Ch. Charach

Solidification in a finite, initially overheated slab

Abstract An approximate theory of solidification in a finite, initially overheated slab is developed for small Stefan numbers. One wall of the slab is taken to be insulated and the other is subject to an instantaneous temperature drop below the freezing point. Our approach combines the heat-balance integral method and the time-dependent perturbation theory. The resulting solution is valid uniformly in time. It predicts quantitatively the deviations of the process considered from solidification with no overheating. Simple expressions for the solidification time are derived. The accuracy of the present model is examined by comparing it with various asymptotic solutions.

Thermodynamic Analysis of Latent Heat Storage in a Shell-and-Tube Heat Exchanger

This work addresses the entropy generation aspects of a latent heat storage in which the energy delivered by a hot gas flowing through a cylindrical tube induces melting of the material surrounding the tube. The heat transfer for conduction-dominated melting is analyzed, taking into account the two-dimensional effects. The storage process irreversibilities associated with both the gas flow and the heat transfer (including entropy generation in the melted layer) are considered. The number of entropy generation units, which is a measure of the thermodynamic imperfection of the energy storage process, is expressed as a function of the main design parameters of the system. Analytic bounds and simplified asymptotic expressions for this quantity are derived. The results are compared with earlier one-dimensional studies.

Inhomogeneous mixmaster universes: some exact solutions

Algorithms for generating new exact solutions of the Einstein-Klein-Gordon field equations, which describe inhomogeneous universes with S3 topology of spatial sections, are developed. The known exact vacuum and stiff-fluid solutions with S3 topology are used as an input. The methods developed are further applied to derive inhomogenous generalizations of Bianchi type IX solutions and inhomogeneous S3 Gowdy models with gravitational and scalar waves. It is shown that the new solutions, which are generalizations of the Bianchi type IX models, permit identification of the scalar field with the velocity potential of the stiff irrotational fluid. The latter result is further used to study the growth rate of density perturbations of the isotropic and anisotropic Bianchi type IX universes in a fully nonlinear relativistic regime. The role of anisotropy of the rate of growth of density perturbations is studied in detail.

The Einstein-Rosen gravitational waves and cosmology

This paper reviews recent applications of the Einstein-Rosen type space-times to some problems of modern cosmology. An extensive overview of inhomogeneous universes filled with gravitational waves, classical fields, and relativistic fluids is given. The dynamics of primordial inhomogeneities, such as gravitational and matter waves and shocks, their interactions, and the global evolution of the models considered, is presented in detail.

Inhomogeneous generalization of some Bianchi models

Abstract Vacuum Bianchi models which can be transformed to the Einstein-Rosen metric are considered. The models are used in order to construct new inhomogeneous universes, which are generalizations of Bianchi cosmologies of types III, V and VI h . Recent generalizations of these Bianchi models, considered by Wainwright et al., are also discussed.

Pressure‐temperature effects in planar Stefan problems with density change

An extension of the classical thermal Stefan problem by incorporating the dependence of the phase transition temperature on pressure generated by the flow of the liquid phase due to a density change in the transition process is presented. Two prototypical planar situations are considered. The first is the onset of freezing in an incompressible liquid layer of finite thickness in a gravity field. Asymptotic solutions developed for this problem demonstrate that the initial singularities of the interface velocity and acceleration, typical for the solutions of the classical Stefan problem with an instantaneous temperature drop at the fixed boundary, are regularized by the dynamic pressure effect. The second problem addressed is the freezing or melting of a saturated porous half‐space with a flow governed by the Darcy law. Exact similarity solutions (accounting for compressibility of the fluid in the case of freezing) are developed. They indicate that the pressure dependence of the transition temperature may a...

On entropy generation in phase‐change heat conduction

This paper addresses the entropy production in heat conduction, accompanied by melting/solidification. The expressions for the time derivative of the entropy and the excess entropy production in selected Stefan problems are derived. These physical quantities are shown to be meaningful evolution characteristics for several phase‐change processes that evolve towards equilibrium or self‐similar asymptotic attractors. Prigogine’s theorem of minimal steady‐state entropy production is shown to be invalid for the phase‐change heat conduction.

Thermodynamic design of a phase change thermal storage module

This paper analyzes the irreversibilities due to the heat transfer processes in a latent heat thermal storage system. The Thermal Storage Module (TSM) consists of a cylindrical shell that surrounds an internal coaxial tube. The shell side is filled by a Phase Change Material (PCM); a fluid flows through the inner tube and exchanges heat along the way. The most fundamental assumption underlying this study is that the exergy of the hot fluid stream in the active phase is discharged into the environment and completely destroyed, unless it is partially intercepted by the storage system. A numerical study is conducted to identify and to minimize the thermodynamic losses of the storage and removal processes. The dependence of the second-law efficiency of the system on various design parameters is investigated and discussed.

Perturbative analysis of planar phase change processes with time", dependent temperature at the boundary

The perturbation method developed recently for analysis of planar phase change processes is extended to the case of time‐dependent temperature boundary conditions. Approximate solutions uniformly valid in time are derived. The role of time scales, that of the driving signal and the (time‐dependent) response time of the emerging phase, in the dynamics of a weakly nonlinear melting process is clarified. The short and long time asymptotics are studied in detail. The analytical results are compared with the numerical solution for the problem of melting in a semi‐infinite slab induced by a periodically varying boundary condition.

New perturbation method for planar phase-change processes with time-dependent boundary conditions

A new perturbation method is developed for one‐dimensional and conduction‐controlled melting in a planar slab. The approach is suitable for boundary conditions with small amplitude but almost arbitrary time dependence. The results are uniformly valid in time. The method is applied to the case of time‐dependent heat flux boundary conditions and illustrated by the example of a steplike heat pulse.