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A novel computing method for the fractal paradigm of straight fin energy problem arising in the heat transfer


Fractal theory can explain extremely complicated, self-similar hierarchies and theoretical implementation for physical structures present a challenge resulting from the failure to identify widely and frequently generated physical quantities. The primary goal of this research is to investigate a fractal model of straight convective fins with a constant thermal conductivity that varies with temperature. From the thermo-geometric fin parameter, one can determine the temperature of the fin. A method that has been developed to solve the fractal order energy equation is called the Maclaurin series method (MSM). The applied method is designed for engineers and is straightforward, effective, and efficient. The simulation results are presented in figures for temperature and fin tip temperature. The findings are used in thermal design to investigate straight fins with thermal conductivity both constant and dependent upon temperature. Furthermore, the outcome of the MSM approach is compared to established literature solutions, and an excellent agreement is observed. Nevertheless, its efficiency and usefulness culminate in contrast with the numerical solution.

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This research work was funded by institutional fund projects under no. (IFP-A-2022-2-5-24). Therefore, authors gratefully acknowledge technical and financial support from the ministry of education and University of Hafr Al Batin, Saudi Arabia.


This research work was funded by institutional fund projects under No. (IFP-A-2022–2-5–24).

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YK contributed to formal analysis; YK contributed to investigation; YK contributed to conceptualization; YK contributed to methodology; NF contributed to data curation; YK contributed to writing—original draft: NF contributed to writing—review and editing. All authors have read and agreed to the submitted version of the manuscript.

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Correspondence to Yasir Khan.

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Khan, Y., Faraz, N. A novel computing method for the fractal paradigm of straight fin energy problem arising in the heat transfer. Soft Comput 27, 2269–2277 (2023).

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  • Maclaurin series
  • Fractal calculus
  • Extended surfaces
  • Thermal conductivity
  • Heat transfer