Minimizing hot spot temperature of porous stackings in natural convection

Due to their large surface of heat transfer per volume, porous structures such as metallic foams are considered as an interesting alternative to fins. In this paper, we investigate the optimal configuration of a porous medium structure with the objective to minimize the hot spot temperature in natural convection. The heat sink is adjacent to a heat-generating plate, and consists of a stacking of porous layers, in which a cooling fluid circulates strictly driven by natural convection. The objective of this work is to minimize the hot spot temperature of the system. The design variables are the porosity and the material of each layer. The thermal performance is evaluated with a CFD code based on a finite volume approach. The hot spot temperature minimization is pursued with a genetic algorithm (GA) under global mass and cost constraints. The GA determines the optimal porosity and selects the most appropriate material of each layer. Furthermore, the optimal total length of the stacking is indirectly determined by the GA as layers can be added or removed in order to improve the global performance and/or satisfy the constraints. A mapping of the designs generated by the GA as a function of the mass and cost constraint combination reveals that an appropriate distribution of porosity and material benefits the overall thermal performance of the layered porous medium.