Memetic computing for imprecise solution of T-shaped heat transfer fins

Abstract

In this article, a model of a T-shaped fin, consisting of a set of ordinary differential equations (ODEs), is considered. The purpose of this article is to numerically solve ODE systems of a T-shaped fin (there is no reported exact and analytical solution) using an alternative approach. Utilizing a base approximation function, some mathematical principles and metaheuristics, an approximate solution very close to the existing numerical solution was found. The weighted residual function is used as an objective function along with its constraints, such as boundary and initial values. For the sake of comparison, a generational distance metric is used to evaluate the obtained results compared with the existing results in the literature. The approximate solution found by the applied approach demonstrates its efficiency and performance compared with the existing numerical approach.

KEYWORDS:

• Metaheuristics
• analytical solution
• weighted residual function
• Fourier series
• T-shaped fins

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) [no. 2019R1A2B5B03069810].