Geometric optimization of highly conductive inserts with variable thickness embedded in a fin

In the present study, it is proposed to reduce the thermal resistance of a straight fin by embedding highly conductive routes with variant thickness into a fin. Due to economic constraints, only a limited fraction of fin's volume can be devoted to these materials. Therefore, in this research, an optimal geometric structure for the inserts is presented. The purpose of optimization is to maximize the heat transfer from the fin by increasing the degrees of the freedom-to-morph under the constraint of the fixed volume fraction of the inserts. The geometric structure of conductive materials is presented by distributing the inserts with variable thicknesses or a linear distribution. The effects of several parameters such as the aspect ratio of the fin, Biot number, the volume fraction of highly conductive materials and the thermal conductivity ratio on the optimization results are presented in details. It is shown that the increment in the number of insert branches with different thinness results in higher heat transfer. It is also indicated that the linear distribution performs the best.