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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Reproducing Kernel Method to Detect the Temperature Distribution for Annular Fins with Temperature-Dependent Thermal Conductivity

Journal of Applied Nonlinear Dynamics 11(2) (2022) 283--295 | DOI:10.5890/JAND.2022.06.002

M. Fardi$^{1}$, J. Tenreiro Machado$^{2}$

$^{1}$ Department of Mathematics, Faculty of Mathematical Science, Shahrekord University, Shahrekord, P. O. Box

115, Iran

$^{2}$ Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, Porto 4249-015, Portugal

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Abstract

The efficiency of convective straight fins with temperature dependent thermal conductivity is determined by means of the reproducing kernel (RK) method. The RK space $W^3 [0,\lambda-1]$ is constructed so that every function satisfies the boundary conditions of the problem. The representation of the exact solution is given in the form of a series and the approximation is obtained by its truncation. The paper (i) derives the error estimates, (ii) proves the convergence and (iii) develops an iterative algorithm for obtaining the solution in the space $W^3 [0,\lambda -1]$. The results obtained by the proposed method are compared with those given by schemes in previous works demonstrating a fast convergence and high precision.

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