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When the casting speed of the thin slab continuous caster is increased, the ratios of the solid and liquid phases in the solidification front of the molten steel in the mold change, which affects the thickness of the solidified shell. In order to accurately calculate the thickness of the solidified shell and determine the value range of the mushy zone coefficient suitable for the mathematical model of solidification heat transfer at high casting speed, this paper established the solidification heat transfer mathematical model in thin slab funnel mold, and the influence of different mushy zone coefficients on the accuracy of solidification heat transfer mathematical model was analyzed and compared with the actual solidified shell thickness. The results showed that, when the casting speed was increased to 4~6 m/min and the coefficient of the mush zone coefficient was 3 × 108~9 × 108 kg/(m3⋅s), the thickness of solidified shell calculated by the solidification heat transfer model was in good agreement with that measured in practice. The research in this paper provides an important reference for the establishment of the solidification heat transfer mathematical model at high casting speed in the future. [ABSTRACT FROM AUTHOR]

In this paper, we present a mathematical analysis to a Cahn-Hilliard/Allen-Cahn system with degenerate mobility that models an isothermal process of solidification of a binary alloy. This model is able to predict an observable phenomenon called solute trapping. The existence of global weak solutions for the system is proved. We approximate the degenerate system and show the convergence of solutions to the approximated non-degenerate problem to a solution of the degenerate one. We also investigated deeply the non-degenerate system by showing the existence of global weak solutions, the existence of global strong solutions in the two-dimensional case, and local strong solutions in the three-dimensional case, as well as, providing conditions to the uniqueness be satisfied. [ABSTRACT FROM AUTHOR]

In this paper, an application of the Picard's iterative method for finding the solution of two phase Stefan problem is presented. In the proposed method an iterative connection is formulated, which allows to determine the temperature distribution in considered domain. Another unknown function, describing position of the moving interface, is approximated with the aid of linear combination of some base functions. Coefficients of this combination are determined by minimizing a properly constructed functional. [ABSTRACT FROM AUTHOR]

The paper presents the procedure for solving the inverse problem for the binary alloy solidification in a two-dimensional space. This is a continuation of some previous works of the authors investigating a similar problem but in the one-dimensional domain. Goal of the problem consists in identification of the heat transfer coefficient on boundary of the region and in reconstruction of the temperature distribution inside the considered region in case when the temperature measurements in selected points of the alloy are known. Mathematical model of the problem is based on the heat conduction equation with the substitute thermal capacity and with the liquidus and solidus temperatures varying in dependance on the concentration of the alloy component. For describing this concentration the Scheil model is used. Investigated procedure involves also the parallelized Ant Colony Optimization algorithm applied for minimizing a functional expressing the error of approximate solution. [ABSTRACT FROM AUTHOR]

In this paper we consider a one-dimensional one-phase Stefan problem corresponding to the solidification process of a semi-infinite material with a convective boundary condition at the fixed face. The exact solution of this problem, available recently in the literature, enable us to test the accuracy of the approximate solutions obtained by applying the classical technique of the heat balance integral method and the refined integral method, assuming a quadratic temperature profile in space. We develop variations of these methods which turn out to be optimal in some cases. Throughout this paper, a dimensionless analysis is carried out by using the parameters: Stefan number (Ste) and the generalized Biot number (Bi). In addition it is studied the case when Bi goes to infinity, recovering the approximate solutions when a Dirichlet condition is imposed at the fixed face. Some numerical simulations are provided in order to estimate the errors committed by each approach for the corresponding free boundary and temperature profiles. [ABSTRACT FROM AUTHOR]

The paper is devoted to a model for the procedure of formation of a composite material constituted of solid fibers and of a solidifying matrix. The solidification process for the matrix depends on the temperature and on the degree of cure, which are used for the modeling of the mechanical properties of the matrix. Namely, the mechanical properties are described by Kelvin-Voigt viscoelastic equation with rapidly oscillating periodic coefficients depending on the temperature and the degree of cure. The latter are in turn solutions of a thermo-chemical problem with rapidly varying coefficients. We prove an error estimate for approximation of the viscoelastic problem by the same equation but with the coefficients depending on solution to the homogenized thermo-chemical problem. This estimate, in combination with our recent estimates for the viscoelastic (with time-dependent coefficients) and thermo-chemical homogenization problems, generates the overall error bound for the asymptotic solution to the full coupled thermo-chemo-viscoelastic model. [ABSTRACT FROM AUTHOR]

Continuous casting is a mature, sophisticated technological process, used to produce most of the world's steel, so is worthy of fundamentally‐based computational modeling. It involves many interacting phenomena including heat transfer, solidification, multiphase turbulent flow, clogging, electromagnetic effects, complex interfacial behavior, particle entrapment, thermal‐mechanical distortion, stress, cracks, segregation, and microstructure formation. Furthermore, these phenomena are transient, three‐dimensional, and operate over wide length and time scales. This paper reviews the current state of the art in modeling these phenomena, focusing on practical applications to the formation of defects. It emphasizes model verification and validation of model predictions. The models reviewed range from fast and simple for implementation into online model‐based control systems to sophisticated multiphysics simulations that incorporate many coupled phenomena. Both the accomplishments and remaining challenges are discussed. [ABSTRACT FROM AUTHOR]

The paper presents an approach of numerical modelling of alloy solidification in permanent mold and transient heat transport between the casting and the mold in two-dimensional space. The gap of time-dependent width called "air gap", filled with heat conducting gaseous medium is included in the model. The coefficient of thermal conductivity of the gas filling the space between the casting and the mold is small enough to introduce significant thermal resistance into the heat transport process. The mathematical model of heat transport is based on the partial differential equation of heat conduction written independently for the solidifying region and the mold. Appropriate solidification model based on the latent heat of solidification is also included in the mathematical description. These equations are supplemented by appropriate initial and boundary conditions. The formation process of air gap depends on the thermal deformations of the mold and the casting. The numerical model is based on the finite element method (FEM) with independent spatial discretization of interacting regions. It results in multi-mesh problem because the considered regions are disconnected. [ABSTRACT FROM AUTHOR]

When looking for solutions to nonstationary problems in the field of binary melts or solutions, the scientific community regularly faces the need to transform the classical Stefan‐type approach in order to obtain both new analytical results and explicit solutions. Within the framework of the current paper, we present the analysis of the problem of directional crystallization of binary solutions or melts in the presence of a mushy layer, based on the consideration of field data under the prism of a modified formulation, which made it possible to obtain such characteristics of the behavior of the mushy zone as the thickness and growth rate of the solid phase, temperature distribution, and also to determine heat‐conducting and latent heat flows. The simulation results are presented, including in the form of illustrative material; a good agreement was noted between the predicted values of the growth rates and temperature profiles of the mushy zone and the area of solid matter with the existing observations of young sea ice dynamics. [ABSTRACT FROM AUTHOR]

Paper is devoted to the development of the mathematical model and analysis of the problem of corium melt interaction with low-temperature melting blocks in the passive protection systems against severe accidents at the NPP, which is of high importance for substantiation of the nuclear power safety, for building and successful operating of passive protection systems. In the third-generation reactors passive protection systems against severe accidents at the NPP are mandatory, therefore this paper is of importance for the nuclear power safety. A few configurations for the cooling blocks' distribution have been considered and an analysis of the blocks' melting and corium's cooling in the pool under reactor vessel have been done, which can serve more effective for further improvement of the safety current systems and for the development of new ones. The ways for solution of the problems and the methods for their successful elaboration were discussed. The developed mathematical models and the analysis performed in the paper might be helpful for the design of passive protection systems of the corium melt retention inside the containment after corium melt eruption from the broken reactor vessel. [ABSTRACT FROM AUTHOR]