THERMAL SCIENCE

International Scientific Journal

Xiumei Li

,

Weiwei Ling

,

Wenbo Xiao

,

Zhiliang Zhan

,

Feng Zou

VARIATIONAL PRINCIPLE OF THE 2-D STEADY-STATE CONVECTION-DIFFUSION EQUATION WITH FRACTAL DERIVATIVES

ABSTRACT
The convection-diffusion equation describes a convection and diffusion process, which is the cornerstone of electrochemistry. The process always takes place in a porous medium or on an uneven boundary, and an abnormal diffusion occurs, which will lead to deviations in prediction of the convection-diffusion process. To overcome the problem, a fractal modification is suggested to deal with the “abnormal” problem, and a 2-D steady-state convection-diffusion equation with fractal derivatives in the fractal space is established. Furthermore, its fractal variational principle is obtained by the semi-inverse method. The fractal variational formula can not only provide the conservation law in the fractal space in the form of energy, but also give the possible solution structure of the equation.
KEYWORDS
the convection-diffusion equation, He’s fractal derivatives, two-scale transform, fractal variational formulation
PAPER SUBMITTED: 2022-05-01
PAPER REVISED: 2022-07-20
PAPER ACCEPTED: 2022-07-20
PUBLISHED ONLINE: 2023-06-11
DOI REFERENCE: https://doi.org/10.2298/TSCI2303049L
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2023, VOLUME 27, ISSUE Issue 3, PAGES [2049 - 2055]
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Variational principle of the 2-D steady-state convection-diffusion equation with fractal derivatives

© 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