Multi-objective shape optimization of fin using IGA and NSGA-II

Fins are extensively used in combustion chambers, electronic devices, heat exchangers, etc., to improve the heat transfer between a solid surface and the surrounding. There are two ways in which heat can transfer from a fin to its surroundings: conduction and convection. The cross-sectional area of the fin and the temperature gradient determine how much heat is transferred by conduction. Convection heat transfer is influenced by the surface area of the fin and temperature differentials. The performance of fin can be measured by multiple criteria such as efficiency, heat transfer, and effectiveness. Among these, efficiency and heat transfer are more important criteria for fin performance. The fin can have different shapes with respect to chosen criteria. The present study numerically investigates how the shape of the one-dimensional (1D) fin affects heat transfer and efficiency. Multi-objective optimization technique is chosen for getting optimum shape which satisfies both max heat transfer and efficiency. Traditional finite element method (FEM) requires a large number of nodes, to accurately represent the shape of the fin, and this increases the computational time. Isogeometric analysis (IGA), which overcomes this drawback of FEA methods, is used in the present work to solve the fin problem because it can accurately capture the geometry with fewer control points, thereby reducing the computational time. Moreover, another advantage of IGA is that the design, analysis, and optimization models are all consistently defined by NURBS, allowing for easy interaction between the three models and resulting in a smooth boundary. In the present work, a fast and elitist non-dominated sorting genetic algorithm (NSGA-II) is used to determine a set of multiple optimum solutions. Two types of fins are considered: a conical fin and a variable cross-section rectangular fin. The results of the conical fin are reported and compared with the previous literature, and they are found to be in good agreement. The optimization of a variable rectangular fin profile resulted in four distinct Pareto-optimal solutions, balancing maximum efficiency and heat transfer. The Pareto set includes a maximum heat transfer of 22.498 for Shape A and a maximum efficiency of 71% for Shape D.