Heat mass transfer in a turbulent layer above permeable membranes

The temperature and concentration fields in a boundary layer above perforated membranes are presented, and their relationship with the velocity fields given in [1] is established. Measurements of the thermal state of membranes are made with various geometric and thermophysical properties and various coolant drafts. Empirical formulas are also presented for thermal flux and temperature of the permeable walls.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 22–31, July–August, 1973.     

Translation of Walter Noll’s “Derivation of the Fundamental Equations of Continuum Thermodynamics from Statistical Mechanics”

This article represents a translation of the original paper, “Die Herleitung der Grundgleichungen der Thermomechanik der Kontinua aus der Statistischen Mechanik”, which was written by Walter Noll and appeared in the Journal of Rational Mechanics and Analysis 4 (1955), 627–646. In the original paper, Noll addressed and analyzed the seminal paper of Irving & Kirkwood, published five years earlier, on “The statistical mechanical theory of transport processes. IV, The Equations of Hydrodynamics.” Noll gave new interpretations and provided a firm setting for ideas advanced by Irving & Kirkwood that clearly and directly related to the basic principles of continuum mechanics. This translation aims to expose the important contribution of Noll to a wider community of researchers at a time when the atomistic modeling of material behavior is being advanced. Noll’s use of elementary mathematics to discover physical effects, to explain physical concepts, and to draw conclusions of a physical nature is exhibited. Noll’s paper emerged from a report that he presented in a seminar at Indiana University in the summer of 1954. The seminar was organized by Clifford Truesdell, whose inspiration Noll gratefully acknowledged.     

Setvalued Dynamical Systems for Stochastic Evolution Equations Driven by Fractional Noise

We consider Hilbert-valued evolution equations driven by Hölder paths with Hölder index greater than 1/2, which includes the case of fractional noises with Hurst parameters in (1/2,1). The assumptions of the drift term will not be enough to ensure the uniqueness of solutions. Nevertheless, adopting a multivalued setting, we will prove that the set of all solutions corresponding to the same initial condition generates a (multivalued) nonautonomous dynamical system \(\Phi \). Finally, to prove that \(\Phi \) is measurable (and hence a (multivalued) random dynamical system), we need to construct a new metric dynamical system that models the noise with the property that the set space is separable.

     

Asymptotic model of active resonance absorber of acoustic vibrations in a closed region

Novosibirks. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 6, pp. 44–55, November–December, 1994.     

Dynamic analysis of interacting coplanar cracks in a half space with a clamped boundary condition using boundary integral equations

The three-dimensional dynamic problem of coplanar circular cracks in an elastic half-space with a clamped boundary condition is considered. The crack faces are subjected to harmonic loads. The problem is reduced to a system of two-dimensional boundary integral equations of the type of the Helmholtz potential for unknown discontinuities in the displacements of the opposite faces of the cracks. The stress intensity factors at the crack contours are obtained and discussed.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 153–159, January–February, 2005     

On moving heat sources

The two-dimensional thermal problem due to relative motion of a medium and a suddenly activated circular heat source is solved for several boundary conditions. The solutions can be interpreted as for a moving heat source in a stationary medium or a medium moving past a stationary heat source. Uniform and non-uniform temperature, and uniform and non-uniform heat flux boundary conditions are considered. The effect of velocity and radial direction on the temperature distribution is examined. Average, steady-state Nusselt numbers are derived. The transient response of a continuous line source is obtained as a limiting case of the prescribed heat flux solution. Received on 24 September 1996     

Application of Topological Methods to Quasilinear Parabolic Boundary-Value Problems

We apply a topological approach to the investigation of quasilinear parabolic boundary-value problems. The class of problems under investigation is reduced to an operator equation with an operator satisfying condition (S)₊. We establish theorems on solvability and give an example of the application of the approach indicated to the case of second-order parabolic equations.     

Stoßwellen in Gas-Partikel-Gemischen mit Massenaustausch zwischen den Phasen

Zusammenfassung Die Nichtgleichgewichts-Austauschprozesse, die in einem Gas-Partikel-Gemisch hinter einer Stoßwelle ablaufen, werden in dieser Arbeit untersucht. Sie werden sowohl mit den Erhaltungsgleichungen für zwei interaktive Kontinua als auch mit den vereinfachten Gleichungen für Einzelpartikel in einem Gaskontinuum beschrieben. Der besondere Akzent liegt auf den Transportvorgängen sehr kleiner Partikel, die im Übergangsbereich zwischen Kontinuumsbedingungen und freier Molekülströmung stattfinden. Sie werden durch einfache Knudsenzahlansätze berücksichtigt. Beispiele zeigen die Geschwindigkeits-, Temperatur- und Partikelgrößenrelaxation hinter Stoß-wellen in Argon mit DOP-Tröpfchen und mit festen NaCl-Salzpartikeln.

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Shock waves in gas-particle mixtures with mass transfer between the phases

The nonequilibrium transfer processes, which take place in a gas-particle mixture behind shock waves, are investigated in this study. They will be described both by the conservation equations of two interactiv continua and by the simplified equations of a single particle in a gas continuum. The special accent is on exchange processes of very small particles, which take place in the transition regime between continuum and free molecular conditions. They are taken into account by simple Knudsen number corrections. Examples show the velocity, the temperature and the particle size relaxation behind shock waves in argon containing DOP droplets or solid NaCl particles.

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Die Arbeit entstand im Rahmen des Sonderforschungsbereiches SFB 209 Stoff- und Energietransport in Aerosolen der Universität — GH — Duisburg. Die Autoren danken der Deutschen Forschungsgemeinschaft für die finanzielle Unterstützung     

Determination of the stress distribution in assemblies of photoelastic particles

An optical measuring method and a calculation procedure for determining the distribution of the stress tensor in a plane-strained three-dimensional assembly of random-shaped photoelastic particles are described. The stress tensor at an arbitrary point of the model is determined by an integration procedure, based on the equations of equilibrium of stresses. The distribution of the principal-stress direction and the relative principal-stress difference and at least two normal stresses in a plane have to be known to perform the integration. The distribution of the principal-stress directions and their difference are measured optically by scanning the model with an optical filter system with a single rotating polarizer.     

Onset of oscillatory thermocapillary convection in systems with a deformable interface

Oscillatory interfacial instability is investigated with allowance for the deformation of the interface. The possibility of two types of oscillations being excited is established. One of these is similar to the well-known type in systems with a plane interface, while the other is determined by the oscillations of the deformable surface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 11–16, July–August, 1991.