Geometric optimization of isothermal cavities according to Bejan’s theory

In this paper we consider the optimization of shape of an isothermal cavity that intrudes into a solid conducting wall. The main objective is the minimization of the global thermal resistance between the solid wall and the cavity, which removes heat from the wall. Two sets of geometries have been considered: T and Y-shaped cavities. The double optimization with reference to the two degrees of freedom D0/D1 and L0/L1 has demonstrated that the global thermal resistance decreases as the volume fraction occupied by the rectangle defined by the ‘stem’ intrusion increases. The geometrical optimization of Y-shaped cavity has been performed by varying the angle between the tributary branch and the horizontal axis, as well as, by varying the ratio between the volume of the fin and the rectangular volume that circumscribes it (ψ), while the other geometric parameters are maintained fixed. For the same values of ψ, it was observed that there was one specific angle α that optimized the heat removal from the conducting solid wall to the cavity. It was also highlighted that the optimal angle is the one that distributes more uniformly the hot spots along the conducting solid wall, in accordance to the Constructal principle of “optimal distribution of imperfections”. Finally, the performance of the Y-shaped cavity proved to be approximately 35% superior to that of the C-shaped cavity under the same geometric and thermal conditions.