocity ballistic fl ights are presented. Relations allowing one to estimate the dependence of the magnetic
induction in the core of a variable reluctance pickup on the value of the air gap between a magnet and the pickup
are presented

**Author:**
S. I. Gerasimov, V. I. Erofeev, A. V. Zubankov, V. A. Kikeev, and V. V. Pisetskii

**Keywords:**
ballistic-fl ight tests, variable reluctance pickup, contactless measuring section, synchronization, magnetic fl ux, scattering coeffi cient.

**Page:**
165

**RECORDING OF HIGH-SPEED PROCESSES IN IMPACT DESTRUCTION OF A CONTAINER FILLED WITH A FLUID**

An experimental procedure has been developed to record phenomena in impact destruction of a container with a
fl uid. The phenomena were recorded using x-ray pulse devices and a high-speed fi lming technique. The propagation
of compression waves in the fl uid was registered using bubble-markers in the form of air curtains in the fl uid mass.
The pressure in the compression wave was measured by a gallium arsenide crystal-based sensor. An investigation
has been made into the characteristics of the phenomena occurring during the destruction of a container with a fl uid
by a high-speed striker. We have established the dependences of cavity development in the fl uid, the striker motion
law, the time dependence of pressure, and the pressure attenuation in the fl uid. The obtained dependences make it
possible to establish objective physical data on phenomena in impact-stressed containers and to solve the issue of
strength of a container with a fl uid.

**Author:**
V. M. Zakharov and A. N. Ishchenko

**Keywords:**
enclosed fl uid volume, high-speed striker, air bubble-marker, impact phenomena, compression wave, destruction

**Page:**
171

**A NUMERICAL METHOD FOR SOLVING THE EQUATIONS OF HYDRAULICS AND OF NONLINEAR ELECTRIC DC CIRCUITS**

The hydraulics equations are reduced to the form of the equations of nonlinear electric circuits by introducing
hydraulic resistances, which are analogous to electric resistances. The hydraulic resistances depend on unknown
discharges and are calculated from the discharges on the previous iteration. As a result, on the new iteration step it is
possible to solve a system of linear equations, from which discharges on the iteration half-step are found. Discharges
on the new iteration step are represented as linear combinations of discharges on the half-step and on the previous
step. The possibilities of the method are shown using the example of a hydrosystem with two pumps and three fl ow
governors

**Author:**
K. O. Sabdenov

**Keywords:**
pipeline, hydraulic system, numerical methods of hydraulics, iteration method

**Page:**
179

**REYNOLDS ANALOGY BASED ON THE THEORY OF STOCHASTIC EQUATIONS AND EQUIVALENCE OF MEASURES***

A new dependence has been obtained to calculate the Reynolds analogy in a nonisothermal turbulent fl ow in a
circular tube. The formula for the Reynolds analogy was obtained from stochastic turbulence theory, which is based
on stochastic differential equations of the laws of conservation of mass, momentum, and energy, and also on the
regularities of equivalence of measures between deterministic and random motions. A comparison has been made of
the calculation results for the classical formula and for the new formula for various Prandtl numbers.

**Author:**
A. V. Dmitrenko

**Keywords:**
stochastic equations, equivalence of measures, Reynolds analogy

**Page:**
186

**SIMILARITY SOLUTION FOR THE FLOW BEHIND A MAGNETOGASDYNAMIC EXPONENTIAL SHOCK WAVE IN A PERFECT GAS WITH VARYING DENSITY, HEAT CONDUCTION, AND RADIATION HEAT FLUX **

Similarity solutions are obtained for the propagation of a shock wave driven by a piston moving with time dependence
according to an exponential law in a perfect gas with azimuthal magnetic fi eld as well as with conduction and
radiation heat fl uxes. Heat conduction is described by the Fourier law, and radiation is considered to be of diffusion
type for the optically thick grey gas model. The thermal conductivity and absorption coeffi cient are assumed to vary
with temperature and density. The density and magnetic fi eld strength ahead of the shock front are assumed to vary
exponentially. The effects of the variations in the strength of the ambient magnetic fi eld, heat transfer parameters,
adiabatic exponent, and in the ambient density variation index on the fl ow fi eld characteristics are studied. The shock
strength is shown to be independent of the heat transfer parameters. The medium compressibility increases in the
absence of a magnetic fi eld.

**Author:**
R. Bajargaan, A. Patel, and M. Singh

**Keywords:**
exponential shock wave, self-similar solution, magnetic fi eld, conduction heat fl ux, radiation heat fl ux

**Page:**
194

**ON DISTRIBUTION OF VELOCITIES INSIDE A VAPOR–GAS BUBBLE OCCURRING IN AN ACOUSTIC FIELD**

A study has been made of the distribution of gas particle velocities inside a vapor–gas spherical bubble oscillating in
a liquid under the action of an acoustic fi eld. Calculations conducted for different vapor concentrations in the bubble
and different Peclet and Lewis numbers have shown that the deviation of the profi le of these velocities from a linear
dependence usually does not exceed 30%.

**Author:**
R. N. Khabeev and N. S. Khabeev

**Keywords:**
vapor–gas bubble, acoustic fi eld, radial oscillations, profi le of velocities

**Page:**
207

**ENTROPY ANALYSIS OF THE PROCESS OF BURNING OF A GAS IN THE FURNACE OF A WATER-TUBE BOILER WITH A SECONDARY RADIATOR**

An analytical study has been made of the operating processes of burning of natural gas in the furnace of a steam
water-tube boiler. The authors have determined the fi elds of the combustion-product temperature and of the heat-fl ux
density in the furnace volume, and also the thermodynamic parameters of the reaction of combustion of methane and
the enthalpy and entropy change of combustion products in the furnace with a secondary radiator and without it.
The distribution of the entropy fi elds has been given and the regions of high entropy production near heat-transfer
surfaces during the heat exchange of combustion products have been determined. To obtain optimum results, the
authors used the model of minimum entropy generation in the thermodynamic system. An exergy analysis has been
made of the operating processes of the chemical reactions of combustion and heat exchange of the combustion
products with the tubular surfaces of the steam boiler. The infl uence of structural and regime parameters of the boiler
furnace on the exergy loss has been shown.

**Author:**
Andriy Redko, Igor Redko, Yurii Burda, Serhii Pavlovskiiy, Andriy Redko,a Igor Redko, Yurii Burda, Serhii Pavlovskiiy,

**Keywords:**
entropy analysis, entropy generation, burning of a gas, water-tube boiler, furnace, secondary radiator

**Page:**
210

**EXPERIMENTAL SIMULATION AND MULTIOBJECTIVE OPTIMIZATION OF THE WORK OF A PELLET BURNER FOR A TUBULAR GAS HEATER**

Results are presented from an experimental investigation into the working regime of a pellet burner for a tubular gas heater. A transition is shown from a set of primary measurements of input and output parameters to dimensionless groups. Regressional dependences of CO and NO_{x} concentrations in combustion products have been obtained. The
problem of multiobjective optimization of the work of a pellet burner has been solved.

**Author:**
V. F. Irodov, R. V. Barsuk, G. Ya. Chornomorets, and A. A. Chernoyvan

**Keywords:**
Results are presented from an experimental investigation into the working regime of a pellet burner for a tubular gas heater. A transition is shown from a set of primary measurements of input and output parameters to dimensionless groups. Regressional dependences of CO and NOx concentrations in combustion products have been obtained. The problem of multiobjective optimization of the work of a pellet burner has been solved.

**Page:**
219

**METHODS OF DETERMINING THE PERMEABILITY OF SELECTIVELY PERMEABLE MEMBRANES**

An exact solution of the problem on the dynamics of separation of a gas mixture in membrane separators of different
designs has been obtained. A procedure for interpreting the time dependence of the pressures on different sides
of a selectively permeable membrane for determining the coeffi cients of its permeability is proposed. The direct
and inverse problems on determination of the parameters of membrane separators were posed and solved. It was
established that the accuracy of determining the permeability coeffi cients of a selectively permeable membrane
depends on the duration of an experiment.

**Author:**
R. M. Ganopol′skii, A. Ya. Gil′manov, M. A. Demenchuk, I. O. Dmitriev, K. M. Fedorov, and A. P. Shevelev

**Keywords:**
selectively permeable membrane, separation, gas mixture, thermodynamics, nonstationary problem, mass transfer

**Page:**
226

**THERMAL PROPERTIES OF HUMAN SOFT TISSUE AND ITS EQUIVALENTS IN A WIDE LOW-TEMPERATURE RANGE**

A prescribed amount of heat to be removed from biotissues during cryogenic treatment is currently calculated with the use of simple prediction models. Therefore, a signifi cant distinction exists between the calculated and actual doses during the operation. For reliable simulation, it is necessary to have accurate thermal properties of human tissues in a wide low-temperature range, but in the literature the data regarding these thermal properties are inconclusive. In the present paper, the thermal properties of human prostate, kidney, liver, and pancreatic tissues are analyzed. Using differential scanning calorimetry (DSC), the specifi c heat capacity in the temperature range from –160 to 40^{o}
С, the latent heat of melting, and the initial ice melting temperature are measured. The moisture content and
cryoscopic temperature of these tissues are also investigated. Due to the diffi culties with getting access to a human
cardiac muscle and large specimens of other human biotissues, in the present study equivalents (porcine tissues)
are used on the basis of their high similarity to human biotissues. In this case, only the thermal conductivity of a
porcine cardiac muscle is determined. Based on the measurement results, the thermal properties of the same tissue
type and of different types (including healthy tissues and tumors) are compared. The adaptation of experimental
data for simulation software is proposed. The impact of the accuracy in determining the thermal properties on the
thermal diffusivity is analyzed. The prospects in predicting the thermal properties of different biological tissues are
considered. Based on the data obtained, it is possible to more accurately simulate heat transfer during cryoexposure.

**Author:**
I. V. Agafonkina, A. G. Belozerov, A. O. Vasilyev, A. V. Pushkarev, D. I. Tsiganov, A. V. Shakurov and A. A. Zherdev

**Keywords:**
differential scanning calorimetry (DSC), heat capacity, thermal conductivity, biological tissue, prostate, liver, pancreas, heart, kidney

**Page:**
233

**ON THE PROBLEM OF DESIGNING THE ANISOTROPIC MATERIAL OF SHELL SLEEVES WITH A FREE EDGE IN THE CORE OF A NUCLEAR ROCKET ENGINE**

The author gives numerical results on taking account of the infl uence of anisotropy of physicomechanical properties
of free-edge cylindrical shell sleeves from orthotropic material on the stressed state in fuel assembles of the core of
a nuclear rocket engine in their probable local radial interaction, which is important in designing.

**Author:**
B. V. Nerubailo

**Keywords:**
differential equation, boundary conditions, Fourier series, stressed state, local load, physically orthotropic, transversally isotropic

**Page:**
247

**CALCULATION OF THE HEAT AND MASS TRANSFER AND THE STRAINED STATE OF SANITARYWARE IN THE PROCESS OF ITS CONVECTION DRYING**

A numerical calculation of the heat and mass transfer and the strained state of sanitaryware in the process of its
drying in a convection drier is presented. The problem on the convection drying of this ware was solved in the
three-dimensional formulation with the use of the ANSYS program complex, allowing one to construct visual threedimensional geometric models of objects.

**Author:**
V. A. Sychevskii

**Keywords:**
convection drying, sanitaryware, heat and mass transfer, strained state, numerical calculation, computational experiment

**Page:**
254