Geometric Size Optimization of Annular Step Fin Using Multi-Objective Genetic Algorithm

Although an annular stepped fin can produce better cooling effect in comparison to an annular disk fin, it is yet to be studied in detail. In the present work, one-dimensional heat transfer in a two-stepped rectangular cross-sectional annular fin with constant base temperature and variable thermal conductivity is modeled as a multi-objective optimization problem. Taking cross-sectional half-thicknesses and outer radii of the two fin steps as design variables, an attempt is made to obtain the efficient fin geometry primarily by simultaneously maximizing the heat transfer rate and minimizing the fin volume. For further assessment of the fin performance, three more objective functions are studied, which are minimization of the fin surface area and maximization of the fin efficiency and effectiveness. Evaluating the heat transfer rate through the hybrid spline difference method, the well-known multi-objective genetic algorithm, namely, nondominated sorting genetic algorithm II (NSGA-II), is employed for approximating the Pareto-optimal front containing a set of tradeoff solutions in terms of different combinations of the considered five objective functions. The Pareto-optimal sensitivity is also analyzed for studying the influences of the design variables on the objective functions. As an outcome, it can be concluded that the proposed procedure would give an open choice to designers to lead to a practical stepped fin configuration.