Heat transfer from convecting-radiating n through optimized Chebyshev polynomials with interior point algorithm

Elyas shivanian | Mehdi Keshtkar | Hamidreza Navidi

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URL :   http://research.shahed.ac.ir/WSR/WebPages/Report/PaperView.aspx?PaperID=137201
Date :  2019/12/28
Publish in :    Nonlinear Engineering Modeling and Application
DOI :  https://doi.org/10.1515/nleng-2017-0163
Link :  https://www.degruyter.com/view/j/nleng.2020.9.issue-1/nleng-2017-0163/nleng-2017-0163.xml
Keywords :Chebyshev polynomial of the first kind; Interior point method; Temperature distribution; Fin efficiency; Heat transfer rate

Abstract :

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In this paper, the problem of determining heat transfer from convecting-radiating fin of triangular and concave parabolic shapes is investigated.We consider one-dimensional, steady conduction in the fin and neglect radiative exchange between adjacent fins and between the fin and its primary surface. A novel intelligent computational approach is developed 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. Additionally, heat transfer rate and the fin efficiency are reported.