Geometric Size Optimization of Annular Step Fin Array for Heat Transfer by Natural Convection

Abstract

Although a substantial amount of research is available on annular step fin, only a few works are dedicated to the study of annular step fin array. In the present work, an annular fin array consisting of two-stepped rectangular cross-sectional identical fins is modeled as a multi-objective optimization problem for simultaneously maximizing the total heat transfer rate from the fin array and minimizing the total volume of the fins. Maximization of the surface efficiency and augmentation factor of the fin array are also studied as two additional objective functions for further assessment of the fin array. Considering a constant base temperature and one-dimensional heat flow along the radial direction of the fins, the cross-sectional half-thicknesses and outer radii of the two steps of a fin as well as the total number of fins in the fin array are taken as five design variables. The hybrid spline difference method is used to solve the one-dimensional heat transfer equations and then NSGA-II is applied for approximating the Pareto-optimal fronts for different cases. In order to investigate the influence of various design variables on the objective functions, a Pareto-optimal sensitivity analysis is also carried out. The proposed procedure should aid designers in adopting suitable fin array configurations as per their requirements and practicability.