Solution of the Classical Stefan Problem: Neumann Condition View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2017-07

AUTHORS

V. A. Kot

ABSTRACT

A polynomial solution of the classical one-phase Stefan problem with a Neumann boundary condition is presented. As a result of the multiple integration of the heat-conduction equation, a sequence of identical equalities has been obtained. On the basis of these equalities, solutions were constructed in the form of the second-, third-, fourth-, and fifth-degree polynomials. It is shown by test examples that the approach proposed is highly efficient and that the approximation errors of the solutions in the form of the fourth- and fifth-degree polynomials are negligible small, which allows them to be considered in fact as exact. The polynomial solutions obtained substantially surpass the analogous numerical solutions in the accuracy of determining the position of the moving interphase boundary in a body and are in approximate parity with them in the accuracy of determining the temperature profile in it. More... »

PAGES

889-917

References to SciGraph publications

  • 1979-05. On free boundary problems with arbitrary initial and flux conditions in ZEITSCHRIFT FÜR ANGEWANDTE MATHEMATIK UND PHYSIK
  • 2016-09. Integral Method of Boundary Characteristics in Solving the Stefan Problem: Dirichlet Condition in JOURNAL OF ENGINEERING PHYSICS AND THERMOPHYSICS
  • 2005-09. Exponential numerical methods for one-dimensional one-phase Stefan problems in ARCHIVE OF APPLIED MECHANICS
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    http://scigraph.springernature.com/pub.10.1007/s10891-017-1638-2

    DOI

    http://dx.doi.org/10.1007/s10891-017-1638-2

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1091212384


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