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

Abstract

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.