**HEAT AND MASS TRANSFER IN DISPERSE AND POROUS ****MEDIA EXPERIMENTAL AND NUMERICAL INVESTIGATIONS ****OF NONSTATIONARY EVAPORATION OF LIQUID DROPLETS**

V. I. Terekhov,a V. V. Terekhov,a

N. E. Shishkin,a and K. Ch. Bib

UDC 532.526

The results of experimental and numerical investigations of the nonstationary process of evaporation of droplets of pure liquids into a dry air at variable initial temperature of a droplet, temperature of the gas medium, and relative velocity of flow around a droplet are presented. The regions of application of the well-known laws of change in the size of an evaporating droplet in time depending on the thermal gas-dynamic conditions and thermophysical properties of the liquid and gas phases have been analyzed.

**Keywords:** evaporation of droplets, binary liquids, phase transition, heat and mass transfer.

**MATHEMATICAL MODELING OF THE HEAT ****TREATMENT AND COMBUSTION OF A COAL**

**
PARTICLE. I. HEATING STAGE**

Kh. Enkhzhargala and V. V. Salomatovb UDC 621.311

Mathematical modeling of the heat treatment and subsequent combustion of a coal particle as a multistage

process has been carried out. The basic parameters of the following sequential stages of this process have been calculated by approximate-analytic dependences: heating of particles; their drying; yield of volatiles, their ignition and combustion; and burning out of the coke residues. A detailed parametric analysis of the influence of the physical and regime characteristics of the process on the burning mechanism of a coal particle (with the example of coal from the Shivee-Ovoo deposit in Mongolia) has been performed. The conditions for effective burning of a single coal particle as the main element of the whole process in the furnace have been determined.

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

**SPATIAL FRACTIONATION OF PARAMAGNETIC PARTICLES ****PRECIPITATING IN A HIGH-GRADIENT MAGNETIC FIELD ****OF A SHORT MAGNETIZED CYLINDER**

A. M. Zholud’ UDC 577.3

The motion of dia- and paramagnetic particles precipitating in a liquid near a vertical magnetized cylinder of

finite length in a plane transverse to the direction of magnetization has been studied, the phenomenon of spatial separation of paramagnetic particles by the value of magnetic susceptibility is described, and a comparison of the efficiency of separation of paramagnetic particles in the fields of a short cylinder and a sphere has been carried out.

**Keywords:** paramagnetic microparticles, magnetophoresis, high-gradient magnetic separation.

**DEPOSITION OF AEROSOL PARTICLES IN VERTICAL CHANNELS FROM AN ISOTROPIC TURBULENT FLOW**

G. I. Kelbaliev, Z. I. Ibragimov,

and R. K. Kasimova

UDC 541.182.2

Equations for the rate of turbulent deposition of aerosol particles in vertical tubes are suggested. It is noted

that the rate of deposition of particles is determined by the gravitation component and turbulent diffusion. The thickness of the layer of depositions and its influence on the basic characteristics of a turbulent flow are determined. The results obtained are compared with available experimental values of the rate of deposition of particles in vertical tubes.

**Keywords: **deposition, aerosol particles, turbulent diffusion, turbulence scale, dissipation energy, resistance coefficient, thickness of depositions, correlation factor.

**THEORETICAL AND EXPERIMENTAL STUDIES ****OF THE POROUS STRUCTURE AND ADSORPTION ****PROPERTIES OF CARBOFIBROUS MATERIALS**

A. F. Dolidovich and G. S. Akhremkova UDC 541.183

We have made theoretical and experimental studies of the porous structure and adsorption properties of activated carbon fibrous materials and granular activated carbon with respect to vapors of benzene, toluene, ethylacetate, and acetone. The parameters of the porous structure of adsorbents have been determined by the adsorption by them of the standard substance — benzene — and used to calculate their adsorption characteristics with respect to the investigated organic solvents. A good agreement between the calculated and experimental characteristics for all investigated adsorbents has been obtained. The dependence of adsorption properties of activated carbon fibrous adsorbents and granular activated carbon on the volume and size of adsorbing pores, as well as on the molecular polarizability of the adsorptive, has been established.

**Keywords: **adsorption, granular activated carbon, activated carbon fiber, vaporous volatile organic substance, isotherm.

**COMPUTATIONAL SCHEMES FOR THE ****PROCESSES OF CONVECTIVE-DIFFUSION**

**
TRANSPORT OF WATER-SOLUBLE COMPOUNDS**

G. P. Brovka, I. N. Dorozhok,

and S. N. Ivanov

UDC 517.958

We have developed and tested computational schemes for a one-dimensional equation of convective-diffusion transport of water-soluble compounds providing results satisfactory for practical purposes for various forms of the initial concentration profile and relations between the convective-diffusion transport parameters.

**Keywords: **convection, diffusion, water-soluble compounds, computational scheme, numerical dispersion.

**
HYDROGASDYNAMICS IN TECHNOLOGICAL PROCESSES ****THERMAL CRISIS IN THE FLOW FIELD ****OF A CYLINDRICAL OR SPHERICAL SOURCE**

A. N. Kucherov UDC 533.6+535.211

Variants of the physical phenomenon of thermal crisis in the field of a stationary cylindrical source and a spherical source have been compared in the approximation of an ideal, perfect gas within the framework of Euler equations.

**Keywords: **gas, source, sink, energy supply, density, pressure, velocity, Mach number, flow choking, thermal crisis.

**COMPUTATIONAL-THEORETICAL INVESTIGATION ****OF BUOYANT JET FLOWS**

O. G. Martynenko and V. N. Korovkin UDC 536.25

The results of mathematical simulation of fully developed plane buoyant jet flows are presented. The solution is found within the framework of the model of a laminar boundary layer in the Boussinesq approximation using the method of matched asymptotic expansions. Analytical dependences of the basic characteristics of a jet flow on the Prandtl number and density parameter have been constructed.

**Keywords: **vertical plane jet flows, free-convective heat transfer, laminar regime, mathematical simulation.

**FEATURES OF CALCULATING THE DESCENT VELOCITY ****OF THE LOWER BOUNDARY OF THE NEAR-CEILING ****LAYER IN A FIRE IN AN ATRIUM**

S. V. Puzach and Nguen Tkhan’ Xai UDC 614.841

Results of calculating the dynamics of descent of the lower boundary of the near-ceiling gas layer in a model atrium using various zone approaches and a field model are presented. Comparison with experimental data is made. It is shown that when a zone mathematical model is used it is necessary to take account of the shape of the convective column formed above the source of combustion. It is pointed out that the application of the approximation of an unrestricted buoyant plume to describing parameters of the convective column does not reflect the actual thermodynamic picture of the fire development (primarily the effect of the atrium ceiling)

and can lead to both an understatement and an overstatement of the fire danger of atria.

**Keywords:** fire, atrium, near-ceiling gas layer, heat and mass transfer, thermal gasdynamics, field mathematical model, mathematical zone model, convective column, combustion, buoyant plume.

**LINEAR ANALYSIS OF THE FREE-CONVECTIVE ****STABILITY OF A BINARY ELECTROLYTE SOLUTION ****IN AN ELECTROCHEMICAL CELL WITH HORIZONTAL**

**
ELECTRODES**

V. M. Volgin,a A. D. Davydov,b

and A. V. Zhukovc

UDC 541.135:519.713

The influence of the electrode reaction kinetics on the critical Rayleigh number for a binary electrolyte solution situated between flat horizontal electrodes has been investigated. The equations of motion of an incompressible viscous fluid in the Boussinesq approximation and the material balance equations with the electrical neutrality condition have been used as a mathematical model. Analytical and numerical solutions of the linear stability problem have been obtained. The influence of the kinetic parameters of the electrode reaction (exchange current density, transport number of cations) and the transport properties of the solution on the critical value of the Rayleigh number has been investigated.

**Keywords:** free convection, convective instability, binary electrolyte, electrochemical cell.

**COMPARISON OF THE RESULTS OF MODELING ****CONVECTIVE HEAT TRANSFER IN TURBULENT ****FLOWS WITH EXPERIMENTAL DATA**

A. I. Fomichev UDC 536.2(075.8):621.1.016

The results of simulation of natural turbulent convection in a square air cavity measuring 0.75 × 0.75 m and having isothermal vertical and highly heat-conducting horizontal walls are compared with the experimental data obtained for this cavity at a Rayleigh number equal to 1.58⋅109. In carrying out numerical investigations, a two-dimensional, low-turbulence, two-parameter k–ε model known as the low-Reynolds-number k–ε turbulence model was used. The results of investigations are presented for the distributions of the velocity and temperature components, as well as local and average values of the Nusselt number. The model was also used in calculating forced turbulent convection in a low-velocity channel with a backward facing step. The results of modeling are compared with experimental data on heat transfer in a turbulent separation flow downstream

of the step. In both cases, a satisfactory agreement of the measured values with those predicted by the k–ε turbulence model is obtained.

**Keywords: **convective heat transfer, low-Reynolds-number turbulence model, natural and forced convection.

**CRYSTAL GROWTH IN TWO-LAYER ****FLUID SYSTEMS IN MICROGRAVITY**

A. I. Feonychev UDC 532.5:532.78.538.4

A numerical study of the crystal growth in zero gravity with the use of an additional liquid layer for the ampoule- free variant of zone melting (floating-zone method) has been conducted. The crystallization process was investigated both without the magnetic-field action and with a static magnetic field at two directions of the magnetic field vector. A classification of the flow structure depending on the dominance of the thermocapillary effect on the free surface or at the interface between the liquids has been made. The radial microsegregation of the dopant for the above crystal growth methods with several combinations of physical parameters of the liquids has been investigated. The dependences of the radial microsegregation of the dopant on the flow conditions and the strength and sense of the magnetic field have been determined. It has been shown that the strongest effect of a decrease in the microsegregation of the dopant is achieved for flows with a dominance of the thermocapillary effect on the free outer boundary of the liquid two-layer system at a certain magnetic field strength.

Keywords: fluid mechanics, crystal growth, encapsulation, dopant segregation, magnetic field.

**MODELING OF THE OPERATION OF A MINE ****COUNTERROTATION FAN BY MEANS**

**
OF THE FLUENT SUITE**

E. I. Gurina UDC 532.516

Mathematical modeling of the processes in the flow part of an axial counterrotation fan has been carried out by means of the FLUENT suite. Distributions of the gas-dynamic parameters characterizing the basic laws of the investigated process such as air flow velocity, mass flow rate, and air flow pressure have been obtained and dead regions of the construction have been revealed. It has been shown that mathematical modeling can be used for virtual (being developed) models of fans which are further embodied in real objects. The experimental

data have been compared with the results of the computational modeling.

**Keywords: **mathematical modeling, finite-difference scheme, axial fan, aerodynamic characteristics.

**AXIAL-THRUST RESPONSES DUE TO A GAS ****TURBINE’S ROTOR BLADE DISTORTIONS**

B. T. Lebele-Alawa UDC 532.695

The axial thrust imposed on the shaft of a gas turbine depends upon its rotor blade inlet inclination to the turbine’s axial direction: this inclination can change due to the distortions resulting from fouling, aging, tip rubbing, erosion, thermal-fatigue cracks, and corrosion. Relevant influential parameters for an operational gas turbine were measured. Theoretical predictions for the behavior of the same turbine were obtained from computer simulations. The results of both measurements and theoretical predictions were compared and showed qualitative correspondence. The rotor blade profile distortions result in significant increases in the axial thrust on the compressor, which adversely affects the gas turbine’s thermodynamic performance, reliability, and operational

life.

**Keywords: **gas turbine, compressor, rotor blade, axial thrust, vibration.

**TEMPERATURE SHOCK WAVES IN MAGNETIC ****HYDRODYNAMICS WITH ACCOUNT FOR THE**

**
HYPERBOLIC HEAT TRANSFER (SOLUTION ****OF THE RUNNING–WAVE TYPE)**

P. P. Volosevich, I. I. Galiguzova, V. A. Gasilov,

A. Yu. Krukovskii, E. I. Levanov*, and V. A. Marchenko

UDC 519

By the method of running waves the solution of magnetic hydrodynamics equations for media with infinite electrical conduction and heat transfer at heat-flow relaxation has been investigated. The characteristics of the considered system of hyperbolic equations have been determined. By means of the theory of generalized solutions of first-order, quasi-linear equations the stability of strong discontinuities of magnetohydrodynamic

and thermal values has been proved.

**Keywords:** magnetic hydrodynamics with account for the heat transfer, heat-flow relaxation, relations at the

strong discontinuity front, stability of discontinuities of magnetohydrodynamic and thermal values.

** **

**
DEVELOPMENT OF AN IDENTIFICATION SYSTEM ****FOR BIAXIALLY ORIENTED POLYMER FILMS BASED ****ON THE DEGREE OF THEIR TRANSVERSE EXTENSION**

V. V. Goncharenko, I. O. Mikulenok,

D. G. Shvachko, and D. N. Shved

UDC 678.01:539.3

An expression has been developed that generalizes three basic geometric schemes of film deformation (axial,

planar, and biaxial extension) and also all intermediate schemes. The system of quantitative identification of

nonuniformly biaxially oriented films according to their transverse extension has been tested on six different

film types.

**Keywords:** polymer, film, biaxial extension, orientation, identification.

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

**
SIMULATION OF A MANUAL ELECTRIC-ARC ****WELDING IN A WORKING GAS PIPELINE. **

**
1. FORMULATION OF THE PROBLEM**

V. I. Baikov, I. A. Gishkelyuk, A. M. Rus’,

T. V. Sidorovich, and B. A. Tonkonogov

UDC 517.958:621.791.92

Problems of mathematical simulation of the temperature stresses arising in the wall of a pipe of a cross-country

gas pipeline in the process of electric-arc welding of defects in it have been considered. Mathematical

models of formation of temperatures, deformations, and stresses in a gas pipe subjected to phase transformations

have been developed. These models were numerically realized in the form of algorithms representing a

part of an application-program package. Results of verification of the computational complex and calculation

results obtained with it are presented.

**Keywords: **cross-country gas pipeline, metal, phase composition, electric-arc welding, mathematical simulation,

algorithm, numerical methods, temperature stresses.

**SIMULATION OF A MANUAL ELECTRIC-ARC ****WELDING IN A WORKING GAS PIPELINE.**

**
2. NUMERICAL INVESTIGATION OF THE ****TEMPERATURE-STRESS DISTRIBUTION**

**
IN THE WALL OF A GAS PIPE**

V. I. Baikov, I. A. Gishkelyuk, A. M. Rus’,

T. V. Sidorovich, and B. A. Tonkonogov

UDC 517.958:621.791.92

A numerical simulation of the action of the current experienced by an electric arc and the rate of gas flow

in a pipe of a cross-country gas pipeline on the depth of penetration of the electric arc into the wall of this

pipe and on the current and residual stresses arising in the pipe material in the process of electric-arc welding

of nonthrough cavity-like defects in it has been carried out for gas pipes with walls of different thickness.

**Keywords:** mathematical simulation, numerical investigation, electric-arc welding, temperature stresses, crosscountry

gas pipeline, penetration depth.

**INFLUENCE OF TRANSPARENCE OF HEAT-RESISTANT ****COATINGS ON THE THERMAL REGIME OF CONSTRUCTIONS**

L. Ya. Paderin, B. V. Prusov,

and O. D. Tokarev

UDC 536.3

We present a computational-experimental method and the results of investigating the influence of transparence

to solar radiation of the heat-resistant coating on the thermal regime of the space-vehicle construction in orbital

flight.

Keywords: radiating capacity, absorptivity, reflectivity, transmission capacity, solar radiation, semitransparent

materials, vehicles in orbital flight.

**ACOUSTIC AND THERMODYNAMIC ****PROPERTIES OF THE BINARY LIQUID**

**
SYSTEM n-DODECANE+n-HEXADECANE**

T. S. Khasanshin, V. S. Samuilov,

A. P. Shchemelev, and F. M. Mosbach

UDC 536.7:547.21

By the method of direct measurement of the pulse-passage time, the velocity of sound in a binary liquid mixture

n-dodecane+n-hexadecane has been investigated in the temperature range 298–433 K and in the pressure

range 0.1–100.1 MPa. The maximum measurement error is 0.1%. Experimental data on the velocity of sound

for the investigated mixture have been obtained for the first time. On the basis of the data on the velocity of

sound, we have determined the density, the isobaric expansion coefficient, the isobaric and isochoric heat capacities,

and the isothermal compressibility coefficient of a mixture of three compositions in the 298–433 K

temperature range and in the 0.1–100.1 MPa range of pressures. The coefficients of the Tate equations in the

above range of parameters have been calculated. A table of thermodynamic properties of the mixture is presented.

**Keywords:** n-dodecane, n-hexadecane, binary mixtures, velocity of sound, density, heat capacity, compressibility,

isobaric expansion coefficient.

**METHOD OF EXTENSION OF BOUNDARIES ****FOR PROBLEMS OF HEAT CONDUCTION**

**
IN BODIES OF MOBILE SHAPE**

A. D. Chernyshov UDC 536.517.946.539

The first boundary-value problem of heat conduction was solved by the method of extension of boundaries

with the simplest example of a variable-length segment. An analytical solution of the problem was obtained

for arbitrary initial conditions and the law of motion of a boundary with the aid of the Fourier rapidly convergent

series. An example of the solution of the problem for the case where the left end of the segment is

fixed and the right one moves with a constant velocity is given.

**Keywords:** mobile shape of the boundary, heat conduction, boundary function, Fourier convergent series.

**STUDY ON THE HEAT-TRANSFER CHARACTERISTICS ****AND PRESSURE DROP IN CHANNELS WITH ARC-SHAPED ****WAVY PLATES**

Naphon Paisarn UDC 536.24

The heat-transfer characteristics and pressure drop in a channel with arc-shaped wavy plates are presented.

The test channel with two opposite wavy plates, whose peaks are in-phase or out-of-phase, are tested under

constant wall heat flux conditions. The experiments are made for the Reynolds number and heat flux in the

ranges 1500–2500 and 0.5–1.2 kW/m2, respectively. The effects of relevant parameters on the heat-transfer

characteristics are considered. A turbulent mathematical model is employed to simulate the temperature and

velocity distributions. The predicted results are verified by comparing with measured data, and reasonable

agreement is obtained. Due to the onset and growth of the recirculation zones, the convective heat transfer in

the channel with wavy plates is higher than that with flat plates.

**Keywords: **heat-transfer enhancement, arc-shaped wavy plate.

**STUDY OF THERMODYNAMIC PROPERTIES ****OF LIQUID BINARY ALLOYS BY A PSEUDOPOTENTIAL ****METHOD**

Aditya M. Vora UDC 662.21

On the basis of the Percus–Yevick hard-sphere model as a reference system and the Gibbs–Bogoliubov inequality,

a thermodynamic perturbation method is applied with the use of the well-known model potential. By

applying a variational method, the hard-core diameters are found which correspond to a minimum free energy. With this procedure, the thermodynamic properties such as the internal energy, entropy, Helmholtz free energy, entropy of mixing, and heat of mixing are computed for liquid NaK binary systems. The influence of the local-field correction functions of Hartree, Taylor, Ichimaru–Utsumi, Farid–Heine–Engel–Robertson, and Sarkar–Sen–Haldar–Roy is also investigated. The computed excess entropy is in agreement with available experimental data in the case of liquid alloys, whereas the agreement for the heat of mixing is poor. This may be due to the sensitivity of the latter to the potential parameters and dielectric function.

**Keywords:** pseudopotential method, liquid NaK alloys, Percus–Yevick (PY) hard-sphere model, local-field correction

functions, thermodynamic properties.

**RESPONSE OF FREQUENCY DOMAIN IN GENERALIZED ****THERMOELASTICITY WITH TWO TEMPERATURES**

Sachin Kaushal,a Rajneesh Kumar,b

and Aseem Miglania

UDC 536.21

The paper is concerned with the time-harmonic deformation in a homogeneous, isotropic, generalized thermoelastic medium with two temperatures. The Hankel transform is employed to solve the boundary-value problem in the frequency domain in the context of two generalized theories of thermoelasticity (Lord and Shulman, Green and Lindsay). The inverse transform integral is evaluated by using the Romberg integration in order to obtain the results in the physical domain. The components of the stresses as well as the temperature and conductive temperature obtained in this manner are computed numerically. The effects of two temperatures are presented graphically.

**Keywords:** generalized thermoelasticity, time harmonic, normal point force, conductive temperature, Hankel transform, Romberg integration.

**CERTAIN PROBLEMS OF HEAT AND MASS ****TRANSFER IN ROTATIONAL MOLDING**

M. M. Revyako and E. Z. Khrol UDC 66.021.4:678.067

The basic steps of rotational molding are described. Emphasis is on the heat- and mass-transfer processes occurring

during the heating stage. The basic regularities of variation in the temperature during the cycle of rotational molding are given. Models of motion of a material in the mold in the above stage are considered. The kinetics of heating of an individual spherical particle is described.

**Keywords:** rotational molding, heating, heat transfer, powder, mold, thermal conductivity, temperature, circulation, collapse, sliding.