**HEAT AND MASS TRANSFER IN POROUS AND DISPERSIVE MEDIA ****APPLICATION OF THE DEPRESSURIZATION METHOD**

**
IN HIGH-TEMPERATURE OSCILLATING DRYING**

**
OF LARGE-SIZE LUMBER PRODUCTS**

V. P. Kozhin and N. M. Gorbachev UDC 674.047

This paper presents the results of experimental studies of accelerated drying of pine lumber products (poles,

supports, structural elements, etc.) of diameter up to 0.2 m. The heat treatment time in the oscillating regime

of depressurization is from 8 to 35 h depending on the parameters of the lumber and on its initial and final

moisture. A good quality of drying has been achieved.

**Keywords:** accelerated drying, large-size lumber products, depressurization.

**MATHEMATICAL STUDY OF HYDROCYCLONE ****DISPERSED PHASE SEPARATION IN CLEARING ****VISCOPLASTIC DRILLING FLUIDS**

O. V. Matvienko and E. V. Evtyushkin UDC 621.928.37

On the basis of rheodynamic equations, a numerical investigation of the flow structure of a viscoplastic fluid

and dispersed phase separation in a hydrocyclone has been carried out. The proposed mathematical model

will make it possible to calculate the separation indices and the velocity, pressure, and particle density fields

in the apparatus.

**Keywords:** hydrocyclone, separation, viscoplastic fluid, mathematical modeling, multiphase flows.

**MATHEMATICAL MODELING OF THE HEAT ****TREATMENT AND COMBUSTION OF A COAL ****PARTICLE. II. DRYING STAGE**

Kh. Enkhzhargala and V. V. Salomatovb UDC 621.311

This article is a continuation of the previous article in which, with the aid of mathematical modeling, the regime

of radiative-convective heating of a coal particle was studied in detail and which was devoted to an

analysis of the stage of coal drying, very important in the general picture of coal combustion. The process of

coal drying is formulated as the nonlinear Stefan problem with a moving liquid-vapor phase change interface.

The rate and time of coal particle drying, the temperature distribution inside a particle, and other parameters

of the process have been found approximately analytically depending on the regime of heat supply. A parametric

analysis of the influence of physical and regime factors on the dynamics of drying as an integral part

of heat treatment of a fuel for its ignition and combustion has been carried out.

**Keywords:** coal, combustion, heating, drying, burning, coke residual, mathematical model, evaporation.

**EQUATIONS OF THE KINETICS OF DROPLET ****FRAGMENTATION IN A HIGH-SPEED GAS FLOW**

A. G. Girin UDC 532.529.6

For the conditions of a high-speed gas flow, within the framework of the model of quasi-continuous fragmentation

of a droplet due to the mechanism of gradient instability, a differential equation of mass loss has been

obtained. Within the approximation of the droplet sphericity, the law of variation of its mass, which depends

on droplet acceleration by the gas stream, as well as the conditions and time of complete fragmentation of

the droplet, have been found. A differential equation for the quantity of torn off droplets, has been obtained.

In the event of equality between the rates of dispersion and relaxation equalization of the droplet and gas

flow velocities, the size distribution functions of the number and mass of torn off droplets, as well as the values

of the modal radius and total number of torn off droplets, have been found.

**Keywords:** gradient instability, dispersion, kinetics equation, law of mass variation, size distribution of droplets.

**ON CERTAIN REGIMES OF INCLUSION ****DRIFT IN ACOUSTIC FIELDS**

D. A. Gubaidullin and P. P. Osipov UDC 539.37

The inclusion drift in acoustic fields is investigated by analytical methods. A formula for the total force acting

on a spherical inclusion with allowance for the compressibility of the carrier phase and the inclusion is obtained.

A formula for the frequency after which the total force changes its direction is derived. The total-force

directional diagram proposed by the authors earlier is refined.

**Keywords:** particle drift, forces in acoustic wave fields.

**MODELING OF IRON SCALE REDUCTION BY METHANE ****CONVERSION PRODUCTS IN A PLASMA JET. ****I. THERMODYNAMIC MODELING**

B. B. Khinaa and P. S. Grinchukb UDC 544.536.46:541.128

We have performed thermodynamic modeling of the reduction of iron scale (production waste of metallurgy

and machine-building) by products of incomplete conversion of methane in oxygen for developing a process

of obtaining iron powder with the use of a plasma jet. We have calculated the equilibrium composition of

the gas phase and condensed interaction products at various temperatures and initial compositions of the

reducing medium. The optimal process parameters providing reduction of scale to pure iron, i.e., the temperature

range, the methane/oxygen ratio in the gaseous medium, and the scale/gas mixture mass ratio, have

been determined.

**Keywords:** iron scale, scale reduction, thermodynamic simulation.

**THERMAL CALCULATION OF THE EJECTION COOLING ****TOWER AND METHOD OF IMPROVING ITS EFFICIENCY**

A. A. Brin and A. I. Petruchik UDC 536.423.4

A mathematical model for thermal calculation of the ejection cooling tower has been proposed. New data on

the effect of the air flow rate, meteorological conditions, heat load, and water pressure in the water distribution

system of the cooling tower on the spray characteristics and water cooling have been obtained. A novel

method of improving the efficiency of the ejection cooling tower has been developed.

**Keywords:** evaporative cooling, ejection cooling tower, thermal calculation, water distribution system, efficiency

improvement.

**CHARACTERISTIC FEATURES OF EVAPORATIVE ****COOLING OF DROPLETS IN HIGH-TEMPERATURE**

**
FLOWS**

A. A. Brin, S. P. Fisenko,

and Yu. A. Khodyko

UDC 536.423.4

Numerical investigation of the evaporative cooling of water droplets in a high-temperature gas flow (temperature

above 1000oC) has been carried out for two limiting regimes: a continuous medium and a free-molecular

regime. The results of modeling have shown that with a small content of water vapor in the flow, due to evaporative

cooling the droplet temperature attains a stationary value that is lower than the stream temperature

by hundreds of degrees.

**Keywords:** heat transfer coefficient, droplet temperature, flow reactor, thermophoresis.

**INVESTIGATION OF THE PROPAGATION ****OF POLLUTANTS IN WATER RESERVOIRS**

Sh. A. Kerimova UDC 539.376

A mathematical model for investigating the problem of the propagation of pollutants in water reservoirs on

salvoed (instantaneous) discharge is suggested. To calculate dilution, a method developed on the basis of the

equation of turbulent diffusion in cylindrical coordinates is suggested. The method allows one to determine the

concentration of pollutants at an arbitrary distance from the place of their discharge. The conditions for the

formation of local pollution zones in a water reservoir are considered.

**Keywords: **simulation, pollution, water reservoirs, discharge, sewage, pollutants, diffusion, propagation of

impurities.

**MODELING OF THE SOLID–LIQUID BUBBLE ****INTERFACE IN PARTIAL NUCLEATE BOILING**

M. E. Hocine Benhamza and Fella Chouarfa UDC 536.423

Several models of heat transfer in partial nucleate boiling are identified in order to determine the relationship

between the dominant physical parameters. The correlations are different for different models, so the main

goal of this analysis is to determine the validity of each model and to identify the most dominant physical

phenomenon in the nucleate boiling heat transfer. This is done by comparing the results of different models

with a vast range of reliable experimental data. The comparison shows that the Sakashita and Kumada model

gives the best results in the nucleate boiling heat transfer. It is also shown that the most dominating phenomenon

in isolated partial bubbles zones is the transient conduction taking place mainly under the bubbles.

This is in contradiction with a majority of the models that consider convection as the most important mode

in the nucleate boiling heat transfer. The selected model can also be extrapolated and used in the case of

fully developed bubbles zones.

**Keywords:** partial nucleate boiling, bubble detachment, heat transfer model.

**EFFECT OF DYNAMIC COUPLING ****IN THE FORMATION–WELL SYSTEM ****ON THE EFFICIENCY OF A DEEP-WELL**

**
PUMPING UNIT**

E ′. M. Abbasov UDC 622.276;532.546

A mathematical model of dynamic coupling in the formation–well system is constructed, and on the basis of

theoretical investigations the effect of this coupling on the efficiency of a deep-well pumping unit is determined.

An expression for the fluid inflow to the well in unit time with allowance for the dynamic formation–

pump coupling is obtained. The pressure distribution in the formation is determined. It is found that with a

rise in the dynamic level of fluid in the hole annulus the oscillating component of the fluid inflow to the well

increases.

**Keywords:** filtration, Bessel function, dynamic level, deep-well pumping unit, dynamic coupling, formation, well,

external boundary, pressure.

**ON THE EFFICIENCY OF CERTAIN ****POPULAR METHODS USED IN CALCULATION ****OF DRYING PROCESSES**

M. M. Razin UDC 542.47/664.047(031)

A theoretical analysis of a number of calculation methods widely used in modeling of drying is presented; the

limitation of the methods by the narrow framework of operating parameters is noted. The latter makes it difficult

to apply them to solution of current problems of optimization of processes.

**Keywords:** drying, methods, temperature curves, kinetic equation, equilibrium.

**HEAT CONDUCTION AND HEAT TRANSFER IN TECHNOLOGICAL PROCESSES ****HEAT CONDUCTION EQUATION IN ****FRACTIONAL-ORDER DERIVATIVES**

A. B. Alkhasov, R. P. Meilanov,

and M. R. Shabanova

UDC 536.2.01

Based on the heat conduction equation in fractional-order derivatives, the influence of the nonlocality of the

heat conduction equation in time and space on temperature distribution in media with fractal structure is investigated.

The cases of an infinite and semibounded straight line are considered.

**Keywords:** fractal structure, fractional-order derivatives, nonlocal heat conduction equation, Mittag-Leffler function,

temperature distribution.

**MODELING OF THE TEMPERATURE FIELD ****OF THE CASTING LADLE LINING**

A. V. Zabolotsky UDC 536.248.1/519.688

We propose a method for calculating the temperature field of the casting ladle lining by a modified relaxation

method. Given such initial data as the metal temperature in the ladle, the ambient temperature, and the lining

structure, this method permits calculating the stationary temperature fields both inside the lining and on the

surface of the ladle jacket. The model was tested by comparing experimentally measured temperature values

on the surface of the ladle jacket with calculated temperatures. A satisfactory agreement between calculated

and experimental temperature values of the ladle surface has been obtained.

**Keywords:** temperature field, casting ladle, lining, heat transfer, mathematical model.

**IDENTIFICATION OF REINFORCEMENT STRUCTURES**

**
OF COMPOSITE CONSTRUCTIONS FROM THE RESULTS ****OF THERMOPHYSICAL EXPERIMENTS ON STEADY-STATE ****TEMPERATURE FLUCTUATIONS**

A. P. Yankovskii UDC 536.21

The problem of identification of reinforcement structures of thin-walled composite construction from the results

of experiments on steady-state temperature fluctuations in them has been formulated. The particular case

of shells of revolution with axisymmetric reinforcement structures has been investigated. The reinforcement

structure of a cylindrical shell has been reconstructed under pseudoactual experimental conditions. Satisfactory

accuracy of identification of the reinforcement structure and the effective thermal conductivities has been

demonstrated.

**Keywords:** composites, reinforcement structure, identification, inverse problems, heat conduction.

**TEMPERATURE CONDITIONS AND HEAT SUPPLY ****OF APARTMENTS IN AN APARTMENT HOUSE ****WITH INDIVIDUAL REGULATORS**

L. N. Danilevskii UDC 697.133

This paper presents the results of mathematical modeling of the values of the temperature and the heat source

power in apartments of an apartment house with individual regulators. It has been shown that for the existing

structures of buildings the heat transfer between apartments with individual thermoregulation strongly influences

the values of the heat source power established in apartments in the process of regulation. Without

changing the total heating load of the building, this process leads to considerable deviations of readings of

the thermal energy meters in apartments from the thermal energy actually consumed for their heating. This

fact throws doubt upon the expediency of installing individual calorimeters in an apartment house with thermoregulation

in each apartment.

**Keywords:** heat source power, heat transfer, heat flow, heat supply, regulation, account, air temperature, enclosure

structure, separation walls, floors.

**INVESTIGATION OF HIGH-TEMPERATURE ****REGIMES AND HEAT AND MASS TRANSFER ****OF ELECTRIC-CURRENT-HEATED TUNGSTEN ****CONDUCTORS**

S. G. Orlovskaya, F. F. Karimova,

and M. S. Shkoropado

UDC 536.46

We have solved the stationary heat conduction problem for a metallic conductor heated by electric current

with account for the various mechanisms of heat exchange with the environment. The expressions for the conductor

temperature distribution along its length with account for the heat exchange with the gas and for the

temperature dependence of resistance have been found in analytical form. By means of physicomathematical

modeling the temperature profiles along the length of tungsten conductors with account for the chemical reaction

on their surface have been obtained. They are in good agreement with experimental results.

**Keywords:** high-temperature heat and mass transfer, brightness temperature, temperature field, metals, tungsten,

oxidation kinetics.

**HYDROGASDYNAMICS IN TECHNOLOGICAL PROCESSES ****METHOD OF STRAIGHT-THROUGH CALCULATION ****FOR SOLVING BOUNDARY-LAYER EQUATIONS ****AT AN ARBITRARY INTENSITY OF GAS BLOWING ****THROUGH THE BODY SURFACE**

E. G. Vatolina, V. V. Gorskii,

N. A. Gorskaya, and A. A. Olenicheva

UDC 533.16

A method of straight-through calculation for solving boundary-layer equations is suggested. It preserves stability

at an arbitrary intensity of gas blowing through the body surface. The results of systematic investigations

of heat transfer and friction in an air boundary layer on a permeable wall in the vicinity of the critical

point of a sphere are presented, obtained by the indicated method in the perfect gas approximation.

**Keywords: **heat transfer, friction, laminar boundary layer, critical point, impermeable surface, gas blowing.

**FLOW AND CONJUGATE HEAT EXCHANGE ****IN A ROTATING CAVITY WITH AN AXIALLY ****SUPPLIED WORKING MEDIUM **

K. N. Volkov UDC 532.529

Numerical modeling of the turbulent flow and conjugate heat exchange in a cavity bounded by a rotor and a

stator is carried out. Coupled thermal calculations are based on the unsteady heat-conduction equation describing

the temperature distribution within a solid and Reynolds-averaged Navier–Stokes equations closed

using the k–ε turbulence model, which allow calculation of the velocity, pressure, and temperature distributions

in the fluid-filled region. The space-time distributions of the temperature and the heat flux on the metal–

fluid interface are obtained in two- and three-dimensional formulations of the problem on a structured and an

unstructured grid.

**Keywords:** conjugate heat exchange, cavity, numerical modeling, turbulence.

**UNSTEADY GASDYNAMICS OF A LINEAR ****CASCADE OF AIRFOILS EXECUTING SMALL ****HARMONIC VIBRATIONS**

K. N. Volkov UDC 532.529

Numerical modeling of inviscid compressible gas flow past a linear cascade of airfoils executing small harmonic

translational and rotational vibrations is carried out. The control volume method on moving unstructured

grid structures is used for discretization of basic equations. The influence of the frequency and phase

characteristics of the airfoils on the pressure distribution over their surface and the lift coefficient is investigated.

The results of numerical calculations are compared to the available calculated and experimental data.

**Keywords:** airfoil cascade, unsteady flow, numerical modeling.

**FLOW IN THE WORKING SECTION ****OF A TRANSONIC WIND TUNNEL **

S. K. Betyaev UDC 532.526.5

The features of the gas flow in the working section of a transonic wind tunnel have been considered. On the

basis of the method of joining asymptotic expansions and the theory of detached zones mathematical models of

the flow are proposed. The flow over a perforation and transverse and longitudinal slots has been investigated.

In the latter case, a nonstationary and a stationary analogy with a two-dimensional flow are stated. A deflector

— a new device for reflecting shocks — is proposed. The problems are discussed.

**Keywords:** transonic velocity, working section, circulation zone, perforation, deflector.

**ASYMPTOTIC ANALYSIS OF THE SMALL-SCALE ****STRUCTURE OF THE LAMINAR BOUNDARY ****LAYER WITH SUCTION**

S. K. Betyaev UDC 532.526.2

Unwanted regimes of boundary layer suction when organized vortex structures known from experience arise

have been determined. To this end, we performed an inspection analysis of the three-scale problem of the flow

past a perforated boundary on the assumption that the inner scale equal to the perforation period is small

compared to the outer scale characterizing the global problem. An asymptotic classification of suction regimes

is given. The classical boundary layer problem — moderate suction — has been investigated in detail.

**Keywords:** boundary layer suction, Reynolds number, Navier–Stokes equation, Helmholtz scheme, boundary

layer blowing-off.

**THERMOCHEMICAL DESTRUCTION ****OF CARBON-PHENOL MATERIAL ****IN A HIGH-ENTHALPY PULSATING**

**
GAS FLOW**

A. N. Golovanov and A. S. Yakimov UDC 536.245.022

Mathematical and physical modeling of thermochemical destruction of a heat-shielding material under the action

of a high-temperature pulsating gas flow has been considered.

**Keywords: **heat-shielding material, pulsating gas flow, thermochemical destruction.

**DETERMINATION OF THE FREE ****BOUNDARY OF THE LUBRICANT ****LAYER OF A FERROFLUID BEARING**

P. P. Kuzhir, P. G. Kuzhir, G. I. Gul’kov,

and A. L. Rudenya

UDC 621.822.172:537.84

The free boundary of the lubricant layer of a ferrofluid bearing under the action of a magnetic field and

static load has been determined. The solution has been obtained by simultaneously integrating the Reynolds

equation and the equation of free boundary using a method of expansion in a small parameter, namely, the

eccentricity of a shaft. It has been shown that the magnetic field forms free boundaries of the lubricant layer

and reduces the cavitation bubble, thus hindering the lubricant flowing out from the bearing.

**Keywords:** ferrofluid bearing, ferrofluid, mathematical model, lubricant layer, pressure distribution.

**TURBULENT FLUID FLOWS IN A CIRCULAR ****PIPE AND PLANE CHANNEL AND MODELS ****OF MESOSCALE TURBULENCE***

V. A. Babkina and V. N. Nikolaevskiib UDC 532.517.4

Based on the model of anisotropic wall turbulence in the near-wall layer and the momentum model in the

flow core, velocity profiles in the entire region of the turbulent flow of an incompressible fluid in a circular

pipe and plane channel have been obtained. The differences in the profiles among the layers are due to the

change in the structure of turbulent vortices.

**Keywords:** vortex structures, mesoscale turbulence, wall turbulence, mometum model, pipe and channel flows.

**MISCELLANEA**

**
ANALYSIS OF THE EFFECT OF THE WINDING ANGLE ****OF GLASS FIBER ON THE FREQUENCIES OF FREE**

**
VIBRATIONS OF A SHELL MADE OF GLASS-REINFORCED ****PLASTIC UNDER NONSYMMETRIC BOUNDARY CONDITIONS**

S. M. Bosyakov and Wang Zhi Wei UDC 539.3

Calculated results for the frequencies of free vibrations of a cylindrical anisotropic shell made of oriented

glass-reinforced fiber are presented, which are based on the Rayleigh–Ritz method. Elastic properties of a

shell depend on the orientation of glass fiber and are determined by six elastic moduli. Boundary conditions

correspond to fixation of one end and hinge support of the other end of a shell. Numerical results in the form

of dependences of the frequencies of free vibrations on the winding angle of glass fiber for various parameters

of wave formation and ratios of geometric dimensions of a shell are obtained for fabric glass-reinforced

plastic.

**Keywords: **cylindrical shell, glass-reinforced plastic, Rayleigh–Ritz method, frequency of free vibrations.

**ON A POSSIBLE MECHANISM OF INSTABILITY ****OF PLASTIC DEFORMATION OF METALS**

AND ALLOYS AT 4.2 K

M. E. Bosin,a V. A. Desnenko,b

and V. N. Nikiforenkoa

UDC 548.4.620:539.4:660.017

The fine structure of spontaneous deformation jumps and jumps initiated by both the shock action on a deformation

device and a strong fast-changing magnetic field (up to 2.7 MA ⁄ m) has been investigated in metals

and alloys at liquid-helium temperatures. Oscillography of the signals of changes in the load on the sample

and of acoustic emission has made it possible to reveal the relationship between types of jumps and postulate

on the mechanism of their appearance.

**Keywords**: stepwise deformation, fast process, acoustic emission, magnetic field, cracking.

**INTERVAL VECTORS AND TENSORS ****IN APPLIED ENGINEERING PROBLEMS**

M. G. Boyarshinov UDC 519.6:152.972

In constructing interval vectors and tensors, the requirement of invariance of these objects under transformation

of the system of coordinates is taken into account. For illustrations, interval scalars, vectors, and tensors

are used in solving the simplest engineering problems of deformable solid mechanics to construct distributions

of displacements, strains, and stresses, including residual ones, satisfying the conditions of elastic adaptivity

(J. Zarka methods).

**Keywords:** intervals, scalars, vectors, tensors, interval operations, adaptibility, plastic strains, residual stresses.

**ANALYSIS OF WAVE MOTION AT THE BOUNDARY ****SURFACE OF ORTHOTROPIC THERMOELASTIC MATERIAL ****WITH VOIDS AND ISOTROPIC ELASTIC HALF-SPACE**

Rajneesh Kumar and Rajeev Kumar UDC 536.21

The purpose of this research is to study the effect of voids on the surface wave propagation in a layer of orthotropic

thermoelastic material with voids lying over an isotropic elastic half-space. The frequency equation

is derived on the basis of the developed mathematical model under the boundary conditions for welded and

smooth contacts. The dispersion curves giving the phase velocity and attenuation coefficient versus the wave

number enable one to reveal the effects of voids and anisotropy for welded contact boundary conditions. The

specific loss and amplitudes of the volume fraction, normal stress, and temperature change for welded contact

are obtained and presented graphically for a particular model showing the voids and anisotropy effects. Some

special cases are also deduced.

**Keywords:** wave motion; orthotropic material; voids; isotropic elastic half-space; phase velocity; attenuation

coefficient.

**RADIATION-INDUCED DEFECTS IN InPSn SINGLE ****CRYSTALS IRRADIATED WITH 60Co GAMMA QUANTA**

Sh. Sh. Rashidova UDC 621.315.592

The process of formation of antistructural defects in tin-doped InP crystals exposed to irradiation with gamma

quanta of dose 10–100 kGy has been investigated by the radioluminescence method. It has been found that

an activation energy of level 0.26 eV is favorable for obtaining semi-insulating indium phosphide.

Keywords: antistructural defect, radiothermoluminescence method, activation energy.