# Natural convection porous fin with temperature-dependent thermal conductivity and internal heat generation via optimized Chebyshev polynomials with interior point algorithm

Document Type : Original Paper

Authors

1 Department of Applied Mathematics, Imam Khomeini International University, Qazvin, 34148-96818, Iran

2 Department of Mathematics, Buein Zahra Technical University, Buein Zahra, Qazvin, Iran

3 Department of Mathematics, Marivan Branch, Islamic Azad University, Marivan, Iran.

Abstract

In this study, thermal behaviour analysis of a natural convection porous fin with internal heat generation and temperature dependent thermal conductivity is revisited. The developed symbolic heat transfer models are for the purpose of the investigation of the effects of different parameters on the thermal performance of the porous fin. Regarding the problem formulation, a novel intelligent computational approach is developed for searching the solution. In order to achieve this aim, the governing nonlinear differential 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. Furthermore, the obtained results are more accurate than those reported in previous researches.

Keywords

Main Subjects

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### History

• Receive Date: 15 September 2020
• Revise Date: 16 December 2020
• Accept Date: 28 December 2020