Thermal Conductivity of a Three‐Dimensional Body with a Rough Inclusion

Thermal conductivity of a threedimensional body with a rough inclusion is studied. The problem is reduced to the problem of conjugation of harmonic functions and its exact solution is constructed. Distributions of temperature and heatflux density near distinctions of the interface between media are found. Results are illustrated by a numerical example.     

Modification of a One‐Dimensional Lagrangian Grid for Modeling of Dynamic Processes in Pipelines of Variable Cross Section

Consideration is given to a mathematical model of the nonseparating nonstationary motion of an ideal compressible gas in a pipeline with a variable cross section. A method which enables one to calculate changes in the pressure, density, and the velocity at the sites of contraction and expansion of the pipeline without going beyond the scope of a onedimensional model is presented.     

One Approach to the Analytical Solution of a Two‐Dimensional Nonstationary Problem of Heat Conduction in Regions with Moving Boundaries on the Model of a Half‐Space

With the use of the solution of the Dirichlet nonstationary problem with discontinuous unmixed boundary conditions on the surface of an isotropic halfspace a twodimensional model of the problem with a moving phase boundary is considered. The problem models, for example, the processes of freezing of moist ground or the processes of formation of ice in stagnant water if a temperature lower than the freezing temperature is prescribed on the boundary surface in a circular region of finite radius. The classical onedimensional result follows as a particular case from solution of this problem for an infinite radius of the circle.     

Two‐Dimensional Diffusion of a Binary Mixture of Neutral Gases

An expression for the coefficient of twodimensional diffusion of a binary mixture of neutral gases is obtained within the framework of the kinetic theory.     

Solution of Nonlinear Two‐Dimensional Differential Equations of Transfer with Discontinuity Boundary Conditions on the Surface of an Isotropic Semiinfinite Body in Its Heating Through a Circle of Known Radius

An analytical solution of the heatconduction problem is obtained by the method of linearization of a nonlinear equation of transfer and combined application of integral transforms to the linearized problem for an isotropic halfspace heated through a circular region 0 < r < R on its surface z = 0.     

Heat Transfer in Straight Channels with Two‐Dimensional Cross‐Sectional Profiles under Conditions of Nonisothermal Stabilized Flow of a Fluid

Heat transfer in stabilized regimes of nonisothermal flows in a round tube and in channels with twodimensional convex cross sections is investigated with allowance for the velocity profile of a heating or cooling flow of a fluid. Mathematical models of unsteady processes of cooling by convection and radiation in pulling of rods and plane sheets at a constant velocity and of heat transfer (mass transfer) in a thin runningdown layer of a medium (fluid) are solved.     

Filtration of a High‐Viscosity Oil in an Electromagnetic Field

Results of experimental investigations of the time dependences of the change in the temperature of an oil pool and in the discharge of an oil well under the action of a microwave electromagnetic field are presented. An experimental setup is described. It is shown that the temperature is distributed nonuniformly over the thickness of the oil pool depending on the initial discharge of the well and the time of the microwave electromagnetic action on the face zone of the pool.     

Thermophoresis of Large Volatile One‐Component Drops

The work is devoted to the theory of motion of aerosol particles in temperatureinhomogeneous gases. An investigation is made of the influence of the Dufour effect on the thermophoresis rate of large volatile onecomponent drops. Estimates of the resultant formula show that this effect exerts an insignificant influence on the velocity of motion of the drops under actual conditions.     

One‐step Synthesis of Water‐soluble Fullerenols Bearing Nitrogen‐containing Substituents

We found a facile one‐step synthetic method for water‐soluble fullerenols bearing 8–16 nitrogen‐containing substituents as well as more than 16 hydroxyl groups from commercially available C₆₀ as a starting material. The water solubility of one of the products showed the same as the highest one reported (>200 mg/mL). Other fullerenols bearing hydrogen or diethylamino group on the same fullerene cage were also synthesized by the modified method using hydrogen peroxide as a simple hydroxylation reagent.     

Stochastic‐Deterministic Modeling of the Development of Hydrodynamic Instability in Filtration of Mixing Fluids

The stochasticdeterministic approach to modeling of the Saffman–Taylor hydrodynamic instability in filtration of mixing fluids in a porous medium is considered. The numerical model is used to study the dynamics of development of the instability in displacement of a more viscous fluid by a less viscous one in uniformly and nonuniformly permeable media. Results of the modeling are compared to experimental data.     

Generalized Couette flow in channels of irregular cross‐section

Abstract

The flow behavior of non‐Newtonian power‐law fluids in channels of irregular cross‐section is examined. The driving force of the flow may be a constant pressure gradient (Poiseuille flow), a moving boundary (Couette flow) or the combination of the two (generalized Couette flow). There are three factors that influence the fluid motion in a channel, namely, the power‐law index n, the channel geometry and a dimensionless quantity E which can be viewed as the ratio of drag flow to pressure flow. The effects of these variables on velocity distributions and volumetric flow rates for various channel geometries are analyzed. The direct application of the numerical results on extruder design and operation is discussed.     

Improvement of the Convergence of Fourier–Hankel Series in Solving Two‐Dimensional Heat‐Conduction Problems

In the present work, an analytical solution of a boundaryvalue problem of nonstationary heat conduction in a twodimensional solid (a prism, a cylinder) with improved convergence of Fourier–Hankel series is given. Using as an example a problem with cyclic inhomogeneous boundary conditions of the third kind, the author shows the uniformity of the convergence of the obtained solution on the boundaries of the solid and the matching of temperatures in passage from one period of the cycle to another.     

Two‐Dimensional Calculation of the Parameters of a Steam‐Air Mixture in a Film‐Type Heat and Mass Exchanger

A mathematical model for twodimensional calculation of the temperature and density of the steam in a steamair mixture which rises between two water films flowing down adiabatic shields has been proposed. The parameters of the films have been calculated in a onedimensional approximation. The results of calculating the parameters of air according to the onedimensional and twodimensional models of the processes of heat and mass transfer have been compared. The range of applicability of the former to a filmtype heat and mass exchanger has been determined.     

Broadening of Photonic Band Gap in a One—Dimensional Superconductor Star Waveguide Structure

The present paper describes the theoretical investigation of enlarged reflection bands (photonic band gaps) in a 1D star waveguide (SWG) structure consists of superconductor and dielectric as its constituent materials. For the present study, we take the different combinations of superconductor and dielectric materials as a backbone and side branches of the SWG structure. In order to obtain the dispersion relation, Interface Response Theory (IRT) has been employed. Photonic band gaps of SWG structure having superconductor?Csuperconductor, superconductor?Cdielectric, and dielectric?Csuperconductor materials are compared with the band gaps of the conventional photonic crystal (PC) structure having superconductor?Csuperconductor and dielectric?Csuperconductor materials. Analysis of the dispersion characteristics shows that there exists no band gaps for conventional PC when both layers are made of the same superconducting materials (as the usual case) while the SWG structure shows forbidden bands of finite width even the backbone and side branches are made of same materials. Also, the SWG structure having superconductor?Cdielectric shows the wider reflection bands in comparison with the structure having dielectric?Csuperconductor as its constituent materials, while for the conventional PC structure it is same in both the cases. Further, the effect of temperature and the effect of variation of number of grafted branches on the photonic bands of SWG structure have been studied.     

Mathematical Model of a Recuperative Heat Exchanger in a Two‐Dimensional Formulation

A twodimensional model of a recuperative heat exchanger which allows calculation of flows through a heattransfer wall and temperature at any point of it has been developed. The results of the calculations are in satisfactory agreement with experimental data.     

Numerical Modeling of the Three‐Dimensional Unsteady Convection of a Silicon Melt in a Vessel Typical of Czochralski‐Method Apparatuses

Calculations of the quasiperiodic and stochastic regimes of threedimensional convection of a silicon melt (Pr = 0.015) have been performed for a rotating vessel whose complicated shape is typical of crucibles used in growing crystals by the Czochralski method. A large set of data on the structure of the convection and the spectral composition of pulsations has been obtained. The influence of the rotation of a crystal and a crucible on the convection and the thermal state of a melt has been investigated.     

Calculation of the Outflow of a One‐Velocity Heterogeneous Mixture into Vacuum

The outflow of a waterair mixture (an incompressible fluid) and a mixture of two ideal gases has been studied within the framework of the generalizedequilibrium model of a heterogeneous medium. In the first problem, the solution has been obtained in the form of analytical dependences. In the other, for a complete determination of all the dependent variables both analytical relations and an ordinary differential equation have been integrated numerically. The outflow of a mixture with an arbitrary number of components into vacuum is calculated similarly.     

Two‐Dimensional Model of Transfer Processes on a Bubble Plate in Multicomponent Rectification

A mathematical model of the process of rectification of a multicomponent mixture on a bubble plate is presented. The transfer processes in the twophase gas–liquid flow are described using a twoliquid model with account for the distinctive features of the phase interaction on the plate. The results of calculations according to the Young model are compared to the experimental data on the rectification of an nhexane–ethanol–methylcyclopentane–benzene mixture on a sieve plate 0.302 m in diameter.     

Photoluminescence Study of the Two‐Dimensional Tetragonal and Rhombohedral Polymers of C60 at High Pressure

Abstract

The pressure behavior of the photoluminescence (PL) spectra of the planar polymeric phases of C₆₀ have been studied at pressure up to 4 GPa. The PL spectra and the pressure‐induced shift of the principal bands differ considerably for the pristine C₆₀, two‐dimensional tetragonal (2D‐T) and rhombohedral (2D‐R) polymers of C₆₀. The changes in the PL spectra may be related with the transformation of the electron energy spectrum of polymers.     

Raman Modes and Stability at High Pressure of the Two‐Dimensional Rhombohedral Polymer of C60

Abstract

Phonon modes and stability of the planar rhombohedral polymer of C₆₀ have been studied at pressure up to ～30 GPa by means of in situ Raman scattering. At P ～ 15 GPa the phonon frequencies show an irreversible transition to a new phase related with random covalent bonding between the molecules in adjacent polymeric sheets.