Mathematical Models and Numerical Solutions of Liquid-Solid and Solid-Liquid Phase Change

Abstract

This paper presents numerical simulations of liquid-solid andsolid-liquid phase change processes using mathematical models inLagrangian and Eulerian descriptions. The mathematical modelsare derived by assuming a smooth interface or transition region between the solid and liquid phases in which the specific heat, density,thermal conductivity, and latent heat of fusion are continuous anddifferentiable functions of temperature. In the derivations of themathematical models we assume the matter to be homogeneous,isotropic, and incompressible in all phases. The change in volumedue to change in density during phase transition is neglected in allmathematical models considered in this paper. This paper describesvarious approaches of deriving mathematical models that incorporate phase transition physics in various ways, hence results in different mathematical models. In the present work we only considerthe following two types of mathematical models: (i) We assume thevelocity field to be zero i.e. no flow assumption, and free boundaries i.e. zero stress field in all phases. Under these assumptionsthe mathematical models reduce to first law of thermodynamics i.e.the energy equation, a nonlinear diffusion equation in temperatureif we assume Fourier heat conduction law relating temperature graNomenclature

Keywords

• liquid-solid, solid-liquid, phase change, Lagrangian, Eulerian, mathematical models, space-time methods, time-marching

Mathematical Models and Numerical Solutions of Liquid-Solid and Solid-Liquid Phase Change

Abstract

Keywords

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References

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