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

Heat transfer from convecting-radiating fin through optimized Chebyshev polynomials with interior... AbstractIn 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Engineering de Gruyter

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

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Publisher
de Gruyter
Copyright
© 2020 E. Shivanian et al., published by De Gruyter
ISSN
2192-8029
eISSN
2192-8029
DOI
10.1515/nleng-2017-0163
Publisher site
See Article on Publisher Site

Abstract

AbstractIn 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.

Journal

Nonlinear Engineering – de Gruyter

Published: Nov 7, 2019

References

  • New formulae for higher order derivatives and applications