Group Invariant Solutions and Local Conservation Laws of Heat Conduction Equation Arising Laser Heating Carbon Nanotubes Using Lie Group Analysis

Year 2022, Volume: 10 Issue: 2, 102 - 113, 01.06.2022

Emrullah Yaşar , Yakup Yıldırım

https://doi.org/10.36753/mathenot.926867

Cited By: 1

Abstract

In this study, based on the continuous transformations of Lie groups, the exact analytic solutions of the laser heating carbon nanotubes formulated by using the classical heat conduction equation with various physical properties were constructed. These solutions are the type of group invariant solutions. The constructed solutions have expanded and enriched the solution forms of this new model existing in the literature. With the help of the Maple package program, 3D, density, and contour graphs were drawn for the special values of the parameters in the solutions, and the physical structures of the solutions obtained in this way were also observed. The solutions obtained can be used in the explanation of physical phenomena occurring in cancer investigations.

Keywords

Carbon nano tubes, Lie groups, Group-invariant solutions

Supporting Institution

Bursa Uludag University Scientific Research Project Unit (BAP)

Project Number

KUAP(F)-2019/11

Thanks

This study was supported by the Scientific Research Project Unit (BAP) of Bursa Uludağ University, under project number: KUAP(F)-2019/11. The authors thank Bursa Uludag University.

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