On the existence, uniqueness, and new analytic approximate solution of the modified error function in two‐phase Stefan problems

2021 ◽  
Author(s):  
Lazhar Bougoffa ◽  
Randolph C. Rach ◽  
Abdelaziz Mennouni
Keyword(s):  
Approximate Solution ◽  
Error Function ◽  
Two Phase ◽  
Stefan Problems

scholarly journals Solving two‐phase freezing Stefan problems: Stability and monotonicity

2019 ◽  
Vol 43 (14) ◽  
pp. 7948-7960
Author(s):  
Miguel A. Piqueras ◽  
Rafael Company ◽  
Lucas Jódar
Keyword(s):  
Two Phase ◽  
Stefan Problems

Exact Solutions of a Class of Two-Phase Stefan Problems in Heterogeneous Cylinders and Spheres

2014 ◽  
Author(s):  
Olawanle P. Layeni ◽  
Olusoji Ilori ◽  
Ebenezer O. B. Ajayi
Keyword(s):  
Difference Equations ◽  
Spherical Symmetry ◽  
Spatial Dimension ◽  
Similarity Solutions ◽  
Suitable Model ◽  
Two Phase ◽  
Stefan Problems ◽  
Temperature Regimes ◽  
Arduous Task ◽  
Cylinders And Spheres

The classical Stefan problem proffers a suitable model for determining the temperature regimes as well as conjugate interfacial positions for multiphase problems. Obtaining the solutions to these problems exactly, especially in systems with cylindrical or spherical symmetry, is often an arduous task. This is largely due to inherent nonlinearities in the mathematical statements of Stefan problems. In this paper, a tractable and effective approach is proposed. Subsequent to a recast as a system of differential-difference equations, and a methodical reduction to constant coefficient difference equations, exact similarity solutions are derived for a class of heterogeneous two-phase Stefan problems with cylindrical or spherical symmetry in one spatial dimension, under either Gaussian or hypergeometric perturbations.

Macroscopic models for melting derived from averaging microscopic Stefan problems I: Simple geometries with kinetic undercooling or surface tension

2000 ◽  
Vol 11 (2) ◽  
pp. 153-169 ◽  
Author(s):  
A. A. LACEY ◽  
L. A. HERRAIZ
Keyword(s):  
Free Boundary ◽  
Multiple Scales ◽  
Two Dimensions ◽  
Macroscopic Model ◽  
Mushy Region ◽  
Free Boundaries ◽  
Two Phase ◽  
Macroscopic Models ◽  
Stefan Problems ◽  
Kinetic Undercooling

A mushy region is assumed to consist of a fine mixture of two distinct phases separated by free boundaries. For simplicity, the fine structure is here taken to be periodic, first in one dimension, and then a lattice of squares in two dimensions. A method of multiple scales is employed, with a classical free-boundary problem being used to model the evolution of the two-phase microstructure. Then a macroscopic model for the mush is obtained by an averaging procedure. The free-boundary temperature is taken to vary according to Gibbs–Thomson and/or kinetic-undercooling effects.

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