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A mathematical model of diffusion of vaporized interacting metal molecules in a fireproof material is considered. The model is based on microscopic kinetic equations describing the process under condition of a strongly non-homogeneous temperature field. A two-dimensional structure is examined, where the inner hot surface acts as the source of metal vapour and the outer surface - as a cooler. Due to...
The macroscopic equations describing the process of solidification in binary systems are usually introduced via the volume averaging technique. A different approach to obtain these equations, based on the ensemble averaging technique, is proposed in the paper. This technique was used to derive energy and solute conservation equations and the basic constitutive relations appearing in the macroscopic...
Numerical computations of the yttrium distribution in the BaO-CuO melt were performed for the single crystal growth of yttrium barium copper oxide superconductor (YBa_2Cu_3O_(7-x)) with the Czochralski method. The finite volume method was used to calculate the fluid flow, heat transfer and yttrium distribution in the melt with staggered numerical grid. The flow in the melt was assumed to be axisymmetric...
A modified Allen-Cahn equation is combined with the compressible Navier-Stokes system. After a physically motivated modification of the stress tensor, for the resulting equations the second law of thermodynamics is valid. The model can be used to describe the forming of gas phases in a flowing liquid.
Frontal polymerization has been studied for many years experimentally and theoretically. This technique can exhibit a phase change between a liquid monomer and a solid polymer and many studies, both theoretical and experimental, have been devoted to the stability of the front which separates the two phases in the presence of thermal convection. We present here a new technique for the numerical simulation...
This paper provides an analysis of the results of a comparison exercise on the numerical 2D solution of melting from a vertical wall, dominated by natural convection in the liquid phase. The thirteen contributions to this exercise cover the great variety of mathematical models and numerical procedures most commonly used in this field. The main conclusions presented at the AMIF Workshop (PCC99) held...
Finite Element Method (FEM) calculations have been performed to address the problem of the influence of anisotropy of permeability and of thermal conductivity of a mushy region on a temporary flow pattern and temperature during solidification of binary mixtures. Computationally effective FEM algorithm is based on the combination of the projection method, the semi-implicit time marching scheme and...
A finite element model has been developed for the computation of melting/solidifying process under the combined action of buoyancy and surface tension forces. Validated on the square cavity benchmark of Gobin and Le Quéré (Bertrand et al. [1], Gobin and Le Quéré [2]), the numerical model is used to extend this previous analysis to the free surface case where surface tension can drive the flow (capillary...
The spreading of fluid under gravity occurs in both nature and man-made situations and has been the subject of many previous studies. Considerably less attention has been paid to cases in which there is a strong thermal coupling influencing the flow. In this paper, simple models of the spreading of materials with temperature-dependent viscosity are presented and features that are commonly seen in...
In this paper the multiphase diffusion-convection problem is solved numerically by using upwind and characteristic schemes. Discretization for the schemes are performed by finite difference method. For solving the algebraic equations on every time level the modified S.O.R. method is used. In the numerical results computing time, number of iterations and accuracy of the schemes are analysed.
We study a phase-field model for the isothermal solidification of a binary alloy which involves the relative concentration and the order parameter. We prove the existence of weak solutions as well as regularity and uniqueness results under Lipschitz and boundeness assumptions for the nonlinearities. A maximum principle holds that justifies these assumptions. A numerical approximation and some numerical...
A numerical and experimental study is presented of unsteady natural convection during freezing of water in a differentially heated cube shaped cavity. A boundary fitted grid as well as the enthalpy-porosity fixed grid numerical models are used in this study. Both numerical models show very good agreement with the experimental data only for pure convection and initial time of freezing process. As time...
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