Constructal design of T-shaped cavity cooled by convection

In this paper, we rely on the Constructal method to optimize the geometry of a T-shaped cavity intruded into a conducting solid wall. The cavity is cooled by a steady stream of convection while the solid generates heat uniformly and it is insulated on the external perimeter. The structure has four degrees of freedom: L0/L1 (ratio between the lengths of the stem and bifurcated branches), H1/L1 (ratio between the thickness and length of the bifurcated branches), H0/L0 (ratio between the thickness and length of the stem) and H/L (ratio between the height and length of the conducting solid wall) and one restriction, the ratio between the cavity volume and solid volume (). The purpose of the numerical investigation is to minimize the global thermal resistance between the solid and the cavity. The simulations were performed for the following values of the cavity volume fractions (after having fixed H/L=1):  = 0.05, 0.1, 0.2 and 0.3. The first optimization, referred to the degree of freedom L0/L1, highlighted one “intermediate” optimal shape, i.e., the best geometry was not obtained for the extremes values of L0/L1. As for the degree of freedom H1/L1, the optimal geometries were obtained for lowest ratio of H1/L1. When compared to the C-shaped cavity, the T-shaped cavity performs approximately 45% better under the same thermal and geometric conditions. Finally, it was also observed that all the optimal shapes discovered in the numerical investigation were reached according to the constructal principle of “optimal distribution of imperfections”.