## THERMAL SCIENCE

International Scientific Journal

### 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**

PAPER SUBMITTED: 2022-09-17

PAPER REVISED: 2022-10-06

PAPER ACCEPTED: 2022-10-12

PUBLISHED ONLINE: 2023-01-07

**THERMAL SCIENCE** YEAR

**2023**, VOLUME

**27**, ISSUE

**Issue 4**, PAGES [2831 - 2837]

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