Journal of Applied Nonlinear Dynamics
Reproducing Kernel Method to Detect the
Temperature Distribution for Annular Fins with TemperatureDependent Thermal Conductivity
Journal of Applied Nonlinear Dynamics 11(2) (2022) 283295  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 4249015, 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 $W^3
[0,\lambda1]$ 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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