Journal ArticleDOI
A Galerkin method for Stefan problems
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TLDR
In this paper, a finite-element method for the solution of a one-dimensional Stefan problem is developed and illustrated using the heat transfer in an ice-water medium, which is in very good agreement with the results produced earlier by several authors.About:
This article is published in Applied Mathematics and Computation.The article was published on 1992-12-01. It has received 23 citations till now. The article focuses on the topics: Stefan problem & Free boundary problem.read more
Citations
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Journal ArticleDOI
Finite difference solution of one-dimensional Stefan problem with periodic boundary conditions
Svetislav Savović,James Caldwell +1 more
TL;DR: In this paper, a finite difference method is used to solve the one-dimensional Stefan problem with periodic Dirichlet boundary condition, and the temperature distribution, position of the moving boundary and its velocity are evaluated.
Journal ArticleDOI
A numerical solution of the Stefan problem with a Neumann-type boundary condition by enthalpy method
Alaattin Esen,S. Kutluay +1 more
TL;DR: The enthalpy method based on suitable finite difference approximations has been applied to the one-dimensional moving boundary problem with a Neumann-type boundary condition known as the Stefan problem and it is shown that all results are found to be in very good agreement with each other.
Journal ArticleDOI
A discussion of modelling idealised ablative materials with particular reference to fire testing
TL;DR: In this paper, a mathematical model of an idealised ablative material of finite thickness, which is mounted horizontally and exposed to a constant, uniform heat flux, is made of a mathematical modeling of the mass loss rate of a material mounted on a real substrate.
Journal ArticleDOI
The iterative transformation method : Numerical solution of one-dimensional parabolic moving boundary problems
TL;DR: In this article, the authors applied the iterative transformation method to the numerical solution of the sequence of free boundary problems obtained from one-dimensional parabolic moving boundary problems via the implicit Euler's method.
Journal ArticleDOI
Nodal Integral and Finite Difference Solution of One-Dimensional Stefan Problem
TL;DR: The nodal integral and finite difference methods are useful in the solution of one-dimensional Stefan problems describing the melting process as mentioned in this paper, however, very few explicit analytical solutions are available in the literature for such problems, particularly with timedependent boundary conditions.
References
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Book
Conduction of Heat in Solids
H. S. Carslaw,John Conrad Jaeger +1 more
TL;DR: In this paper, a classic account describes the known exact solutions of problems of heat flow, with detailed discussion of all the most important boundary value problems, including boundary value maximization.
Book
Free and moving boundary problems
TL;DR: In this paper, a front-tracking method is used to solve moving boundary problems and an analytical solution of seepage problems is proposed. But this method is not suitable for solving free boundary problems.