THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

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Weihua Cai

,

Wen Chen

,

Fajie Wang

THREE-DIMENSIONAL HAUSDORFF DERIVATIVE DIFFUSION MODEL FOR ISOTROPIC/ANISOTROPIC FRACTAL POROUS MEDIA

ABSTRACT
The anomalous diffusion in fractal isotropic/anisotropic porous media is characterized by the Hausdorff derivative diffusion model with the varying fractal orders representing the fractal structures in different directions. This paper presents a comprehensive understanding of the Hausdorff derivative diffusion model on the basis of the physical interpretation, the Hausdorff fractal distance and the fundamental solution. The concept of the Hausdorff fractal distance is introduced, which converges to the classical Euclidean distance with the varying orders tending to 1. The fundamental solution of the 3-D Hausdorff fractal derivative diffusion equation is proposed on the basis of the Hausdorff fractal distance. With the help of the properties of the Hausdorff derivative, the Huasdorff diffusion model is also found to be a kind of time-space dependent convection-diffusion equation underlying the anomalous diffusion behavior.
KEYWORDS
anomalous diffusion, Hausdorff derivative, Hausdorff fractaldistance, fundamental solution
PAPER SUBMITTED: 2017-06-30
PAPER REVISED: 2017-11-10
PAPER ACCEPTED: 2017-11-17
PUBLISHED ONLINE: 2018-01-07
DOI REFERENCE: https://doi.org/10.2298/TSCI170630265C
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2018, VOLUME 22, ISSUE Supplement 1, PAGES [S1 - S6]
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Three-dimensional Hausdorff derivative diffusion model for isotropic/anisotropic fractal porous media

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