Effect of solidification on drop fragmentation in liquid–liquid media

 This paper presents results of experimental and analytical investigation on molten alloy drop fragmentation in water pool. Emphasis is directed towards delineating the roles which melt to coolant heat transfer and melt solidification play in the fragmentation process. The strong impact of coolant temperature upon fragmentation process is addressed. A set of 23 drop fragmentation experiments were performed, in which 8 experiments employed a low melting point alloy, cerrobend-70 and 15 experiments using Pb–Bi eutectic alloy as drop fluid. The results show strong impact of coolant temperature on particle size distribution of the fragmented drops. A linear stability analysis of the interface between the two liquid fluids with thin crust growing between them, is performed. A modified dimensionless Aeroelastic number, for Kelvin–Helmholtz instability, is obtained and used as a criteria for fragmentation of molten drops penetrating into another liquid coolant media with lower temperature. The nondimensionalized mean diameter of the fragmented particles is correlated with the Aeroelastic number. Received on 26 March 2000     

High-velocity penetration of a melting solid by a slender body

The high-velocity penetration of a melting solid by a thermally insulated slender body is considered. Under certain constraints on the dimensionless melting parameters the flow in the molten layer can be described within the framework of lubrication theory. The local angle of inclination of the body and the surfaces of the molten layer with respect to the velocity is assumed to be small and is taken into account in the linear approximation. The heat flow into the solid is found by simulating the body and the molten layer by means of a segment with distributed heat sources. Within the framework of this simple formulation a closed solution of the problem of the fusion zone around a moving slender body is constructed. The dependence of the shape of the molten layer and the structure of the temperature and longitudinal velocity fields in the layer on the shape of the body and the other governing parameters of the problem is investigated. The results obtained also give a solution of the problem of the melting of a solid rubbing at high velocity against a thermally insulated rough substrate, when the characteristic height of the roughness is of the order of the thickness of the layer and the characteristic length of the order of the contact length.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.6, pp. 43–48, November–December, 1992.     

Motion and heat and mass transfer in a disperse admixture in turbulent nonisothermal jets of a gas and a low-temperature plasma

The motion and heat and mass transfer of particles of a disperse admixture in nonisothermal jets of a gas and a low-temperature plasma are simulated with allowance for the migration mechanism of particle motion actuated by the turbophoresis force and the influence of turbulent fluctuations of the jet flow velocity on heat and mass transfer of the particle. The temperature distribution inside the particle at each time step is found by solving the equation of unsteady heat conduction. The laws of scattering of the admixture and the laws of melting and evaporation of an individual particle are studied, depending on the injection velocity and on the method of particle insertion into the jet flow. The calculated results are compared with data obtained with ignored influence of turbulent fluctuations on the motion and heat and mass transfer of the disperse phase. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 95–108, May–June, 2008.     

An analytical solution to non-axisymmetric heat transfer with viscous dissipation for non-Newtonian fluids in laminar forced flow

Forced convection heat transfer in a non-Newtonian fluid flow inside a pipe whose external surface is subjected to non-axisymmetric heat loads is investigated analytically. Fully developed laminar velocity distributions obtained by a power-law fluid rheology model are used, and viscous dissipation is taken into account. The effect of axial heat conduction is considered negligible. The physical properties are assumed to be constant. We consider that the smooth change in the velocity distribution inside the pipe is piecewise constant. The theoretical analysis of the heat transfer is performed by using an integral transform technique – Vodicka’s method. An important feature of this approach is that it permits an arbitrary distribution of the surrounding medium temperature and an arbitrary velocity distribution of the fluid. This technique is verified by a comparison with the existing results. The effects of the Brinkman number and rheological properties on the distribution of the local Nusselt number are shown.     

Method of effective length for the boundary layer on a thin filament drawn out of a half-space

Heat transfer from a thin filament pulled from a half-space is considered. On the basis of the self-similar solution, obtained in the study, and using the method of effective length, the friction and heat transfer coefficients on the surface of a thin filament of varying radius and with distributed surface temperature and velocity are determined. The results obtained with this approximate method agree well with the results of a numerical solution of the boundary layer equations. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 23–28, January–February, 1994.     

Flow of power-law fluids over a moving wedge surface with wall mass injection

The boundary layer problem of a power-law fluid flow with fluid injection on a wedge whose surface is moving with a constant velocity in the opposite direction to that of the uniform mainstream is analyzed. The free stream velocity, the injection velocity at the surface, moving velocity of the wedge surface, the wedge angle and the power law index of non-Newtonian fluid are assumed variables. The fourth order Runge–Kutta method modified by Gill is used to solve the non-dimensional boundary layer equations for non-Newtonian flow field. Without fluid injection, for every angle of wedge β, a limiting value for velocity ratio λ _cr (velocity of the wedge surface/velocity of the uniform flow) is found for each power-law index n. The value of λ _cr increases with the increasing wedge angle β. The value of wedge angle also restricts the physical characteristics of the fluid to be used. The effects of the different parameters on velocity profile and on skin friction are studied and the drag reduction is discussed. In case of C = 2.5 and velocity ratio λ = 0.2 for wedge angle β = 0.5 with the fluid with power law-index n = 0.5, 48.8% drag reduction is obtained.     

Analytical Investigation of the Effect of Viscous Dissipation on Couette Flow in a Channel Partially Filled with a Porous Medium

An analytical study of viscous dissipation effect on the fully developed forced convection Couette flow through a parallel plate channel partially filled with porous medium is presented. A uniform heat flux is imposed at the moving plate while the fixed plate is insulated. In the fluid-only region the flow field is governed by Navier–Stokes equation while the Brinkman-extended Darcy law relationship is considered in the fully saturated porous medium. The interface conditions are formulated with an empirical constant β due to the stress jump boundary condition. Fluid properties are assumed to be constant and the longitudinal heat conduction is neglected. A closed-form solution for the velocity and temperature distributions and also the Nusselt number in the channel are obtained and the viscous dissipation effect on these profiles is briefly investigated.     

Thermophysical and heat transfer properties of phase change material candidate for waste heat transportation system

A waste heat transportation system––trans-heat (TH) system––is quite attractive that uses the latent heat of a phase change material (PCM). The purpose of this paper is to study the thermophysical properties of various sugars and sodium acetate trihydrate (SAT) as PCMs for a practical TH system and the heat transfer property between PCM selected and heat transfer oil, by using differential scanning calorimetry (DSC), thermogravimetry-differential thermal analysis (TG-DTA) and a heat storage tube. As a result, erythritol, with a large latent heat of 344 kJ/kg at melting point of 117°C, high decomposition point of 160°C and excellent chemical stability under repeated phase change cycles was found to be the best PCM among them for the practical TH system. In the heat release experiments between liquid erythritol and flowing cold oil, we observed foaming phenomena of encapsulated oil, in which oil droplet was coated by solidification of PCM.     

Melting heat transfer in steady laminar flow over a moving surface

The steady laminar boundary layer flow and heat transfer from a warm, laminar liquid flow to a melting surface moving parallel to a constant free stream is studied in this paper. The continuity, momentum and energy equations, which are coupled nonlinear partial differential equations are reduced to a set of two nonlinear ordinary differential equations, before being solved numerically using the Runge–Kutta–Fehlberg method. Results for the skin friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are presented for different values of the governing parameters. Effects of the melting parameter, moving parameter and Prandtl number on the flow and heat transfer characteristics are thoroughly examined. It is found that the problem admits dual solutions.     

Mass transfer effects on the non-Newtonian fluids past a vertical plate embedded in a porous medium with non-uniform surface heat flux

 The present study is devoted to investigate the influences of mass transfer on buoyancy induced flow over vertical flat plate embedded in a non-Newtonian fluid saturated porous medium. The Ostwald–de Waele power-law model is used to characterize the non-Newtonian fluid behavior. Similarity solution for the transformed governing equations is obtained with prescribed variable surface heat flux. Numerical results for the details of the velocity, temperature and concentration profiles are shown on graphs. Excess surface temperature as well as concentration gradient at the wall associated with heat flux distributions, which are entered in tables, have been presented for different values of the power-law index n, buoyancy ration B and the exponent λ as well as Lewis number Le. Received on 26 April 2000     

Mixed convection flow over a vertical wedge embedded in a highly porous medium

 The steady mixed convection flow over a vertical wedge with a magnetic field embedded in a porous medium has been investigated. The effects of the permeability of the medium, surface mass transfer and viscous dissipation on the flow and temperature fields have been included in the analysis. The coupled nonlinear partial differential equations governing the flow field have been solved numerically using the Keller box method. The skin friction and heat transfer are found to increase with the parameters characterizing the permeability of the medium, buoyancy force, magnetic field and pressure gradient. However the effect of the permeability and magnetic field on the heat transfer is very small. The heat transfer increases with the Prandtl number, but the skin friction decreases. The buoyancy force which assists the forced convection flow causes an overshoot in the velocity profiles. Both the skin friction and heat transfer increase with suction and the effect of injection is just the reverse. Received on 21 May 1999     

Self-similar solution of the unsteady mixed convection flow in the stagnation point region of a rotating sphere

An analysis is performed to present a new self-similar solution of unsteady mixed convection boundary layer flow in the forward stagnation point region of a rotating sphere where the free stream velocity and the angular velocity of the rotating sphere vary continuously with time. It is shown that a self-similar solution is possible when the free stream velocity varies inversely with time. Both constant wall temperature and constant heat flux conditions have been considered in the present study. The system of ordinary differential equations governing the flow have been solved numerically using an implicit finite difference scheme in combination with a quasilinearization technique. It is observed that the surface shear stresses and the surface heat transfer parameters increase with the acceleration and rotation parameters. For a certain value of the acceleration parameter, the surface shear stress in x-direction vanishes and due to further reduction in the value of the acceleration parameter, reverse flow occurs in the x–component of the velocity profiles. The effect of buoyancy parameter is to increase the surface heat transfer rate for buoyancy assisting flow and to decrease it for buoyancy opposing flow. For a fixed buoyancy force, heating by constant heat flux yields a higher value of surface heat transfer rate than heating by constant wall temperature.     

Special case of a traveling wave in one model of a multicomponent medium

The Kuropatenko model for a multicomponent medium whose components are polytropic gases is considered. It is assumed that, as x → ±∞, the multicomponent medium is in a homogeneous state with constant gas-dynamic parameters — velocity, pressure, and temperature. For the traveling wave flows, conditions similar to the Hugoniot conditions are obtained and used to uniquely determine the flow parameters for x → −∞ from the flow parameters x → +∞ and traveling wave velocity. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 39–47, July–August, 2009.     

Gravity-induced motion of a uniformly heated solid particle in a gaseous medium

The steady motion of a uniformly heated spherical aerosol particle in a viscous gaseous medium is analyzed in the Stokes approximation under the condition that the mean temperature of the particle surface can be substantially different from the ambient temperature. An analytical expression for the drag force and the velocity of gravity-induced motion of the uniformly heated spherical solid particle is derived with allowance for temperature dependences of the gaseous medium density, viscosity, and thermal conductivity. It is numerically demonstrated that heating of the particle surface has a significant effect on the drag and velocity of gravity-induced motion. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 74–80, January–February, 2008.     

New analysis of contact melting of phase change material around a hot sphere

The process of contact melting of the solid phase change material (PCM) around a hot sphere, which is driven by the temperature difference between the PCM and the sphere, is analyzed in this paper. Considering the difference of the normal angle between the sphere surface and the solid–liquid interface of the melting PCM, the fundamental equations of the melting process are derived with the film theory. The new film thickness and pressure distribution inside the liquid film and the variation law of the normal angle of the solid–liquid interface and the melting velocity of the sphere are also obtained. It is found that (1) while normal angle at sphere surface φ is within a certain value φ₀, which is related to Ste number and the outside force F, it has no obvious effect on the pressure distribution inside the liquid film and the numerical results by the present model are in accordance with the analytical results in the published literature, (2) the film thickness at φ = ±90° is constringent to a certain value and not the infinity, (3) the analytical results can be employed approximately to analyze the contact melting process except for the film thickness at φ = ±90°.     

Effect of heat transfer on the plane-channel poiseuille flow of a thermo-viscous fluid

A steady-state plane channel flow of viscous incompressible fluid with no-slip and heat transfer boundary conditions is considered. The flow is induced by a fixed pressure difference and the fluid viscosity depends on the temperature in accordance with a power law. It is shown numerically that the dependence of the Peclet number on the nondimensional pressure difference is not single-valued. An investigation of the solution’s dependence on the Biot number shows that for Biot numbers greater than unity the velocity profile has a point of inflection. Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 75–80, March–April, 2000. The work received financial support from the Russian Foundation for Basic Research (project N97-01-00063).     

Plane strain wave in an isotropic layer of a viscoelastic material

The velocity and the rate of decay of a strain wave in a layer of a viscoelastic material rigidly fixed on a solid foundation are determined. The wave structure (ratio of the longitudinal to the transverse displacement) and the profiles of these displacements are analyzed. Attenuation of waves in the first mode is found to be more significant than that in an infinite space. The most intense decay is observed at resonance frequencies. A strong effect of compressibility of the medium on wave parameters is revealed. Conditions at which such a system operates as a waveguide are found. For a loss tangent higher than 0.13 (for an incompressible medium), the character of the dispersion dependence is observed to change drastically: the wave velocity decreases with decreasing frequency. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 104–111, May–June, 2006.     

Stress waves in a rod subjected to a moving load

The wave processes in a semi-infinite rod located in an elastic medium and subjected to a point load moving at a constant velocity are considered. The system of two differential equations of motion of Timoshenko beam theory is solved using the Laplace transform in time. The integrals obtained are determined numerically. Variation of the bending moment on the longitudinal coordinate behind the elastic-wave front and the region of action of the point force at various times is shown. The results of the solution are influence functions. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 112–122, March–April, 2007.     

Response to Comments on the Article Titled ‘The Starting Flow in Ducts Filled with a Darcy–Brinkman Medium’

The fully developed flow and constant flux heat transfer in super-elliptic ducts filled with a porous (Darcy–Brinkman) medium are studied. Super-elliptic ducts resemble rectangular ducts with rounded corners. An efficient Ritz method is used to determine the velocity and temperature fields. Extensive tables for friction factor–Reynolds number product and Nusselt number are given.