From the Guest Editors of Part One: ANALYTICAL METHODS TO NON-LINEAR HEAT TRANSFER AND DIFFUSION

Abstract

Exact and approximate analytical solutions of diffusion problems concerning heat or mass are well developed and form a classic literature background for any scholar starting in modelling and simulation [1, 2]. Generally, the analytical solutions simplify or reduce the initial models after scaling and establish general relationships upon imposed constrains. In many cases they are the initial stages of refined numerical methods so we have to take into account the deep physical background of the analytical approaches [3]. We focus the attention on analytical techniques for solution of non-linear problems in diffusion of heat, mass and momentum. The collection conveys strong, reliable, efficient, and promising developments of articles on analytical problems and we will try to present briefly the main results. An approximate solution of one-phase solidification Stefan problem with the unknown time-varying boundary of the region in which the solution is sought is developed in [4]. The method is based on the known formalism of initial expansion of a sought function describing the field of temperature into the power series; the coefficients of the series are determined by solving appropriate differential equations constructed by using the boundary conditions. The solution is compared to a numerical one developed by the boundary element method.

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    References

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    Volume 17, Issue 3, Pages0 -0