Shahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-808811120210421Natural convection porous fin with temperature-dependent thermal conductivity
and internal heat generation via optimized Chebyshev polynomials with interior
point algorithmNatural convection porous fin with temperature-dependent thermal conductivity
and internal heat generation via optimized Chebyshev polynomials with interior
point algorithm1091231675010.22055/jamm.2021.35045.1855FAElyasShivanianDepartment of Applied Mathematics, Imam Khomeini International University, Qazvin, 34148-96818, IranMahdiKeshtkarDepartment of Mathematics, Buein Zahra Technical University, Buein Zahra, Qazvin, IranHedayatFatahiDepartment of Mathematics, Marivan Branch, Islamic Azad University, Marivan, Iran.Journal Article20200915In 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.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.https://jamm.scu.ac.ir/article_16750_ee46254ec25b9325fcd244fd40cdc756.pdf