Stability of convective flows in a rotating liquid layer under various heating conditions

For a rotating liquid layer with boundaries of low thermal conductivity, an amplitude equation is obtained that describes the evolution of secondary convective flows in uniform heating and above a hot spot. The dependence of the coefficients of the amplitude equation on the rotation parameter, Prandtl number, and heat-flux nonuniformity is obtained. The influence of rotation on the stability of nonlinear regimes is analyzed for uniform heating. The boundaries of flow stability are investigated for variously shaped hot spots. Perm'State University, Perm'614600. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika. Vol. 39, No. 1, pp. 69–74, January–February, 1998.     

Conditions in a node of one-dimensional gas flows

Perm' State University, Perm' 614600. Translated from Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 36, No. 4, pp. 98–109, July–August, 1995.     

Model for plasticity effects in metals under nonproportional cyclic loading

A possible physical mechanism for additional hardening is proposed on the basis of an analysis of experiments on nonproportional cyclic loading of metals. A model for an elastoplastic polycrystal with a hardening law taking into account the interaction of slip systems is developed. The effect of additional hardening for elliptic strain paths and the shapes of stress paths and hysteresis loops typical of elliptic strain paths are described qualitatively. A violation of the assumption of the local determinacy and orientations of stress paths is considered for the square strain paths taking place in tests of chromium-nickel austenite stainless steels. Perm' State Technical University, Perm', 614600. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 144–151, November–December, 1999.     

Exact periodic and localized solutions of the equationh t =Δ inh

New exact regular solutions of the nonlinear-diffusion equation are found. Various types of evolution of certain classes of localized initial perturbations are described. We show that, when a localized distribution in the form of a ring is specified, the instantaneous occurrence of the singularity in its center results from the diffusive spreading. Institute of Mechanics of Continua, Ural Division, Russian Academy of Sciences, Perm' 614013. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 22–26, January–February, 1999.     

Vibration and dissipative heating of a layered rectangular viscoelastic prism under harmonic shear loading

The vibration and vibrational heating of a rectangular prism with copper and polyethylene layers is studied by solving numerically a coupled problem of thermoelasticity. The cases of kinematic and mechanical harmonic shear loads on a section of the prism surface are examined. Local heating regions are revealed. They are due to the stress fields in the neighborhood of the points at which the type of boundary conditions changes. The temperature–time curves have preresonance, resonant, and postresonance sections. The heating process reaches a steady thermal state under kinematic loading and may become avalanche-like (which is typical of thermal instability) under mechanical loading Translated from Prikladnaya Mekhanika, Vol. 45, No. 2, pp. 70–78, February 2009.     

Near-resonance highly nonlinear gas oscillations in tubes

Near-resonance highly nonlinear ideal perfect gas oscillations in tubes are studied numerically for boundary conditions of various types. The oscillations are initiated by weak periodic perturbations at one end of the tube. As distinct from earlier studies [1–10], the oscillation amplitudes were not assumed to be small and the entropy increase at the shock waves formed was taken into account. Periodic flow regimes result as a limit of the solution of a Cauchy problem for one-dimensional time-dependent gasdynamic equations. The frequency responses of the oscillations under consideration are determined for boundary conditions of various types. It is shown that in specific cases the attainment of a periodic regime is accompanied by the appearance of long-wave modulations. The “repeated resonance” effect is revealed. This is due to the change in the tube's natural acoustic frequency, which takes place during the heating of the gas in the tube by the shock waves traveling in it. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 150–157, July–August, 1994.     

Convective instability in the presence of volume energy release

The problem of the convective instability of a plane fluid layer bounded by rigid walls with heating in a narrow layer running parallel to the walls inside the volume in question is solved. Instability criteria depending on the location of the heated layer and the Rayleigh numbers of the upper and lower layers are found. The results are compared with those for a plane layer with uniform energy release inside the volume. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 8–15, January–February, 1997. The work was carried out with partial support from the Russian Foundation for Fundamental Research (project No. 95-01-00354a).     

Numerical modeling of the single-phase Stefan problem in a layer with transparent and semitransparent boundaries

Numerical modeling of the single-phase Stefan problem in a semitransparent layer with transparent, nonabsorbing, and partially radiation-absorbing boundaries is performed. It is shown that at low temperatures of the medium, convection is a determining factor on the boundary of the irradiated sample, and at high temperatures, radiation is predominant. The absence of absorption on the boundaries of the layer leads to acceleration of the heating of the plate and considerable deceleration of melting processes. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 84–91, May–June, 2006.     

Thermomechanical dynamic behavior of a disk subject to an impulsive thermal load at the center

The dynamic coupled thermoelastic problem formulation and the thermodynamically consistent theory of inelastic behavior of materials are used to solve an axisymmetric problem for a steel disk subject to a heat pulse at the center. The temperature dependence of the physical and mechanical properties of the disk is taken into account. The problem is solved by the FEM. The evolution in time and features of the strain-stress and thermal states of the disk and the dynamic effects accompanying the processes of heating and gradual cooling are studied __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 5, pp. 45–57, May 2008.     

Contact interaction of a rigid heat-conducting punch with an elastic layer involving nonstationary frictional heating

A mathematical formulation is given and a solution is found to the quasistatic contact problem of thermoelasticity for a rigid heat-conducting punch moving over an elastic layer with fixed base. The interaction is accompanied by heating due to frictional forces obeying Amonton’s law. The problem is reduced to a system of integral equations with time-varying limits of integration. The structure of these equations depends on the type of thermal and physical conditions on the contact surface. An algorithm is proposed for the numerical solution of this kind of equations. The variation in the contact pressure and contact area with time is studied __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 12, pp. 35–46, December 2005.     

Thermo–elasto–plastic stresses in functionally graded materials under consideration of the fabrication process

Summary  The present study analyzes elasto–plastic thermal stresses in some particle-reinforced functionally graded material plates (FGP) by taking into consideration residual stresses of the fabrication process. For the FGP, the region near the cooling metal surface consists of distributed ceramic particles in a metal matrix, while the region near the heating ceramic surface contains distributed metal particles in a ceramic matrix. We use the thermo–elasto–plastic constitutive equation of a particle-reinforced composite, taking into consideration temperature changes and damage as well as the reinforcing effect of particles. Elasto–plastic thermal stresses are discussed here with the goal of reducing the thermal stresses. Two kinds of particle-reinforced FGP are considered: the first kind (FGP1) represents distributed ceramic particles in the metal matrix, and the second one (FGP2) represents distributed metal particles in the ceramic matrix. We modify the thermo–elasto–plastic constitutive equation of a particle-reinforced composite for the FGP2 by taking into consideration temperature changes and damage as well as the reinforcing effect of particles. Using the temperature-dependent material properties, three cases of temperature conditions are studied. The first one is the cooling from the fabrication temperature to the room temperature, the second one is the heating from the room temperature, and the last one is the heating after cooling from the fabrication temperature. The particle volume fraction is assumed to vary according to a power function in the thickness direction of the FGPs. Using the finite element method, the effects of the distribution parameter of the composition on the macroscopic stress, the stress in the matrix and the stress in the particle in the FGPs are discussed. Also, the effects of the particle volume fraction and the fabrication temperature on the maximum tensile matrix stress are discussed. Received 22 November 2000; accepted for publication 24 April 2001     

Resonant vibrations of a clamped viscoelastic rectangular plate

The paper examines the effect of dissipative heating on the performance of a sensor in a viscoelastic rectangular plate undergoing resonant vibrations. The thermoviscoelastic behavior of materials is described using the concept of complex characteristics. The coupling of the electromechanical and thermal fields is taken into account. The nonlinear problem is solved by the Bubnov–Galerkin method. The effect of the mechanical boundary conditions and dissipative-heating temperature on the performance of the sensors is analyzed     

Behaviour of the Fokker–Planck–Boltzmann equation near a Maxwellian

We consider the initial value problem for the Fokker–Planck–Boltzmann equation namely, viewed as the Boltzmann equation with an additional diffusion term in velocity space to describe, for instance, the transport in thermal baths of binary elastic collisional particles. The strong solution for initial data near an absolute Maxwellian is proved to exist globally in time and tends asymptotically in the -norm to another time dependent self-similar Maxwellian in large time. The effect of the diffusion in phase space is investigated. It produces a diffusion process in velocity space and results in a heating process on the macroscopic fluid-dynamic observable, accelerating the convergence of solutions to the equilibrium of a self-similar Maxwellian at a faster time-decay rate than the Boltzmann equation. This phenomena is also observed for homogeneous Fokker–Planck–Boltzmann equations, where the time-decay rate in the -norm to the self-similar Maxwellian is proved to be faster than exponential. Moreover, the Fokker–Planck–Boltzmann equation is shown to converge (under an appropriate scaling) strongly to the Boltzmann equation in the process of the zero diffusion limit.     

Linearized Burnett Equation for the Dynamic Pressure of a Relativistic Gas

The linearized Burnett equation for the dynamic pressure of a relativistic gas of hadrons is calculated from a relativistic kinetic theory. It is shown, as in a previous paper [1], that the coefficient of the term with a non-homogeneous temperature field, – the heating term – is bigger than the one with the divergence of the four-velocity, – the bulk viscosity term.     

Solving initial–boundary-value creep problems

The Galerkin–Bubnov method with global approximations is used to find approximate solutions to initial–boundary-value creep problems. It is shown that this approach allows obtaining solutions available in the literature. The features of how the solutions of initial–boundary-value problems for oneand three-dimensional models are found are analyzed. The approximate solutions found by the Galerkin–Bubnov method with global approximations is shown to be invariant to the form of the equations of the initial–boundary-value problem. It is established that solutions of initial–boundary-value creep problems can be classified according to the form of operators in the mathematical problem formulation     

Transverse vibrations and vibrational heating of a rectangular bimorphous plate of dissipative piezoelectric material

The problem of induced resonance vibrations and dissipation heating in a rectangular bimorphous plate made of a dissipative piezoelectric material under a harmonic potential difference is tackled. The edges of the plate are considered to be hinged and ideally thermally insulated. The dissipation properties of the material are taken into account on the basis of the concept of complex characteristics, which are assumed to be temperature-independent. An exact solution is found for the problem. The critical value of the load parameter is determined when the maximum temperature reaches the Curie point. A finite-element method has been developed for investigating the dynamic behavior and temperature of vibrational heating that bimorphous plates made of a viscoelastic material undergo under a harmonic load. The results obtained for the electromechanical vibrations of plates by finite-element calculations and by an analytical solution are compared. Translated from Prikladnaya Mekhanika, Vol. 35, No. 9, pp. 85–93, September, 1999.     

Convective mass transfer across fluid interfaces in straight angular pores

Steady convective mass transfer to or from fluid interfaces in pores of angular cross-section is theoretically investigated. This situation is relevant to a variety of mass transport process in porous media, including the fate of residual non-aqueous phase liquid ganglia and gas bubbles. The model incorporates the essential physics of capillarity and solute mass transfer by convection and diffusion in corner fluid filaments. The geometry of the corner filaments, characterized by the fluid–fluid contact angle, the corner half-angle and the interface meniscus curvature, is accounted for. Boundary conditions of zero surface shear (‘perfect-slip’) and infinite surface shear (‘no-slip’) at the fluid–fluid interface are considered. The governing equations for laminar flow within the corner filament and convective diffusion to or from the fluid–fluid interface are solved using finite-element methods. Flow computations are verified by comparing the dimensionless resistance factor and hydraulic conductance of corner filaments against recent numerical solutions by Patzek and Kristensen (J. Colloid Interface Sci 236, 305–317 2001). Novel results are obtained for the average effluent concentration as a function of flow geometry and pore-scale Peclet number. These results are correlated to a characteristic corner length and local pore-scale Peclet number using empirical equations appropriate for implementation in pore network models. Finally, a previously published “2D-slit” approximation to the problem at hand is checked and found to be in considerable error.     

Entropy generation in laser heating in relation to machining

Entropy generation during laser evaporative heating of solid substrate in relation to machining is considered and entropy generation rate due to different pulse intensities is computed. Energy method is used when simulating the phase change process and mushy zone formation across solid–liquid and liquid–vapor interfaces are accommodated. Since the heating duration is greater than the electron relaxation time, the Fourier heating model based on the equilibrium transport is employed in the simulations. Entropy generation in the substrate material is formulated during laser heating pulse. It is found that entropy generation rate in the surface region of the substrate material attains high values. Increasing power intensity ratio enhances the total entropy generation rate in a non-linear fashion.     

Transient radiative-conductive heat transfer in a flat layer of a selectively absorbing and radiating medium

Results of a numerical solution of the unsteady boundary-value problem of radiative-conductive heat transfer in a flat layer of a selective nonscattering medium with semitransparent mirrorreflecting boundaries are presented. This problem reduces to a nonlinear integral equation in the unknown temperature with the use of a Green function. The optical properties of the walls are shown to have a strong effect on the formation of a temperature field in the layer. The intensity of heating of the layer depends on the radiative fluxes to a greater extent than on the conductive fluxes. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 1, pp. 105–109. January–February, 1998.     

Resonant vibrations of a hinged viscoelastic rectangular plate

The paper examines the effect of dissipative heating on the performance of a sensor in a hinged thermoviscoelastic rectangular plate undergoing resonant flexural vibrations. The thermoviscoelastic behavior of materials is described using the concept of complex characteristics. The coupling of the electromechanical and thermal fields is taken into account. The nonlinear problem is solved by the variational and Bubnov–Galerkin methods. The effect of the dissipative-heating temperature and the dimensions of the sensor on its performance during resonant vibrations of the plate is analyzed.