Symmetries of Cylindrical Equations of Hydrodynamics and Convective Heat Exchange

Consideration has been given to the interrelation of the symmetries (in terms of the Lie groups) of a system of Navier–Stokes and Fourier–Kirchhoff equations and selfsimilar forms of these equations. It has been shown how various selfsimilar forms can be determined on the basis of the symmetries. Ordinary selfsimilar differential equations have been obtained.     

Inertial‐Capillary Surface Waves and their Influence on Crystal Growth in Zero Gravity

The results of the numerical calculations of oscillations of the liquid column free surface under the action on it of axial vibration in zero gravity are presented. On the basis of these calculations, an analytical model of the surface standing wave named the inertialcapillary wave has been developed. Comparison of the analytical calculations with the data of the numerical calculations and the experiment performed in microgravity under the TEXUS program has been made. The numerical study of the thermocapillary convection stability in the presence of inertialcapillary waves has shown that the change to the oscillation regime is very sharp upon reaching certain values of the vibration frequency and amplitude. The heatandmass transfer in growing semiconductor crystals by the floatingzone method in zero gravity under the action of vibration with allowance for the surface waves has been investigated. The possibility of measuring vibrational accelerations onboard space vehicles by means of oscillations of the liquidcolumn free surface are discussed.     

Method of Summation‐Integral Equations for Solving the Mixed Problem of Nonstationary Heat Conduction

The solution of a mixed axisymmetric nonstationary problem of heat conduction is obtained in the region of Laplace transforms. In solution of this problem, there occur summation–integral equations with the parameter of the integral Laplace transform (Lparameter) and the additional parameter of the finite integral Hankel transform (Hparameter). The laws governing the development of spatial nonstationary temperature fields in a bounded cylinder and a halfspace when one end surface of the cylinder is in contact with the surface of the halfspace in a circular region are determined.     

Influence of Multiple‐Scattering Processes on the Laser Probing of Biological Tissues

Theoretical aspects of multiplescattering processes in laser probing of biological tissues have been considered. The method of digital dynamic specklephotography has been described. The results of experimental studies of the nearsurface blood flow and stressedstrained states in a pinstructure–toothroot model are presented.     

Self‐Organization and Dynamic Chaos in Chemical‐Technology and Heat‐Exchange Devices: Problems and Tasks

Nonlinear phenomena in thermophysical and chemicaltechnology processes are considered in the context of nonlinearity, instability, nonuniqueness, nonstationarity, and irreversibility. The perturbation frequency (phase)toamplitude ratio is the governing parameter of the nonlinear interaction of perturbations that are described by the proposed general nonlinear parabolic equation. The nonlinearity of this ratio characterizes turbulence, while its linearity characterizes selforganization. It is shown that chaotic conditions can be selforganized under the action of white noise, which favors the system getting into the domain of attraction of a stable node. The mechanism of the occurrence of turbulence is substantiated.     

Ray Method of Solution of the Ablation Problem

Consideration is given to a threedimensional problem of heating of a halfspace by the Gaussian energy flux with allowance made for the heatflux inertia. It is assumed that the ablation front is formed at the points at which the temperature is equal to the melting temperature and the Stefan condition is satisfied. The mechanism of removal of mass is not considered. Using the ray method and taking into account three expansion terms, an ablationsurface equation and temperature have been obtained. Account for the inertia of the heat flux leads to the fact that the ablationfront velocity at the initial instant of time is finite. The condition for the onset of ablation of the material at the initial instant of time has been obtained. The solutions for the fronts of ablation and temperature are illustrated by the graphs.     

Study of Interaction of Disturbances in an Internal Flow

Data on narrowband acoustic disturbances that arise in manifold pipes with one or two blind branches and in wind tunnels with an open working section are analyzed. The ranges of acoustic instability that correspond to excitation of selfoscillations in a flow in the cases mentioned are determined. The dependence of the intensity of acoustic radiation in two blind branches and in the manifold between them on the multiplicity of the length of the resonance section to the length of halfwaves of resonance frequency is considered. The possibility of attenuation of selfoscillations by organizing hydrodynamic structures that interact with formations generating acoustic oscillations is determined.     

Quasi‐Self‐Similar Description of an Exhaust Jet

The method of construction of an analytical solution for the far field of an exhaust jet on the basis of the quasiselfsimilar solution of Prandtl equations and the turbulence model with one differential equation for the coefficient of kinematic viscosity is described. An exact numerical solution for distances to about 10¹ radii of the nozzle is constructed for the basic version. Then, a numerical solution and its analytical approximation by the quasiselfsimilar solution are constructed. Approximations of the similarity parameters of the selfsimilar problem as functions of the similarity parameters of the initial problem in the form of polynomials allow construction of analytical solutions for different situations, which are in satisfactory agreement with the exact numerical solution at distances of radii.     

Identification of the Parameters of a Nested Cylindrical Heat Source under Stationary Self‐Heating of a Raw Material Mass of the Same Form

This paper describes a computer method for determining the coordinate of the center, the heatrelease power, and the sizes of a homogeneous internal cylindrical heat source in a stationary axially symmetric temperature field arising under selfheating of a plant raw material.     

Influence of the Viscosity of Filled Epoxy Resins on Their Spreading on a Horizontal Surface

The rheological properties of ÉD20epoxyresinbased compositions filled (10–50 vol.%) with quartz sand, quartz flour, or their mixture have been investigated on Reotest2 and RV8 rotational viscosimeters. The relative viscosity of the filled compositions increased with their free volume according to the exponential equation with an exponent of 2.6. The compositions began to show an anomaly of viscosity in flowing for a content of the filler of more than 40 vol.%; the yield stress appeared for 50 vol.%. The rate of spreading of the compositions on a horizontal surface decreased with increase in the composition viscosity according to the exponential equation with an exponent of 1/8, which is similar to that calculated theoretically. The experiments conducted allowed calculation of the formula of epoxybased, selfleveling pouring floors.     

One Method of Determination of the Effective Absorption Coefficient in Pulsed Laser Irradiation of Metals

An experimentaltheoretical method of determination of the absorption coefficients in laser treatment of metals has been proposed based on the solution of the boundaryvalue axisymmetric problem of heat conduction for a halfspace and metallographic measurements of the dimensions of the thermalhardening zone.     

Numerical Modeling of Turbulent Flow inside a Wind‐Driven Plant with Allowance for the Forces on the Impeller

The operating efficiency of a winddriven plant based on a confuserdiffuser accelerator is evaluated within the framework of the multiblock approach to solution of steadystate Reynolds equations closed with the use of a twoparameter dissipative turbulence model.     

Influence of the Mass Transfer of Water in Cartilaginous Tissue on the Temperature Field Induced by Laser Radiation

A study is made of the influence of the mass transfer of water on the temperature field occurring in cartilaginous tissue under the action of laser pulses. Two different mechanism of mass transfer of water in cartilaginous tissue (moleculardiffusion mechanism and laminar flow) have been considered in solving heat and masstransfer equations. The calculations have shown that the maximum temperature is attained inside the sample because of the evaporation of water from the biologicaltissue surface. The influence of different parameters of laser radiation and mass transfer of water on the surface temperature, on the maximum value of the temperature, on the position of the temperature maximum, and on the characteristic time at which the diffusionlimited relaxation of stresses in the cartilaginous tissue occurs has been analyzed.     

Numerical‐Analytical Investigation of Self‐Similar Regimes of Propagation of Nonstationary Convective Jets and Thermals in a Homogeneous Medium over a Point Heat Source

An integral model of a nonstationary vertical convective jet is suggested that involves a universal equation of the propagation of the upper boundary of a convective front depending on the power of the point heat source. A class of selfsimilar solutions is considered; they correspond to the heat sources whose power changes instantly and also according to the power and exponential laws. Analytical and numerical solutions of the selfsimilar equations are constructed. Numerical calculations are compared with the wellknown experimental data on the profiles of the vertical velocity and temperature on the jet axis.     

Numerical Analysis of the Effect of Viscosity on the Vortex Dynamics in Laminar Separated Flow Past a Dimple on a Plane with Allowance for Its Asymmetry

Based on numerical solution of the Navier–Stokes threedimensional stationary equations by a factorized finitevolume method, the influence of physical viscosity on selforganizing jetvortex structures in a dimple on a plane immersed in a laminar flow is analyzed with allowance for the asymmetry of the dimple shape.     

Modeling of Heat and Mass Transfer in Systems of Radiation‐Evaporation Thermal Protection

Results of theoretical and experimental studies of models of different systems of radiationevaporation thermal protection are presented; the overalldimensionweight parameters of these systems and of systems of passive radiation thermal protection are compared.     

Improvement of the Accuracy of the Large‐Particle Method in Calculation of Motions of Energy‐Saturated Media on Superposed Grids

A TVDmodification of the largeparticle method with the algorithm of calculation on superposed grids with a set of cells differing in shape is presented.     

Study of the Temperature Fields in Oil and Gas Strata with Water Injection Based on the Perturbation Method

The problem of the thermal action on oil and gas strata by injection of a heating medium using expansion in a small parameter is reduced to an infinite sequence of boundaryvalue problems that are solved by the method of integral transforms. It is shown that, with an appropriate selection of the small parameter, the zerothorder approximation corresponds to a spaceaveraged (across the stratum thickness) solution of the main problem and leads to a concentratedcapacity scheme that is constructed assuming that the stratum temperature is independent of the vertical coordinate. The first approximation permitted marked refinement of calculations according to the concentratedcapacity scheme and an evaluation of its error. Spacetime temperature distributions are presented that have been calculated using the analytical solutions obtained.     

Modern Problems of Intensification of Heat Exchange in Channels

The current achievements in the field of intensification of heat exchange in tube heatexchange apparatus are considered. Requirements for highefficiency heattransfer surfaces have been formulated. Problems of intensification of heat exchange in bundles of finned tubes and in heatexchange apparatus under conditions of condensation and boiling of heattransfer agents and under scaling conditions have been investigated. Highefficiency designs of heatexchange apparatus are presented.     

Calculation of a Temperature Error by the Conjugate Equation

A temperature error depending on the error of initial information can be calculated by the conjugate problem. On estimation of the error at one time and coordinatelocal point the expenditures of the computation time and computer memory are double the expenditures for calculation of the heatconduction equation. The conjugatetemperature field obtained in this case allows calculation of the effect of the error of any parameter of the problem (initial conditions, boundary conditions, coefficients). In the linear case, the conjugatetemperature field depends on the position of the point under estimation; in the nonlinear case, it additionally depends on the temperature field. The approach considered can be applied to calculation of the error of a wide class of temperature functionals.