Generalized Stefan models accounting for a discontinuous temperature field

We construct a class of generalized Stefan models able to account for a discontinuous temperature field across a nonmaterial interface. The resulting theory introduces a constitutive scalar interfacial field, denoted by and called the equivalent temperature of the interface. A classical procedure, based on the interfacial dissipation inequality, relates the interfacial energy release to the interfacial mass flux and restricts the equivalent temperature of the interface. We show that previously proposed theories are obtained as particular cases when or or, more generally, when for We study in a particular constitutive framework the solidification of an under-cooled liquid and we are able to give a sufficient condition for the existence of travelling wave solutions.Received: 29 January 2003, Accepted: 18 October 2003, Published online: 3 February 2004PACS: 64.70.Dv, 68.35.Md, 68.35.Rh     

Continuity of the temperature in the two-phase Stefan problem

The classical two-phase Stefan problem, a model for ice-water melting, gives rise to a singular, nonlinear partial differential equation which admits a unique weak solution. Here we prove that this solution, and therefore the temperature in the Stefan problem, are continuous.This work was supported in part by NSF Grant 7406375 A01, by NSF Grant MCS 77-01952, and by the Alfred Sloan Foundation,     

Generalization of the Prandtl problem for a creep model

An approximate solution to the problem of compression of an infinite layer of material between rough parallel plates is constructed with the creep equations being fulfilled. Constitutive relations in accordance with which the equivalent stress tends to a finite value as the equivalent strain rate tends to infinity are used. The behavior of the solution in the neighborhood of the maximum friction surface is studied. It is shown that the existence of the solution depends on one of the parameters included in the constitutive equations. If the solution exists, the equivalent strain rate tends to infinity in the neighborhood of the maximum friction surface, and the asymptotic behavior of the solution depends on the same parameter. It is established that there is a range of this parameter in which the nature of the change in the equivalent strain rate near the maximum friction surface is the same as in the solutions for rigid plastic materials.     

Linearized dynamics for step jumps of velocity and displacement of shearing flows of a simple fluid

We consider linearized dynamics associated with step jumps in the velocity or displacement of the boundary of a fluid in a shearing motion. The discontinuity will propagate into the interior with a speed ( is the density) if the initial valuesG(0) andG(0) of the fading memory kernels are bounded, 0 <G(0) < , – <G (0) < 0. IfG(0) butG(0) = – , then the boundary of the support of the solution still propagates with the speedC. However, the solutions on both sides of the boundary match together in aC -fashion. IfG(0) butG(0) = 0, the amplitude of the discontinuity will not damp as in a purely elastic fluid. IfG(0) = , the step change is felt immediately throughout the fluid, without shocks, as in Navier-Stokes fluids. This same type of parabolic behavior can be achieved by a small Newtonian contribution added to the integral form of the stress but if this contribution is small, a smooth transition layer around the shock will propagate with the speedC. In the case of step displacement, from rest to rest, singular surfaces of infinite velocity can propagate into the interior with speed of propagationC. The singular surfaces undergo multiple reflections off bounding walls, but the final steady state reached asymptotically is in universal form independent of material.     

Generalization of the Bedford-Drumheller model for a fluid-saturated porous medium

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 27, No. 6, pp. 44–53, June, 1991.     

Generalization of the Lorenz model to the two-dimensional convection of second-grade fluids

We apply the truncation of the Navier-Stokes-Fourier equations which leads to the Lorenz model, to the investigation of second-grade fluids. The new set of equations proves to work as an approximated approach to 2D-convective dynamics, under the same restrictions as for Newtonian fluids. The different behaviour depends only on α₁ and consists in a “modified” Prandtl number.     

Using strain gages to measure both strain and temperature

A transducer is proposed that measures both temperature and strain by using two different strain gages. The theoretical basis for designing such a transducer is developed. Experimental results indicate that the temperature signal can be measured satisfactorily. Paper was presented at the 1991 SEM Spring Conference on Experimental Mechanics held in Milwaukee, WI on June 10–13.     

Corrections for velocity and temperature derivatives in turbulent flows

Spectral corrections, which are based on local isotropy, are presented for all the spatial derivatives of velocity and temperature fluctuations which feature in the average dissipations of turbulent energy and temperature. The corrections, which compensate for the spectral attenuation due to the separation between sensors, depend only weakly on the choice of the three-dimensional energy (or temperature) spectrum and therefore on the turbulence Reynolds number. Corrections are also obtained for the variances of velocity and temperature derivatives. The diagonal velocity derivatives require smaller corrections than either the off-diagonal velocity derivatives or the temperature derivatives. Corrections of comparable magnitude are required for the average dissipations of turbulent energy and temperature.     

Relative velocity difference model for the car-following theory

To explore and evaluate the impacts of relative velocity difference (RVD) with memory on the dynamic characteristics and fuel economy of traffic flow in the intelligent transportation environment, we first analyze the linkage between RVD with different-step memory and the following car’s behaviors with the measured car-following (CF) data in cities by using the gray correlation analysis method and then present a RVD model based on the previous CF models in the literatures and calibrate it. Finally, we conduct several numerical simulations in the adaptive cruise control (ACC) strategy to explore how RVD with memory affects car’s velocity fluctuation and fuel consumptions, and find that the RVD model can describe the phase transition of traffic flow and estimate the evolution of traffic congestion, and that considering RVD with memory in modeling CF behaviors and designing the advanced ACC strategy can improve the stability and fuel economy of traffic flow.     

Analyzing methods to allow for the damage of material in thermoviscoelastoplastic deformation

Three methods to allow for damage of isotropic materials are discussed. The relations of the theory of deformation along paths of small curvature are used as equations of state. Rabotnov’s scalar equation is used to study the damage of a material during thermoviscoelastoplastic deformation. The stress determined by a stress rupture criterion that accounts for the stress mode is taken as an equivalent stress. An algorithm based on the finite-element method is developed to solve three-dimensional problems of thermoviscoelastoplasticity with allowance for material damage. The numerical results obtained are compared with experimental data __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 12, pp. 110–121, December 2007.     

Measurements of velocity,temperature and velocity fluctuation distributions in falling liquid films

The velocity, temperature and velocity fluctuation distributions within falling spindle oil films in an inclined rectangular channel were measured using hot-wire techniques and thin thermocouples. The interfacial shear was caused by cocurrent air flow.The results indicate that the liquid films are as a whole much more laminar-like than turbulent in a range of Reynolds numbers (4γ/μ) up to the experimental limit of 6000. Mixing motion occurs in the vicinity of the interface; however, the flow near the wall surface exhibits no sign of such eddy motions, as predicted by the wall law for single phase turbulent flow. Although velocity fluctuation is observed within films with interfacial shear, mean velocity profiles are approximately the same as those obtained by the laminar film prediction.     

Combined CARS/LDA instrument for simultaneous temperature and velocity measurements

The performance of a combined CARS/LDA instrument capable of measuring temperature and two velocity components with a time coincidence of about 4 s is evaluated in a turbulent premixed propane-air Bunsen-burner flame. Measurements near the base of the flame exhibit negative axial correlations, indicative of normal gradient transport; those near the flame tip show strong positive axial correlations, indicative of transport counter to the temperature gradient. The radial correlations are positive both in the reaction zone and in the plume. An analysis of temperature data from measurements made (1) independent of and (2) coincidental with LDA measurements indicates that the CARS/LDA instrument provides a density-weighted velocity, temperature, and velocity temperature correlation due to the density variations in the flame.     

Generalization of the Clausius-Clapeyron equation in a coupled thermomechanical model

Several modifications of the Clausius-Clapeyron equation for deformable media, including solid-phase transformations which depend on the change of additional parameters, are proposed. A model of the medium with tensor concentrations of the components for which the unique Clausius-Clapeyron equation is also valid is proposed. The tensor analog of the transition heat is introduced, and an expression for the total transition heat related to the energies of chemical bonds in the crystal lattice is obtained. At least for slow processes, the fundamental possibility of determining the self transition heat in the experiment is shown analytically. Tomsk State University, Tomsk 634050. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 103–111, November–December, 1999.     

Two dimensional half-space problems for the Broadwell discrete velocity model

Stationary boundary value problems for the Broadwell model in a half-space and in a half-infinite channel are considered. By means of the analogy between the stationary boundary value problems for the Broadwell equations and the initial-boundary value problem of Carleman's system, solutions are found for various situations. Uniqueness and non-uniqueness of solutions is discussed as well. The non-uniqueness problem in the channel leads to the investigation of the initial value problem for Carleman's equation with partly negative initial densities. Some new results for this problem are given. Received January 20, 1996     

Boundary value problems for a model Boltzmann equation with frequency proportional to the molecule velocity

Exact solutions of a model Boltzmann equation with a collision frequency that depends on the molecule velocity and with a BGK (Bhatnagar-Gross-Krook) collision operator are constructed for the problems of weak evaporation and temperature jump in a rarefied vapor above a plane surface. The numerical calculations and a comparison with previous results are given.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 140–153, May–June, 1996.     

Generalization of the Prandtl solution to the case of axisymmetric deformation of materials obeying the double shear model

A semianalytic solution of the problem on the compression of an annular layer of a plastic material obeying the double shear model on a cylindrical mandrel is obtained. The approximate statement of boundary conditions, which cannot be satisfied exactly in the framework of the constructed solution, is based on the same assumptions as the statement of the classical plasticity problem of compression of a material layer between rough plates (Prandtl’s problem). It is assumed that the maximum friction law is satisfied on the inner surface of the layer. The solution is singular near this surface. The strain rate intensity factor is calculated, and its dependence on the process and material parameters is shown.