**HEAT AND MASS TRANSFER IN POROUS AND DISPERSION MEDIA**

**
EXTRACTION FROM A POROUS BODY ****IN THE PRESENCE OF PERIODIC FLUID**

**
FLOW ON IT**

A. I. Moshinskii UDC 532.62:66.02

This paper considers the nonstationary process of extraction from a solid body modeled by a system of semiinfinite capillaries connected with a group of no-flow channels when the mass transfer velocity in the flow is composed of two components — a constant velocity component and a time-periodic addition to the first one that is assumed to be small relative to the amplitude. We have obtained analytical dependences for the masstransfer characteristics that are of practical interest: the concentration and the diffusion flow for both the main approximation and with correction for the periodic action on the system.

**Keywords:** two-component model, mass transfer, periodicity, porous body, extraction.

**TRANSFER BY METALLIC SERVICE LINES AND SORPTION**

**
EXTRACTION OF MoF6 FROM THE GAS FLOW**

A. A. Artyukhov, Ya. M. Kravets, M. B. Seregin,

D. Yu. Chuvilin, A. V. Shatrov, and N. G. Shchepetov

UDC 544.723.52

The results of investigation of the sorption of molybdenum hexafluoride MoF6 on granulated sodium fluoride NaF have been presented; the data of measurements of the MoF6 loss in transport by technological service lines of a reactor ampoule plant with molten-salt fuel have been given.

**Keywords:** sorbent, radioisotopes, molten salts, molybdenum hexafluoride, Mo-99, sodium fluoride.

**ON FREE CONVECTION IN A HEAT-RELEASING**

**
GRANULAR BED**

G. I. Kovenskii, Yu. S. Teplitskii,

and V. I. Kovenskii

UDC 536.25

Free convection in a heat-releasing granular bed for constant and exponential forms of heat release has been mathematically modeled on the basis of a two-temperature model. The extremum character of the dependence of the flow rate of the gaseous heat-transfer agent on the heat-release power and bed "choking" (cessation of the heat-transfer-agent filtration) for higher-than-average heat releases have been established. Dimensionless dependences for calculation of the flow rate of the heat-transfer agent and its outlet temperature in the region

of stable convection have been obtained.

**Keywords:** granular bed, free (natural) convection, bed choking, two-temperature model, heat-transfer agent.

**PRESSURE TRANSIENT ANALYSIS**

**
OF DEFORMABLE RESERVOIRS**

A. A. Shchipanov UDC 532.546, 622.276

A new integrated methodology of evaluating the change in the permeability of a fractured or pressure-sensitive porous reservoir based on analytical or numerical simulation of a fluid inflow to a well has been proposed.

The analysis draws on results of well tests. Analytical solutions of direct and inverse problems allow an evaluation of the permeability variation with decreasing pressure. Numerical simulation of an unsteadystate fluid inflow to a well (a direct problem) allows determining the diagnostic signs of variation in the reservoir permeability from the dynamics of the bottom hole pressure and an assessment of the evaluations obtained from solving an inverse problem. The methodology has been approved using results of some well tests.

**Keywords: **deformable reservoir, fractured reservoir, porous medium, fluid flow (filtration), permeability variation, well tests, reservoir simulation.

**SUBSTANCE TRANSFER IN A POROUS MEDIUM**

**
SATURATED WITH MOBILE AND IMMOBILE LIQUIDS**

B. Kh. Khuzhayorov, Zh. M. Makhmudov,

and Sh. Kh. Zikiryaev

UDC 532.546

Consideration has been given to the problem of transfer of a substance in a porous medium consisting of two zones: a) with transit pores (with a mobile liquid) and b) with an immobile liquid (with bound water) with allowance for the effects of convective transfer, hydrodynamic dispersion, substance adsorption, and internal mass transfer between both zones. The fields of substance concentration, adsorption, and internal mass transfer for different cases determined by the character of adsorption and internal mass exchange have been determined.

It has been established that the presence of zones with an immobile liquid significantly influences

the general characteristics of substance transfer in the porous medium.

**Keywords:** substance adsorption, internal mass transfer, hydrodynamic dispersion, zones with a mobile and immobile liquid, substance transfer, porous medium.

**ON MAIN METHODS OF DECREASING THE HEAT**

**
CONSUMPTION IN PROCESSES OF CONVECTION DRYING**

M. M. Razin UDC 664.047(031)

The possibility to substantially decrease the heat consumption in the drying of moist materials by artificial retardation of the process was theoretically substantiated. Main variants of organization of the drying of the indicated materials for the purpose of increasing the efficiency of the process were analyzed.

**Keywords:** drying, saving of energy, heat efficiency, rules, retardation, ballast zones, pulsed regime, recirculation,

methods.

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

**
MODELING OF HEAT CONDUCTION PROCESSES**

**
IN LAYERED HYBRID COMPOSITES OF REGULAR**

**
STRUCTURE WITH SLIT-LIKE LAYERS**

A. P. Yankovskii UDC 536.21

Models of the thermal conductivity of a layered medium with regularly alternating slit-like layers without regard for the time of relaxation of materials of the composition phases and with due regard for this relaxation time are suggested. It is shown that the effective thermal conductivity coefficients of such a medium depend substantially on the composition temperature. Concrete calculations of the effective characteristics of layered compositions depending on temperature, transverse dimension of slit-like layers, and on their specific volume content are carried out.

**Keywords**: heat conduction, hybrid composites, slit-like layers, generalized Fourier law, Stefan–Boltzmann law, relaxation time.

**CONJUGATE HEAT TRANSFER**

**
IN A ROTATING DISC WITH HOLES**

K. N. Volkov UDC 532.529

Problems connected with the simulation of conjugate heat transfer in the flow of a viscous compressible fluid past a rotating disc with holes are considered. The discretization of the equations describing the temperature distribution inside a solid body and the fluid flow characteristics, the construction of computational meshes, and the control of the integration time step are considered. The results of the calculations of the metal temperature at control points of the model and the heat transfer coefficient distribution over its boundaries are

presented.

**Keywords:** conjugate heat transfer, rotating disc, numerical simulation, turbulence.

**INVESTIGATION OF THE MECHANISMS OF HEAT**

**
CONDUCTION IN DIELECTRICS AND METALS**

**
ON THE BASIS OF THE MOLECULAR-RADIATION**

**
THEORY OF TRANSFER**

N. I. Nikitenko UDC 536.2

The activation mechanisms of transfer of a substance in condensed media are described. Analytical expressions defining the dependences of the electron, photon, and diffusion heat conductivity on the temperature, density, and microscopic characteristics of these media are presented. The temperature dependence of the density of free electrons in conductors was obtained. The results of a comparison of theoretical and experimental data are presented.

**Keywords:** electron, photon, and diffusion mechanisms of heat conduction, activation processes, molecular-radiation theory of transfer, density of free electrons.

**CONDITIONS AND METHODS OF DISSOLUTION**

**
OF SCALE IN BOILERS**

B. Ya. Kamenetskii UDC 621.18+536.24

Three methods of dissolution (washing off) of deposits on the surface of heat-exchange channels have been considered.

**Keywords:** heat-exchange channels, scale deposits, calcium carbonate, dissolution of deposits, reduction in the load, nucleate boiling.

**HEAT AND MASS TRANSFER IN CHEMICAL TRANSFORMATIONS AND COMBUSTION**

**
EXPERIMENTAL INVESTIGATION OF THE LENGTH**

**
OF A FREE DIFFUSION JET OF FUEL GASES**

**
DILUTED WITH INERT GASES**

Yu. V. Polezhaev,a B. A. Vorob’ev,b G. K. Korovin,b

D. I. Lamden,a I. L. Mostinskii,a and R. L. Shiginb

UDC 536.461:536.25

Experimental investigation of the length of single burning jets of methane and hydrogen previously diluted with an inert gas (nitrogen or helium) was carried out. Efflux of fuel gases into the atmosphere occurred through cylindrical extension pieces 4 and 8 mm in diameter. The Reynolds numbers at the cut of a piece varied in the range from 400 to 12,000. A clearly defined dependence of the jet length on the quality of the added inert gas is obtained. The correlation of experimental data made it possible to recommend formulas for engineering calculations of free laminar and turbulent jets.

**Keywords:** combustion, flame, jet length, inert gas, dilation.

**STEAM FEED AND EFFECT OF STEAM-THERMAL**

**
SEAL IN THERMOLYSIS OF TIRE SHREDS**

**
IN A SCREW-TYPE REACTOR**

V. A. Kalitko UDC 536.246.2

On the basis of experience in commercial operation, the effect of steam seal in tire-shred pyrolysis in a screw-type reactor with superheated steam has been considered and analytically substantiated; there, local steam feed produces the above effect at the total reduced pressure and keeps air from entering the reactor without sluices or valves used for hermetization of its loading and unloading. It has been shown that the increase in the production rate of pyrolysis due to the heating by steam amounts to 10–15% and is limited by the diffusion transfer in the reactor’s charge bed.

**Keywords:** shreds, tires, processing, pyrolysis, steam, pressure, rarefaction.

**HEAT AND MASS TRANSFER IN HYDROGEN PRODUCTION**

**
BY ELECTROLYSIS OF A WATER-COAL SUSPENSION**

V. B. Troshen’kin, V. P. Markosova,

and B. A. Troshen’kin

UDC 662.76; 622.7.002.82

The possibility of electrochemical gasification of a water-coal suspension at a temperature of 180–460oC and a pressure of 7–20 MPa has been proved experimentally. The obtained producer gas contains mainly hydrogen and carbon dioxide as well as traces of methane, propane, and carbon monoxide. After washing carbon dioxide with weak alkaline solutions hydrogen is dispatched for use in power engineering. The liquid phase contains an insignificant amount of hydrocarbons. Heat and mass transfer between reacting media in the electrolyzer

under the conditions of phase transitions with partial absorption of the formed gases has been considered.

**Keywords:** hydrogen, carbon, coal waste, water-coal suspension, electrolyzer design, Gibbs energy.

**HYDROGASDYNAMICS IN TECHNOLOGICAL PROCESSES**

**
MODELING OF SWIRLING TURBULENT FLOW**

**
IN A SEPARATOR WITH BICONICAL PLATES**

A. V. Shvab and A. G. Chepel’ UDC 532.517.4

Turbulent swirling flow in the gap between rotating cones, which represents the working element of a platetype centrifugal separator, is modeled numerically. On the basis of the introduced orthogonal biconical coordinate system, numerical solution of the Reynolds equations is modeled; these equations are closed using the well-known Wilcox differential two-parameter k–ω turbulence model. The results of the numerical solution are represented in the form of the distribution of the averaged velocity components and the characteristic

turbulence parameters as functions of the operating and geometric parameters in the separator’s working element; the reliability of the results is confirmed by comparing to test calculations and to the existing experimental data.

**Keywords: **turbulent flow, biconical coordinate system, spaced grid, separator, centrifugal force, turbulent stresses, generalized alternating-direction method.

**TURBULENT REGIME OF THERMOGRAVITATIONAL**

**
CONVECTION IN A CLOSED CAVITY**

G. V. Kuznetsova and M. A. Sheremetb UDC 669.86:536.21

We have performed a numerical analysis of the nonstationary turbulent natural convection in a closed region with heat-conducting walls of finite thickness and a heat source located at the cavity base under the conditions of convective-radiative heat exchange with the environment. Typical distributions of the thermohydrodynamic parameters (streamlines, temperature field, field of the kinetic energy of turbulence, and dissipation field of the kinetic energy of turbulence) in a fairly wide range of Grashof numbers 107 ≤ Gr ≤ 109 have been obtained. Results characterizing the scales of influence of the nonstationarity factor and the relative heat conductivity

coefficient of the material of the surrounding walls on the heat transfer intensity are presented. A

correlation for determining the average Nusselt number on the heat source surface has been established.

**Keywords:** conjugate heat transfer, turbulence, natural convection, heat source, closed region.

**INFLUENCE OF THE ANGLE OF INCLINATION**

**
OF ROUND-FINNED TUBES IN A STAGGERED**

**
TUBE BUNDLE ON THE FREE CONVECTIVE**

**
HEAT EXCHANGE BETWEEN IT AND AN UNBOUNDED**

**
AIR SPACE**

V. B. Kuntysha and A. V. Samorodovb UDC 536.25

Results of experimental investigations of the average heat transfer from five-row staggered bundles of tubes

with knurled spiral fins, operating in the free air-convection regime, in the case where the angel of inclination of the longitudinal axis of the tubes changed from 0 to 60o are presented. The investigations were carried out by the method of complete heat simulation. The average heat transfer was measured in the direction of a free air flow in each row of a tube bundle. The experimental data were generalized by similarity equations for calculating the average heat transfer from the tube bundles and their individual rows in the range of change in the Rayleigh number characteristic of the operating conditions of industrial heat exchangers assembled

from finned tubes of the type of the above-indicated tubes.

**Keywords:** round-finned tube, free air convection, reduced heat-transfer coefficient, similarity equation, transverse row, heat simulation.

**ON A VARIANT OF THE METHOD OF CHARACTERISTICS ****FOR CALCULATING ONE-VELOCITY FLOWS ****OF A MULTICOMPONENT MIXTURE**

V. S. Surov UDC 532.529.5

A variant of the method of characteristics for integration of equations defining one-velocity flows of a multicomponent mixture in the adiabatic approximation with the use of fixed grids is described.

**Keywords:** one-velocity flow of a multicomponent mixture, hyperbolic systems, method of characteristics, numerical

simulation.

**ON A METHOD OF APPROXIMATE SOLUTION ****OF THE RIEMANN PROBLEM FOR A ONE-VELOCITY ****FLOW OF A MULTICOMPONENT MIXTURE**

V. S. Surov UDC 532.529.5

A method of approximate solution of the Riemann problem on the basis of characteristic relations that can be used in numerical schemes of the Godunov method for integration of equations defining a one-velocity flow of a multicomponent mixture in the adiabatic approximation is presented.

**Keywords:** one-velocity flow of a multicomponent mixture, hyperbolic systems of nondivergent form, Riemann problem, numerical simulation.

**ANALYSIS OF THE EFFECTS OF INLET ****TEMPERATURE FREQUENCY IN FULLY**

**
DEVELOPED LAMINAR DUCT FLOWS**

A. Hadiouche and K. Mansouri UDC 536.2

Unsteady heat transfer for a fully developed laminar flow inside a parallel-plate channel and circular duct that are subjected to a periodically varying inlet temperature is studied. The thermal capacitance of the duct wall and the boundary condition that accounts for external convection are considered. An exact solution is presented for this extended Graetz problem as the result of using a new methodology based on a variational method. The quasi-steady approach that employs a heat transfer coefficient at the liquid–solid interface is also investigated, and the results are compared with the variational solution. The damping and phase lag coefficients

as functions of the inlet temperature frequency are presented in graphical form.

**Keywords: **conjugated forced convection, internal laminar flow, periodic inlet temperature, quasi-steady model,

analytical solution.

**NANOSTRUCTURES**

**
RADIATION STABILITY OF CARBON NANOSTRUCTURES**

G. Ya. Gerasimov UDC 537.533.9

A theoretical study of the radiation stability of carbon nanostructures irradiated by an electron beam has been made. Calculations have been performed with the use of an analytical expression for the cross-section for scattering of relativistic electrons by carbon atoms, as well as of the data on the threshold energy of atomic displacement from the carbon lattice obtained by the molecular dynamics method. Stability limits of carbon nanostructures and basic parameters of the process have been found. The calculated values of the

characteristic time of the process are in good agreement with the available experimental data.

**Keywords:** carbon nanostructures, fullerenes, carbon nanotubes, graphene, electron beam, radiation stability.

**CHEMICAL REACTIONS IN NANOPARTICLES**

V. V. Levdanskii,a J. Smolik,b

and P. Moravecb

UDC 541.182

The problems related to the influence of the nanoparticle size on the chemical reaction proceeding in it are investigated theoretically. As an example, the reaction of oxidation of a nanosized silicon particle is considered.

**Keywords:** nanoparticle, chemical reaction, size effect.

**MISCELLANEA**

**
GENERATOR OF HIGH-PURITY ABLATION PLASMA ****OBTAINED FROM A DIELECTRIC MATERIAL ****AT ATMOSPHERIC PRESSURE**

V. B. Avramenko, A. M. Kuz’mitskii,

and A. A. Mishchuk

UDC 535.95

A pulsed plasma source providing generation of a high-purity erosion plasma from a dielectric material at atmospheric pressure by analogy with a capillary discharge has been developed. The chemical and ionization compositions of the plasma obtained with this source were determined by the spectroscopic method and its energy parameters were determined by electrophysical methods. The indicated plasma source provides generation

of a low-temperature plasma at a comparatively low pressure in a discharge volume.

**Keywords:** source of ablation plasma, high-purity plasma, spectroscopic investigations of plasma, surface discharge.

**EFFECTIVE CONTROLLABILITY ****OF A COMPOSITE IN STRONG FIELDS**

A. G. Kolpakova and S. I. Rakinb UDC 539.3:517.9

A method and computer program for numerical solution of the problem of averaging of a nonlinear composite of periodic structure have been developed. The effective dielectric constant and effective coefficient of controllability of a composite of the ferroelectric-dielectric type have been calculated for arbitrary values of the averaged electric field (earlier such calculations were performed only in the approximation of weak fields). It has been established that the phenomenon of the stability of the effective coefficient of the controllability is

preserved for arbitrary values of the averaged electric field.

**Keywords:** effective controllability, nonlinear composite of periodic structure, effective dielectric constant, effective

coefficient of the controllability, gradient method.

**MOLECULAR-STATISTICAL DESCRIPTION OF THE SPECIFIC ****HEAT OF THERMAL-VACANCY CRYSTALS. 1. STATISTICAL ****MODEL OF ALLOWANCE FOR THE CONTRIBUTION ****OF THE VACANCY SUBSYSTEM TO THE LATTICE SPECIFIC**

**
HEAT OF CRYSTALS**

I. I. Narkevich, A. V. Zharkevich,∗

and E. V. Farafontova

UDC 536.758+539.311

A simple statistical model of a condensed system with pair particle interaction, which is described by the Lennard-Jones potential, has been proposed. Under the assumption that the probability of filling a microcell pair is equal to the product of the probabilities of filling single cells, a variational problem on minimization of free energy by the model’s internal parameter has been formulated. An analytical expression for the addition to the vibrational specific heat of a molecular vacancy crystal has been obtained. A refined model in which the correlation in filling microcell pairs with pores is allowed for has been considered; a refined expression for the addition to the vibrational specific heat, which contains the corresponding small corrections, has been

obtained.

**Keywords:** condensed molecular system, thermal vacancies, statistical model, correlation, conditional-distribution method, correlative functions, average-force potential, lattice specific heat.

**ESTIMATION OF ARBITRARY-DISTRIBUTION PARAMETERS**

**
FROM THE DATA OF A REPETITIVE EXPERIMENT**

E. V. Chernukho UDC 519.23:53.089.6

Regular statistics making it possible to efficiently estimate the parameters of arbitrary distribution for the case of a repetitive experiment is described and substantiated. The methodology of engineering mathematics is used for derivation and substantiation of the statistics.

**Keywords:** regular statistics, estimation of parameters, repetitive experiment, calibration function.