Computations of anomalous phase change

Abstract

Purpose

The purpose of this paper is to demonstrate how anomalous diffusion behaviors can be manifest in physically realizable phase change systems.

Design/methodology/approach

In the presence of heterogeneity the exponent in the diffusion time scale can become anomalous, exhibiting values that differ from the expected value of 1/2. Here the author investigates, through directed numerical simulation, the two-dimensional melting of a phase change material (PCM) contained in a pattern of cavities separated by a non-PCM matrix. Under normal circumstances we would expect that the progress of melting F(t) would exhibit the normal diffusion time exponent, i.e., F∼t1/2. The author’s intention is to investigate what features of the PCM cavity pattern might induce anomalous phase change, where the progress of melting has a time exponent different from n=1/2.

Findings

When the PCM cavity pattern has an internal length scale, i.e., when there is a sub-domain pattern which, when reproduced, gives us the full domain pattern, the direct simulation recovers the normal ∼t1/2 phase change behavior. When, however, there is no internal length scale, e.g., the pattern is a truncated fractal, an anomalous super diffusive behavior results with melting going as t n; n > 1/2. By studying a range of related fractal patterns, the author is able to relate the observed sub-diffusive exponent to the cavity pattern’s fractal dimension. The author also shows, how the observed behavior can be modeled with a non-local fractional diffusion treatment and how sub-diffusion phase change behavior (F∼t n; n < 1/2) results when the phase change nature of the materials in the cavity and matrix are inverted.

Research limitations/implications

Although the results clearly demonstrate under what circumstances anomalous phase change behavior can be practically produced, the question of an exact theoretical relationship between the cavity pattern geometry and the observed anomalous time exponent is not known.

Practical implications

The clear role of the influence of heterogeneity on heat flow behavior is illustrated. Suggesting that modeling heat and fluid flow in heterogeneous systems requires careful consideration.

Originality/value

The novel direct simulation of melting in a two-dimensional PCM cavity pattern provides a clear illustration of anomalous behavior in a classic heat and fluid flow system and by extension provides motivation to continue the numerical investigation of anomalous and non-local behaviors and fractional calculus tools.

Citation

Voller, V.R. (2016), "Computations of anomalous phase change", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 26 No. 3/4, pp. 624-638. https://doi.org/10.1108/HFF-08-2015-0326