https://doi.org/10.1140/epjp/s13360-023-04031-z
Regular Article
Unified approach for transient heat transfer in a longitudinal fin with functional grading
1
Faculty of Engineering, Department of Software Engineering, Samsun University, 55080, Samsun, Turkey
2
Faculty of Education, Department of Education of Mathematics and Sciences, Ondokuz Mayıs University, 55139, Samsun, Turkey
3
Faculty of Engineering, Department of Mechanical Engineering, Samsun University, 55080, Samsun, Turkey
Received:
25
January
2023
Accepted:
28
April
2023
Published online:
22
May
2023
A longitudinally finned fin composed of functionally graded materials (FGMs) with a constant cross-sectional area is the subject of this article, which aims to present its transient thermal behaviour. The transient thermal performance of the longitudinally finned fin made of FGMs is investigated assuming the fin has an adiabatic tip. The longitudinal variation in thermal conductivity in the FGM fin properties is adapted into four types of variations, namely linear, quadratic, exponential, and power, and this results in non-uniform and two-point linear boundary value problems that are numerically resolved. These problems are solved using the pseudospectral Chebyshev method. Two characteristics, the traditional fin parameter and the fin's thermal conductivity rating parameter, affect how well a fin transfers heat. Results from the study are shown for selected values of the fin parameter and thermal conductivity rating parameter, including dispersion of temporal temperatures, base heat flux, loss of convectional heat, the fin's energy reserve, and fin effectiveness. The results demonstrate that both transient and steady-state performing of the fin are significantly influenced by the functional grading of the fin materiel. The findings suggest that the pseudospectral Chebyshev method is highly accurate and easy to use, making it a suitable option for solving engineering problems. It can be easily applied to such problems without much difficulty.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
