THERMAL SCIENCE

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Kang-Jia Wang

,

Feng Shi

A NEW FRACTAL MODEL OF THE CONVECTIVE-RADIATIVE FINS WITH TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY

ABSTRACT
In this paper, the convective-radiative fins of rectangular profile with temperature-dependent thermal conductivity are considered. By studying the conventional heat transfer equation, its modified fractal form, which can describe the problem in the porous medium, is presented based on He’s fractal derivative for the first time. The fractal two-scale transform method together with the Taylor series are applied to deal with fractal model, and an analytical approximate solution is obtained. The impact of the different fractal orders on the thermal behavior of the fins is also elaborated in detail. In addition, a comparison between our solution and the existing one is given to prove the correctness of the proposed method, which shows that the proposed method is easy but effective, and are expected to shed a bright light on practical applications of fractal calculus.
KEYWORDS
He’s fractal derivative, porous medium, Fractal two-scale transform method, Taylor series
PAPER SUBMITTED: 2022-09-17
PAPER REVISED: 2022-10-06
PAPER ACCEPTED: 2022-10-12
PUBLISHED ONLINE: 2023-01-07
DOI REFERENCE: https://doi.org/10.2298/TSCI220917207W
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2023, VOLUME 27, ISSUE Issue 4, PAGES [2831 - 2837]
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A new fractal model of the convective-radiative fins with temperature-dependent thermal conductivity

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