Design of Cooling Cavities by the Application of the Constructal Design

Abstract

This paper develops a numerical study about the geometry of isothermal cavities in solid bodies with internal heat generation. The solid is constituted of a isotropic material, with low thermal conductivity, and adiabatic external surfaces. The cavity is used to dissipate the internally generated heat. An evolutionary algorithm is proposed, based on Constructal Theory, that builds a cavity able to maximize the heat transfer between the solid body and the ambient. Initial solid geometry (a squared fin) is divided into smaller squared elements (regions) that will be remove in order to build the cavity. First element is removed from the bottom center of the geometry and other elements are, at every step, removed so that minimize the hot spots in the solid domain. At every stage of the building process, thermal diffusion equation is numerically solved by the finite element method (FEM). The cavity construction must be flexible so that it freely progresses (evolves) in direction to the hot spots. Results show that the smaller the elements (resolution) used in the cavity construction the lower will be the maximum temperature. Besides that, present results are compare with similar works for cavities C, H, X e Y, presented in literature, showing that current methodology is very efficient in minimizing maximum solid internal temperature.