Constructal design for helm-shaped fin with internal heat sources

A helm-shaped fin (HSF) with single and multiple internal heat sources (IHSs) are investigated. Based on constructal theory, the volumes of the HSF and IHS are set as the constraints. The dimensionless maximum thermal resistance (DMTR) of the model is selected as the optimization objective, and its optimal construct is obtained. The results show that for the HSF with single IHS, the dimensionless thickness W̃=0.33 should be avoided in the constructal design of the model to improve its heat transfer performance (HTP). For the HSF with multiple IHSs, the DMTR has its double minimum, and it can be further decreased by increasing the IHS's number n and convective heat transfer parameter a, respectively. The DMTR of the optimal construct with n=4 is decreased by 15.35% than that with n=2. The DMTR of the model with HSF and nonuniform heat generation is decreased by 6.57% compared with that with circular-shaped fin. Moreover, the optimal constructs of the models with uniform and nonuniform heat generations are different, and a more uniform heat generation of the IHS leads to a better HTP of the model with HSF. The results obtained in this paper can provide some theoretical guidelines for the fin designs of real thermal systems.