Multi-objective shape optimization of a longitudinal fin with temperature-dependent properties and internal heat generation using orthogonal collocation and differential evolution

This work studies the multi-objective design of a longitudinal fin. The energy transfer process along the fin is modeled by assuming that heat is dissipated from the surface to the environment through natural convection and radiation, while also accounting for internal heat generation within the fin. In this context, the objective is to determine the optimal fin geometry that maximizes both the heat transfer rate at the base and efficiency. To achieve this, Bezier curves are used to define the control points that characterize the geometry. The Orthogonal Collocation Method is employed to simulate the boundary value problem representing the process of interest. The MODE algorithm is then applied to optimize the fin geometry. The influence of the parameters that characterize the mathematical model, as well as the energy contributions, is also investigated. The results demonstrate that the proposed methodology provides a promising approach for integrating the energy balance. Furthermore, it allows for the selection of a point with a good trade-off between the considered objectives, enabling the enhancement of heat transfer through the optimal fin geometry for each point on the Pareto curve.