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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.
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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
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THERMAL SCIENCE YEAR 2018, VOLUME 22, ISSUE Supplement 1, PAGES [S1 - S6]
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© 2019 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence