THERMAL SCIENCE

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Ji-Huan He

,

Fei-Yu Ji

TWO-SCALE MATHEMATICS AND FRACTIONAL CALCULUS FOR THERMODYNAMICS

ABSTRACT
A three dimensional problem can be approximated by either a two-dimensional or one-dimensional case, but some information will be lost. To reveal the lost information due to the lower dimensional approach, two-scale mathematics is needed. Generally one scale is established by usage where traditional calculus works, and the other scale is for revealing the lost information where the continuum assumption might be forbidden, and fractional calculus or fractal calculus has to be used. The two-scale transform can approximately convert the fractional calculus into its traditional partner, making the two-scale thermodynamics much promising.
KEYWORDS
continuum mechanics, fractal space, fractal derivative, fractional derivative, scale-dependent law, two-scale thermodynamics
PAPER SUBMITTED: 2019-05-25
PAPER REVISED: 2019-05-25
PAPER ACCEPTED: 2019-05-25
PUBLISHED ONLINE: 2019-09-14
DOI REFERENCE: https://doi.org/10.2298/TSCI1904131H
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Issue 4, PAGES [2131 - 2133]
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Two-scale mathematics and fractional calculus for thermodynamics

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, 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