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International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board: Angheluta-Bauer, Luiza / Chen, Xi / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi / Yang, Xu


IMPACT FACTOR 2017: 1.162

CiteScore 2017: 1.41

SCImago Journal Rank (SJR) 2017: 0.382
Source Normalized Impact per Paper (SNIP) 2017: 0.636

Mathematical Citation Quotient (MCQ) 2017: 0.12

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2191-0294
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Volume 20, Issue 2

Issues

Thermal Analysis of Longitudinal Fin with Temperature-Dependent Properties and Internal heat Generation by a Novel Intelligent Computational Approach Using Optimized Chebyshev Polynomials

Elyas Shivanian
  • Corresponding author
  • Department of Applied Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran
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  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Ramin Kazemi / Mahdi Keshtkar
  • Department of Applied Mathematics, Imam Khomeini International University, Qazvin, 34149-16818, Iran
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2019-01-18 | DOI: https://doi.org/10.1515/ijnsns-2018-0017

Abstract

In this work, heat transfer in a longitudinal rectangular fin with temperature-dependent thermal properties and internal heat generation is studied and more accurate results obtained in respect of the previous investigations. The advanced heat transfer models have been used to study the effects of thermo-geometric parameters, coefficient of heat transfer and thermal conductivity parameters on the temperature distribution, heat transfer and thermal performance of the longitudinal rectangular fin. It is applied a novel intelligent computational approach for searching the solution. In order to achieve this aim, the governing equation is transformed into an equivalent problem whose boundary conditions are such that they are convenient to apply reformed version of Chebyshev polynomials of the first kind. These Chebyshev polynomials based functions construct approximate series solution with unknown weights. The mathematical formulation of optimization problem consists of an unsupervised error which is minimized by tuning weights via interior point method. The trial approximate solution is validated by imposing tolerance constrained into optimization problem.

Keywords: Chebyshev polynomial of the first kind; interior point method; heat transfer analysis; longitudinal fin; temperature-dependent internal heat

MSC 2010: 34B15; 34B60

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About the article

Received: 2018-01-20

Accepted: 2018-12-16

Published Online: 2019-01-18

Published in Print: 2019-04-26


Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 20, Issue 2, Pages 153–166, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339, DOI: https://doi.org/10.1515/ijnsns-2018-0017.

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