Heat distribution analysis of nonlinear fin equation with variable thermal conductivity using group hidden symmetries techniques

Rashed, Ahmed; Mabrouk, Samah M.

doi:10.22034/cmde.2025.64417.2922

Heat distribution analysis of nonlinear fin equation with variable thermal conductivity using group hidden symmetries techniques

Document Type : Research Paper

Authors

Ahmed Rashed ¹
Samah M. Mabrouk ²

¹ 1. Department of Mathematics, Saveetha School of Engineering, Chennai - 602105, Tamilnadu, India. 2. Department of Physics and Engineering Mathematics, Faculty of Engineering, Zagazig University, Egypt. 3. Basic Science department, Faculty of Engineering, Delta University for Science and Technology, 11152, Gamasa, Egypt.

² Department of Physics and Engineering Mathematics, Faculty of Engineering, Zagazig University, Egypt.

10.22034/cmde.2025.64417.2922

Abstract

The Fin equation is an important model describing heat distribution along the Fin surface. In this work, some cases with variable thermal conductivity are considered, underlining the influence of the Fin parameter. We apply the group-theoretical method and hidden-symmetry technique to obtain new closed-form solutions that improve understanding of heat distribution along the Fin surface. It can be seen that the fin geometry causes variation in the Fin parameter. Thermal conductivity of constant, power-law, and exponential types is considered. New solutions involving Kummer and imaginary error functions are obtained. Fin parameter and thermal conductivity are found to have a considerable impact. With increasing value of the Fin parameter, there is an enhancement of heat distribution along the Fin surface, which decreases with time.

Keywords

Main Subjects

Theoretical approximation in context of PDEs

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