To study the hyperbolic annular fin with temperature dependent thermal conductivity via optimized Chebyshev polynomials with interior point algorithm

Abstract

In this paper, the problem of an annular fin of hyperbolic profile with temperature dependent thermal conductivity is discussed. 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. Furthermore, a more accurate discussion of the effect of fin dimensions, surface convection characteristics and the thermal conductivity parameter on the thermal performance of the fin is graphically presented.