Stefan-type Problem Research Articles

An evolutionary continuous casting problem of Stefan type

A simplified model for the solidification of an ingot being cast continuously by withdrawing it from a mould at constant rate is studied via the variational inequalities approach. Existence, uniqueness and regularity results are given for this one-phase Stefan type problem, together with a detailed analysis for the free boundary (the solid-liquid interface) particularly with respect to the asymptotic behavior as time t ↑ ∞ t \uparrow \infty where the steady state is attained.

Thermal model for lithospheric thinning and associated uplift in the neotectonic phase of intraplate orogenic activity and continental rifts

Many regions of recent tectonic activity are characterized by the existence of mantle inhomogeneties which are revealed by various geophysical methods. It is found that the lithosphere beneath the continental rifts and many recent uplifts (high plateaus) is abnormally thin. This thinning of the lithosphere is connected with the process of intensive convective heating. A study of the thermal evolution of the lithosphere, when the convective heat flow is supplied to its base, is performed in the framework of a Stefan's type problem. Solutions are derived giving the relationship between the evolution of the thickness of the lithosphere and the value of the heat flow at the base of the lithosphere at the neotectonic reactivation stage. The results of computations show that the thickness of the lithosphere can be reduced to one half of its initial value in a time interval of an order of several million years when the value of convective heat flow from the anomalous mantle is of an order of 40–100 mW/m 2. Important data on the evolution of the lithosphere can be obtained from the comparative analysis of the composition of volcanic rocks at different stages of continental rifting. It has been found that the source of magmas has a general tendency to migrate to a shallower depth with time. This process suggests successive thinning of the lithosphere. Based on this deduction, we can use these data to evaluate the time dependence of heat flow from the anomalous mantle. The study of this inverse problem leads to the conclusion that the beginning of rifting should be accompanied by a sudden (like a step-function) increase in heat flow supplied by a mantle plume to the base of the lithosphere. The required values of additional heat flow are in the range 55–102 mW/m 2. Vertical crustal movements are caused by a number of physical processes (thermal expansion of the lithosphere, isostatic forces associated with a density inversion at the base of the lithosphere, tension produced by the flow of heated material and finally the regional tectonic stress field). The role of these factors and their interactions in tectonic processes are discussed.

A Stefan-type free boundary problem in a thermal switch

We study a mathematical model of thermal switch in a glass under the Joule heating. We prove the existence of solutions for the free boundary problem related to the model. This problem is a Stefan-type problem with a source depending on the free boundary and the ≪latent heat≫ depending on the history of the free boundary.

Local and global solutions of the Stefan-type problem

Local and global solutions of the Stefan-type problem

The Stefan type problem occurring in the investigation of salt dissolution and transport process in soil

The boundary value problem associated with a parabolic equation whose coefficients become discontinuous from some instant of time along a beforehand unknown sliding line is considered. Such problem defines, for instance, the dissolution and removal of substances from the soil under hydraulic structure foundations, flushing of saliferous soils, etc.

Interaction of a Planar Premixed Flame with a Parallel Adiabatic End Wall

Abstract The unsteady one-dimensional interaction of a planar laminar isobaric flame (propagating at Lewis number unity through a fuel-lean uniform premixture) with a parallel end wall is described. The reaction rate is characterized by large dimensionless Arrhenius activation energy, such that the reaction zone of the flame structure is very thin. Accordingly, the reaction zone is modeled for convenience as a planar interface that is a Dirac-delta-function-type sink for reactants and a source for chemical heat. The result is a tractable Stefan-type problem, in which regions of unsteady convective diffusion are solved subject to suitable continuity conditions holding at a moving boundary (the flame). The increase in flame speed as the wall is approached is quantitatively described. A'systematic program for utilizing this thin-flame formulation for investigation of more general flame/wall interactions in premtxtures, analogous to the adoption of the Burke-Schumann diffusion flame for vigorously burning unp...

Stefan-type problem for sublimation in a porous body

The mathematical formulation of the problem of heat and mass transfer during evaporation from a semiinfinite porous body consisting of parallel capillaries is given. The asymptotic solution of the problem is obtained for large and small time periods.

On the numerical solution of some sets of differential equations for problems of Stefan's type

A STEFAN type problem for certain sets of partial differential equations is considered. A class of homogeneous difference schemes is suggested, and a method for solving the resulting nonlinear difference problem is investigated. A homogeneous difference scheme for solving evolutionary equations with phase variations was discussed in [1, 2]. In the present paper, the results of [1, 2] are extended to certain classes of such equations.

Solution of a Stefan type problem for a a quasilinear parabolic system

Solution of a Stefan type problem for a a quasilinear parabolic system