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SUBDIFFUSION MODEL WITH TIME-DEPENDENT DIFFUSION COEFFICIENT: INTEGRAL-BALANCE SOLUTION AND ANALYSIS

ABSTRACT
The paper addresses approximate integral-balance approach to a time-fractional diffusion equation of order 0 < μ < 1 with a time-dependent diffusion coefficient of power-law type D(t)=D0tβ where 0 < β < 1. The form of the solution spreading in a semi-infinite medium through an analysis of the second moment of the approximate solution reveals that depending on the sum μ+β the solution can model subdiffusive (μ+β<1), superdiffusive (μ+β>1) or Gaussian (μ+β=1) process of transport. The optimal exponents of the approximate parabolic profiles have been determined by minimization the mean squared error of approximation over the penetration depth.
KEYWORDS
PAPER SUBMITTED: 2016-04-27
PAPER REVISED: 2016-05-30
PAPER ACCEPTED: 2016-06-27
PUBLISHED ONLINE: 2016-10-01
DOI REFERENCE: https://doi.org/10.2298/TSCI160427247H
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE 1, PAGES [69 - 80]
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© 2017 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