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A one-dimensional phase-field model for solidification of a pure material is solved using a numerical approach. Comparisons are made with the solution by an asymptotic approach as well as to solutions of a sharp-interface model. Parameters are varied to examine the impact on the computed solutions, and to determine the parametric range of validity...
Context in source publication
Context 1
... our purposes, if φ = 1, the material is in the liquid phase, if φ = −1, then the material is in the solid phase with φ = 0 on the interface. The parameter, ε, is used to represent the thickness of the interface, as shown in Figure 2. Finally, a free-energy density function, F (φ, u), is introduced to define a double-well potential to describe the solid and liquid phases. ...
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Citations
... A quasi-steady analysis for freezing in different geometries with appropriate boundary conditions is reported by Lin et al. (2003) [5]. Nelson et al. (2005) studied the solidification in a closed domain in the presence of natural convection by combining asymptotic analysis. An ordered parameter is introduced to identify the solid and liquid phases of the material by introducing a value for the ordered parameter for the one-dimensional phase-field model for the solidification process [6]. ...
... Nelson et al. (2005) studied the solidification in a closed domain in the presence of natural convection by combining asymptotic analysis. An ordered parameter is introduced to identify the solid and liquid phases of the material by introducing a value for the ordered parameter for the one-dimensional phase-field model for the solidification process [6]. An analytic solution with quasi-steady approach for temperature distribution reduces the coupled heat and mass transfer processes to a system of ODE and the effect of thermo-physical parameters on the temperature distribution was studied by Mariela Olguin et al. (2008) [7]. ...
Solidification/melting problems are referred as Stephen problems, which are also called as moving boundary problems. This paper studies the extended cubic and exponential approximations to solve the one dimensional Stephan problem in a rectangular encloser. The effect of Stephan number on the temperature distribution, solidification thickness, and the solidification rate in the active solid region are studied. In particular, the solidification model reported in the literature is taken into account. In the final part of the paper, a comparative study on different approximations has been done. The results showed that solidification thickness is more for exponential approximation compared to quadratic and cubic approximations.
