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 .Theauthor'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 tn ; 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∼tn ; 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.
|Original language||English (US)|
|Number of pages||15|
|Journal||International Journal of Numerical Methods for Heat and Fluid Flow|
|State||Published - May 3 2016|
Bibliographical noteFunding Information:
The author acknowledges support from the National Science Foundation through Grant EAR- 1318593, Generalized Transport Models in Earth Surface Dynamics. The author is also indebted to Professor Roland Lewis for his continued wise and open leadership in the filed of computational methods for heat and fluid flow.
- Anomolous diffusion
- Fractional derivatives
- Phase change