Constructal design of a cavity cooled by convection

This paper applies constructal design to optimize the geometry of a C-shaped cavity that penetrates into a solid conducting wall. The objective is to minimize the global thermal resistance between the solid and the cavity. There is uniform heat generation on the solid wall. The total volume and the cavity volume are fixed, but the geometric lengths of the C-shaped cavity can vary. The cavity is cooled by convection heat transfer. The results indicate that the shape of C-cavity is optimal when it penetrates the conducting wall almost completely for the external ratio of the solid wall smaller than 2. For external ratio larger than 2 the optimal cavity ratio is the one that presents the largest cavity aspect ratio H0/L0. The results also show that the cavities with small or large external ratios H/L are the ones that present better performance.