#### Volume 89, №3

**HEAT AND MASS EXCHANGE OF A DROP OF A SOLUTION SUBJECTED TO A COMBINED ENERGY ACTION UNDER CONDITIONS OF DEEPENING OF THE EVAPORATION ZONE**

A model of the heat and mass exchange in the evaporation of drops moving in the carrying gas phase of a solution subjected to the combined energy action of a convective heat flow and electromagnetic infrared and microwave radiations under conditions where the size of the drops changes at the low-temperature stage of their evaporation and the evaporation zone deepens at the high-temperature stage of the evaporation process has been formulated. Kinetic dependences and features of the movement of the evaporation boundary in the process of dehydration of the indicated drops have been determined.

**Author:**
P. V. Akulich

**Keywords:**
heat and moisture transfer, kinetics and dynamics of mass transfer, mass exchange of a drop of a solution

**Page:**
539

**EXPERIMENTAL INVESTIGATION OF THE CHANGE IN TEMPERATURE AT THE CENTER OF A WATER DROPLET IN THE PROCESS OF EVAPORATION IN HEATED AIR**

The paper presents the results of an experimental investigation of the change in the temperature at the interface between water and a thermocouple junction (of diameter 1 mm) in a droplet (initial radius 1.5–3 mm) in the process of heating and evaporation of the latter in an air stream (of temperature 350–800 K at the velocity of motion 0.1–3.5 m/s). The lifetimes of droplets (of their complete evaporation) have been determined. It is shown that the temperature at the droplet center changes by no more than 10 K in the process of evaporation at gas temperatures of less than 500 K. At higher temperatures of the external gas medium the droplet is heated intensely (the temperature field is homogeneous)

**Author:**
A. V. Zakharevich, G. V. Kuznetsov, and P. A. Strizhak

**REDUCTION IN THE VAPOR PRESSURE IN CONDENSATION ON COLD DROPLETS OF A LIQUID**

A physicomathematical model of the process of depressurization in a pure saturated and superheated vapor due to the injection of monodisperse cold droplets of a liquid has been developed. A cellular model has been developed that is based on solving the equation of heat conduction in a liquid phase and on the integral method for a gas phase in a spherically symmetric one-dimensional formulation. Numerical investigation has been carried out of the in fluence of the size and concentration of the droplets and of the initial parameters of the steam on the dynamics of depressurization during the vapor condensation on the droplets.

**Author:**
E. M. Bochkareva, V. A. Nemtsev, b V. V. Sorokin, V. V. Terekhov, and V. I. Terekhov

**Keywords:**
liquid droplets, condensation, saturated and superheated vapor, heat transfer, depressurization, sprinkler systems

**Page:**
553

**MODELING THE DYNAMICS OF MICRO- AND MACROPARTICLES IN A COMBINED GAS-DISCHARGE INSTALLATION**

We present a model of the dynamics of micro- and macroparticles in a combined gas-discharge installation that accounts for the processes of metal explosion ( heating of a metal in its solid state, melting, heating of the liquid
metal, intense evaporation, ionization in metal vapor), a magnetohydrodynamic description of plasma acceleration (on the basis of the mass, momentum, and energy conservation laws neglecting the plasma viscosity and thermal conductivity), and a description of the processes of energy transfer from a high-velocity stream to accelerated particles. It has been established that the process of melting terminates in 1.3 ns after the start of the discharge

and that the evaporation terminates in 480 ns. The stage of cooling starts in 21 μs. The average density of the plasma upon completion of the evaporation process can be estimated to be 1.7·10^{–5} g/cm^{3}, with the pressure being of the order of 1.5·10 ^{4} Pa and the total time of discharge, of about 250 μs.

**Author:**
V. V. Astashinskii, M. I. Bogach, and A. V. Burachevskii

**STUDY OF THE EFFECT OF DECREASE IN THE CONDUCTIVITY AHEAD OF A SHOCK WAVE IN A GLOW-DISCHARGE PLASMA**

The electrical conductivity of a glow-discharge plasma ahead of a shock wave moving perpendicularly to the discharge axis has been investigated using a double electric probe. The obtained results have shown that the interaction of the shock wave with the glow-discharge plasma is accompanied by a change in its conductivity in the entire investigated volume simultaneously.

**Author:**
A. S. Baryshnikov, I. V. Basargin, S. V. Bobashev, N. A. Monakhov, P. A. Popov, V. A. Sakharov, and M. V. Chistyakova

**Keywords:**
shock wave, glow discharge, plasma, double electric probe

**Page:**
565

**MODELING OF THE THERMAL PROTECTION OF A MULTILAYER MATERIAL UNDER FIRE CONDITIONS**

On the basis of the theoretical and known experimental results, a refined mathematical model of the thermochemical destruction of a multilayer heat-shield coating has been developed. Account of the flow across the body has made it possible to forecast more exactly the state of the protected structure under fire conditions. A comparison between the results of numerical calculations and the known data has been made.

**Author:**
V. A. Ovchinnikov and A. S. Yakimov

**Keywords:**
heat shield material, heat conduction, permeable wood, heat exchange

**Page:**
569

**CALCULATION OF THE RATE OF COMBUSTION OF A METALLIZED COMPOSITE SOLID PROPELLANT WITH ALLOWANCE FOR THE SIZE DISTRIBUTION OF AGGLOMERATES**

A physicomathematical model of combustion of a metallized composite solid propellant based on ammonium perchlorate has been presented. The model takes account of the thermal effect of decomposition of a condensed phase (c phase), convection, diffusion, the exothermal chemical reaction in a gas phase, the heating and combustion of aluminum particles in the gas flow, and the velocity lag of the particles behind the gas. The in fluence of the granulometric composition of aluminum particles escaping from the combustion surface on the linear rate of combustion has been investigated. It has been shown that information not only on the kinetics of chemical reactions in the gas phase, but also on the granulometric composition of aluminum particles escaping from the surface of the c phase into the gas, is of importance for determination of the linear rate of combustion.

**Author:**
V. A. Poryazov and A. Yu. Krainov

**Keywords:**
metallized solid propellant, rate of combustion, aluminum powder, granulometric composition, gas phase

**Page:**
579

**IGNITION OF HYDROGEN–OXYGEN MIXTURES BEHIND THE INCIDENT SHOCK WAVE FRONT**

Experimental investigation of the ignition of a stoichiometric hydrogen–oxygen mixture behind an incident shock wave in a shock tube at pressures p = 0.002–0.46 MPa and temperatures T = 500–1000 K is carried out. The existence of three limits of ignition typical of the ignition of hydrogen–oxygen mixtures in a spherical vessel is noted. It is shown that at pressures p ≥ 0.1 MPa the ignition of a hydrogen–oxygen mixture begins at a much lower temperature than the ignition of a hydrogen–air mixture. The measured induction times agree well with theoretical estimates

**Author:**
V. A. Pavlov and G. Ya. Gerasimov

**Keywords:**
hydrogen–oxygen mixtures, combustion, ignition limits, induction time, incident shock wave

**Page:**
587

**RENORMALIZATION GROUP ANALYSIS OF THE STABILITY OF TURBULENT FLOWS IN POROUS MEDIA**

The concept of renormalization groups for modeling the parameters of flow in porous media is considered. An algorithm for the renormalization of the equations from the k–ε model of turbulence is given. An expression is obtained for the coeffi cient of renormalized viscosity. Based on the model developed, conditions of the turbulent flow instability in a porous medium have been analyzed.

**Author:**
A. A. Avramenko, N. P. Dmitrenko, and A. I. Tyrinov

**Keywords:**
renormalized analysis, mathematical model, porosity, instability, turbulence

**Page:**
592

**MATHEMATICAL SIMULATION OF THE EXTRACTION OF A BLENDING AGENT FROM CYLINDRICAL BODIES IN THE SEMICONTINUOUS REGIME**

A problem of the kinetics of extraction of a blending agent from cylindrical bodies in an apparatus of semicontinuous action (periodic for the solid phase and continuous for the liquid phase) in which the liquid phase is completely
mixed was formulated and solved analytically. The kinetics of the indicated process at different specifi c flow rates of the liquid phase was analyzed with the use of a numerical method. Recommendations on the use of the solution
obtained for calculating the kinetics of extraction of technological contaminants from textile materials in the process of their fl ushing are given.

**Author:**
S. P. Rudobashta, M. K. Kosheleva, and É. M. Kartashov

**Keywords:**
extraction, kinetics, flushing, fi brous material, mass conductivity, mass transfer, dwell time

**Page:**
606

**STABILITY OF FLOW IN A STEAM–WATER GEOTHERMAL WALL**

It has been shown that the existing notion about fl ow stability in a steam–water well cannot explain all experimentally observed features of the interrelationship between the wellhead pressure and the fl ow rate. We propose a new interpretation of the stability condition based on the analysis of the reaction of the well and the feed reservoir to bottom hole pressure fl uctuations at given conditions at the well inlet and outlet. It has been established that the stable regime corresponds to a negative value of the criterion defi ned as a ratio between the derivative characteristics of the well and the reservoir, and to obtain a characteristic, it is necessary to take into account the pressure loss in the equipment placed between the wellhead and the medium with a constant pressure. Such an approach and the new interpretation explain the practically observed features of the interrelationship between the wellhead pressure and the fl ow rate. It has been shown that the additional drag on the wellhead can stabilize the operating conditions of the well.

**Author:**
A. N. Shulyupin

**Keywords:**
well, wellhead, bottom hole, steam–water mixture, pressure, fl ow rate, underground reservoir, stability

**Page:**
614

**GENERALIZATION OF THE WET-BULB TEMPERATURE NOTION TO THE CASE OF ELECTROMAGNETIC DRYING**

A method of estimating the stationary temperature of the surface a body blown over by air and subjected to the action of electromagnetic radiation, representing a generalization of the wet-bulb temperature notion to the case of electromagnetic drying, has been developed.

**Author:**
A. M. Afanas′ev and B. N. Siplivyi

**Keywords:**
Luikov equation, drying, electromagnetic radiation, wet-bulb temperature

**Page:**
620

**MATHEMATICAL SIMULATION OF THE STRUCTURAL PROPERTIES OF PACKED AND FLUIDIZED BEDS**

Based on the algorithm of successive fi lling a given volume with single spheres, a mathematical model of random packing of a limited volume of a bed in the fi eld of body forces has been developed. This model can be applied to electrothermal packed- and fl uidized-bed furnaces and will make it possible to investigate the thermal and electrical conductivity of such beds. A check of the adequacy of the model showed its correspondence to the well-known experimental and calculated results, as well as the stability of the solutions obtained with its aid.

**Author:**
S. S. Fedorov, M. V. Gubinskii, and S. N. Foris′

**Keywords:**
random packing of particles, bed conductivity, packing density, voidage, coordination number, elementary volume, near-wall zone

**Page:**
627

**EXPERIMENTAL INVESTIGATIONS OF HEAT AND MASS TRANSFER IN MICROCHANNEL HEAT-TRANSFER ELEMENTS**

The present work seeks to develop and investigate experimentally microchannel heat-exchange apparatuses of two designs: with porous elements manufactured from titanium and copper, and also based on the matrix of filamentary silicon single crystals under operating conditions with high heat loads, unsteadiness, and nonlinear fl ow of the coolant. For experimental investigations, the authors have developed and manufactured a unique test bench allowing tests of the developed heat-transfer elements in unsteady operating regimes. The performed experimental investigations have made it possible to obtain criterial dependences of the heat-transfer coeffi cient on the Reynolds and Prandtl numbers and to refi ne the values of viscous and inertial coeffi cients. It has been established that microchannel heat-transfer elements based on silicon single crystals, which make it possible to remove a heat fl ux above 100 W/cm^{2} , are the most efficient. For porous heat-transfer elements, the best result was attained for wedge-shaped copper samples. According to investigation results, the authors have considered the issues of optimization of thermal and hydraulic characteristics of the heat-transfer elements under study. In the work, the authors have given examples of practical use of the developed heat-transfer elements for cooling systems of radioelectronic equipment.

**Author:**
D. A. Konovalov

**Keywords:**
microchannel element, porous element, silicon single crystals, cooling system, test bed

**Page:**
636

**RHEOLOGICAL PROPERTIES OF AQUEOUS ACID SOLUTIONS OF CHITOSAN: EXPERIMENT AND CALCULATIONS OF THE VISCOMETRIC FUNCTIONS ON THE BASIS OF A MESOSCOPIC MODEL**

The rheological properties of chitosan solutions in acetic acid at 20^{o}C in the range of polymer concentrations from 0.5 to 8 mass% and acid concentrations from 2 to 70% have been investigated. With the use of a modifi ed Vinogradov–Pokrovskii model based on the microstructural approach to the description of polymer fluid dynamics, numerical solutions of gradient dependences of viscometric functions of aqueous acid solutions of chitosan have been obtained. It has been established that the numerical solution describes with good accuracy the experimental viscosity rheograms. The values of the highest Newton viscosity η_{max} have been calculated. The concentration modes of semidiluted and concentrated solutions have been determined by the dependence of η_{max} on the polymer concentration, and the range of concentrations in which the mass transfer mechanism changes and a fluctuation network is formed has been found. It has been shown that the concentration of acetic acid practically does not infl uence the structure and character of flow of chitosan solutions, the formation concentration of a network, and the efficiency of its labile nodes

**Author:**
A. B. Shipovskaya, A. Yu. Abramov, G. V. Pyshnograi, and Al Joda Hyder Nadom Aziz

**Keywords:**
chitosan, acetic acid, solutions, rheological properties, shear viscosity, concentration mode, fl uctuation network, mesoscopic model, viscometric functions

**Page:**
642

**RHEOLOGICAL MODEL FOR DESCRIBING VISCOMETRIC FLOWS OF MELTS OF BRANCHED POLYMERS**

The present paper considers the problem of constructing a rheological constitutive relation for melts of branched polymers with the use of a modifi ed Vinogradov–Pokrovskii rheological model generalized to the case of several noninteracting models, each of which corresponds to the account in the stress tensor of the contribution of a particular polymer fraction and is characterized by its own relaxation time and viscosity. Since the number of model parameters markedly increases thereby, simple dependences of its parameters on the mode number are proposed. On the basis of the obtained model, the nonlinear nonstationary effects at simple shear and uniaxial tensor have been considered.

**Author:**
D. A. Merzlikina, G. V. Pyshnograi, R. Pivokonskii, and P. Filip

**Keywords:**
rheology, polymer melts, mesoscopic approach, rheological equation of state, viscometric flows

**Page:**
652

**FORMATION OF VORTEX STRUCTURES IN THE PRENOZZLE SPACE OF AN ENGINE WITH A VECTORABLE THRUST NOZZLE**

A numerical simulation of the hydrodynamic effects arising in the process of work of the vectorable thrust nozzle of a solid-propellant rocket engine has been performed. The fi elds of the flows of combustion products in the channel of a charge, the prenozzle space, and the nozzle unit were calculated for different angles of vectoring of the nozzle. The distributions of the gasdynamic parameters of the flow of combustion products in the prenozzle space, corresponding to their efflux from the cylindrical and star-shaped channels of charges, were compared. The formation of a vortex fl ow in the neighborhood of the back cover of the nozzle was considered.

**Author:**
K. N. Volkov, V. N. Emel′yanov, and S. V. Denisikhin

**Keywords:**
rocket engine, vectorable nozzle, vectoring, channel, numerical simulation, vortex structure

**Page:**
660

**FORMATION OF ZONES WITH MAXIMUM SUPERSONIC CAVITATION INTENSITY IN SINGLE-COMPONENT AND MULTICOMPONENT MEDIA**

Experimental studies have been made on the formation of highly active cavitation zones in fl uid media at high pressures (up to 6.5 MPa) and temperatures (up to 150^{o} C) with the use of a high-power ultrasonic installation. It has been shown that attempts to increase the cavitation intensity in single-component and multicomponent media by increasing the power of the ultrasonic installation to above a certain limit lead to a strong degradation of the cavitation processes. This is due to the appearance of hydrodynamical fl ows generated by longitudinal vibrations of the installation radiator waveguide. Eliminating or weakening such fl ows makes it possible to increase markedly the effi ciency of cavitation treatment by increasing the medium pressure (in the range of 0.5–1.5 MPa) and choosing the optimum ratio between the temperature of the medium and the power of the ultrasonic installation (specifi c acoustic power of the radiator). We recommend to use for the cavitation intensity index the acoustic activity of the cavitation zone (acoustic noise amplitude in the frequency range of 200 kHz–10 MHz), as well as its physical activity determined by the destruction rate of thin-layer indicators.

**Author:**
B. I. Bakhtin, A. I. Ivashov, A. V. Kuznetsov, and A. S. Skorokhodov

**Keywords:**
cavitation, cavitation intensity (activity), ultrasonic action, ultrasonic radiator (reactors, apparatuses), acoustic radiation, acoustic radiation intensity (power)

**Page:**
671

**EXPERIMENTAL INVESTIGATION OF THE SUPERSONIC FLOW OVER AN AXISYMMETRIC RING CAVITY**

This paper presents the results of the experimental investigation of the supersonic fl ow over a ring cavity of rectangular cross-section on a cylindrical body with a conical tip. The evolution of the fl ow over a cavity with its continuously changing extent has been investigated. The transition zone boundaries within which both an open and a closed schemes of fl ow are possible have been determined by the parameter of the relative extent of the cavity. It has been shown that the fl ow conditions in the transition zone depend on the prehistory of the fl ow. The main stages of cavity fl ow restricuting at the transition zone boundaries have been described.

**Author:**
S. V. Guvernyuk, A. F. Zubkov, and M. M. Simonenko

**Keywords:**
ring cavity, supersonic flow, flow separation, hysteresis.

**Page:**
678

**EFFECT OF SURFACE ENERGY PULSES ON SUPERSONIC FLOW IN A CHANNEL OF VARIABLE CROSS SECTION**

The infl uence of a surface pulse-periodic supply of energy on the formation of shock-wave structures in a plane channel of variable cross section has been studied. Energy is supplied to the constant cross-section units of the channel with the flow Mach number M = 2. The time-average supplied power corresponds to the combustion of hydrogen with the excess-air coeffi cient from 1 to 10. The problem is solved within the framework of the Euler equations. A dimensionless approach is used to analyze the effect of sources. The applicability of the analytical relations obtained is confi rmed by numerical solution of two-dimensional Euler equations.

**Author:**
V. P. Zamuraev and A. P. Kalinina

**Keywords:**
supersonic flow, channel of variable cross section, pulsed supply of energy, Euler equations, similarity criterion

**Page:**
688

**USE OF THE PIV METHOD FOR INVESTIGATION OF MOTION NEAR A CYLINDER IN TRANSVERSE FLOW**

Turbulent fl ow past a cylinder in a wind tunnel has been investigated experimentally. Averaged velocity fi elds near the cylinder have been obtained with the optical PIV method and comparative characteristics have been given for noncavitation and cavitation regimes. From the vector patterns of the averaged velocity fi elds, the author has determined the angles of separation of the boundary layer from the cylinder surface in the considered regimes of fl ow. It has been shown that cavitation causes the vortex zone behind the cylinder to increase, the separation angles to displace upstream, and the hydraulic resistance to grow. A comparative calculation of the separation angles and the coeffi cients of hydraulic resistance of cylinders manufactured from different materials has been given. It has been shown that the vortex zone of a Tefl on cylinder in fl ow having a hydrophobic surface differs from the vortex zone of a steel cylinder, particularly for the cavitation regime in which the angles of separation, especially from the upper part, decrease appreciably and the resistance grows.

**Author:**
K. G. Dobrosel′skii

**Keywords:**
wind tunnel, cylinder, PIV, noncavitation and cavitation regimes, angle of separation of the boundary layer, hydraulic resistance

**Page:**
695

**INFLUENCE OF ACOUSTIC AND ELECTROMAGNETIC ACTIONS ON THE PROPERTIES OF AQUEOUS NANOPARTICLE DISPERSIONS USED AS TEMPERING LIQUIDS FOR DENTAL CEMENT**

The authors have studied the physicochemical properties of aqueous dispersions containing carbon, silver, and iron nanoparticles which were produced by elastic-spark synthesis under the conditions of subaqueous spark discharge,
and also the influence of preliminary acoustic and high-frequency electromagnetic action on them and the change in the functional indices of the glass-ionomer cement tempered by these dispersions

**Author:**
V. V. Azharonok, N. Kh. Belous, S. P. Rodtsevich, S. V. Goncharik, N. N. Chubrik, V. D. Koshevar, K. G. Lopat′ko, E. G. Aftandilyants, A. N. Veklich, V. F. Boretskii, and A. I. Orlovich

**Keywords:**
native colloidal systems, deionized water, electric-spark dispersing, tempering liquid, glass-ionomer cement, high-frequency electromagnetic field, nanomodifi er

**Page:**
702

**SIMULATION OF THE THERMAL PROCESS OF BUTT WELDING OF POLYETHYLENE PIPES AT LOW TEMPERATURES**

A theoretical study has been made of the thermal process of welding polyethylene pipes for gas pipelines at low ambient air temperatures. The mathematical model used takes into account the heat of the phase transition in the
temperature range, as well as the thermal effect of the fin formed by the slip. Computing experiments have shown that it is possible to control the temperature regime in welding at low ambient air temperatures and provide, in the
thermal infl uence zone, the same change in the temperature fi eld as at permissible air temperatures.

**Author:**
N. P. Starostin and O. A. Ammosova

**Keywords:**
polyethylene pipe, welding, temperature fi eld, phase transition, fi n, temperature control

**Page:**
714

**OPTIMUM ORGANIZATION AND MAXIMUM CAPABILITIES OF HEAT-PUMP HEATING SYSTEMS**

The authors obtained a lower bound for the energy consumption in heating (maintaining an assigned temperature
distribution in the system of intercommunicating chambers) and the corresponding distributions of the total heattransfer
coeffi cients and the temperature of the working medium of a heat pump in contact with the chambers and
the environment.

**Author:**
A. M. Tsirlin and V. A. Kuz′min

**Keywords:**
heating system, dissipation, temperature distribution, nonequilibrium temperature field

**Page:**
721

**INFLUENCE OF THE DURATION OF THERMAL ACTION ON THE ERRORS IN DETERMINING THE THERMOPHYSICAL CHARACTERISTICS OF CERAMIC MATERIALS BY A LASER PULSE METHOD**

An analysis of the errors involved in determining the thermophysical characteristics of a special-purpose ceramic material — zirconium carbide — is made. It is shown that the errors of determining the heat capacity and thermal
diffusivity of the indicated material under conditions corresponding to the implementation of the laser pulse method vary nonmonotonically depending on the pulse duration. The possibility of attaining minimum values of methodical
errors by appropriately selecting the thickness of a sample and of the time of its heating is shown.

**Author:**
G. V. Kuznetsov and M. D. Kats

**Keywords:**
thermophysical characteristics, zirconium carbide, laser pulse method, heat capacity, thermal diffusivity, pulse duration

**Page:**
728

**DEPENDENCE OF THE THERMODIFFUSION CONSTANT OF A MIXTURE OF TWO GASES ON THE ADDITION OF A THIRD GAS TO IT**

The dependence of the thermodiffusion constant of a mixture of two gases on the addition of a third gas, whose
molecular mass is larger than the molecular mass of the light component of the mixture and smaller than the
molecular mass of its heavy component, to it was investigated. The investigations were carried out for different
compositions of the initial binary mixture and different concentrations and masses of the additional component.
Good agreement between the calculation and measurement data on the indicated constant has been obtained within
the limits of the calculation and experimental errors.

**Author:**
N. A. Nezovitina, A. F. Bogatyrev, and O. A. Makeenkova

**Keywords:**
binary and ternary gas systems, thermodiffusion separation, experiment

**Page:**
733

**COMPLEXATION OF OPTOELECTRONIC SYSTEMS**

Problems of increasing the effi ciency and the functionality of complex optoelectronic systems for monitoring real
atmospheric conditions and of their use are discussed. It is shown by the example of a meteorological complex
comprising an infrared wind-sensing lidar and an X-range Doppler radar that the complexation of probing systems
working in different electromagnetic-radiation ranges opens up new opportunities for determining the meteorological
parameters of a turbulent atmosphere and investigating the interaction of radiation with it.

**Author:**
A. S. Boreisho, M. Yu. Il′in, M. A. Konyaev, A. S. Mikhailenko, A. V. Morozov, and S. Yu. Strakhov

**Keywords:**
complexation, optoelectronic system, atmospheric turbulence, laser radiation, wind shift

**Page:**
741

**DYNAMIC STABILITY OF A CYLINDRICAL SHELL REINFORCED BY LONGITUDINAL RIBS AND A HOLLOW CYLINDER UNDER THE ACTION OF AXIAL FORCES**

The dynamic stability of a cylindrical orthotropic shell reinforced by longitudinal ribs and a hollow cylinder
under the action of axial forces changing harmonically with time was investigated with regard for the axial
contact interaction of the shell with the ribs. A solution of the differential equations defi ning this process has been
obtained in the form of trigonometric series in the angular and time coordinates. A two-term approximation of
the Mathieu–Hill equations of motion was used for construction of the main region of instability of the shell. As a
result, the problem was reduced to a system of algebraic equations for components of displacements of the shell at
the locations of the ribs. The problem for uniformly spaced ribs was solved in the explicit form. A numerical example
of this solution is presented.

**Author:**
V. N. Bakulin, E. N. Volkov, and A. Ya. Nedbai

**Keywords:**
dynamic instability, cylindrical orthotropic shell, longitudinal ribs, stability region, hollow cylinder

**Page:**
747

**RELATIONSHIP BETWEEN THE STRUCTURE PARAMETERS OF A SOLID BODY AND THE KINETICS OF DONOR–ACCEPTOR INTERACTION IN HETEROGENEOUS SYSTEMS**

Interaction of an organic ligand molecule with the surface of a d-metal or of disperse particles of chemical
compounds containing covalent bonds in a nonaqueous solvent (direct synthesis of complex compounds) is
determined by the structure parameters of the solid body. The relationships of the rate and energy of activation of
the donor–acceptor interaction of the metal with the Grüneisen coeffi cient and the Debye temperature of the metal
have been established.

**Author:**
V. Ya. Khentov and Kh. Kh. Khussein

**Keywords:**
direct synthesis of complex compounds, ligand, nonaqueous solvent, reaction rate, activation energy, structure parameters of a solid body, Grüneisen coeffi cient, Debye temperature of a metal

**Page:**
754

**ANALYSIS OF CONVECTIVE HEAT TRANSFER ENHANCEMENT BY NANOFLUIDS: SINGLE-PHASE AND TWO-PHASE TREATMENTS**

Nanofl uids have been investigated regarding their advantages and potentialities for the purpose of increasing
convective heat transfer rates inside thermal systems where they are used as working fluids. Researchers in
thermophysics have investigated these fluids experimentally and numerically. This review provides extensive
theoretical information concerning nanofl uids in the single-phase and two-phase treatments. Important published
works on nanofl uid properties and correlations are summarized and reviewed in detail. Heat transfer enhancement
by nanofl uids is a challenging problem due to the diffi culties inherent in the model of the physical mechanism of
interaction between the paricles. Here the interaction between the phases is modeled by several two-phase models,
and the results are given in graphical and tabular forms. Despite the advantages of the mixture model, such as
imlementation of physical properties and less computational power requirements, some studies showed that the
results of the single-phase and two-phase models are very similar. The main difference consists in the effect of the
drift velocities of the phases relative to each other

**Author:**
S. Kakaç and A. Pramuanjaroenkij

**Keywords:**
nanofl uids, heat transfer enhancement, convective heat transfer

**Page:**
758