Constructal Design Associated with Genetic Algorithm to Maximize the Performance of H-Shaped Isothermal Cavities

Abstract

The constructal design method associated with the genetic algorithm is used to optimize the geometry of a H-shaped cavity that intrudes into a solid conducting wall. The objective is to minimize the maximum excess temperature between the solid and the cavity. Internal heat generation is distributed uniformly throughout the solid wall. The cavity surface is isothermal, while the solid wall has adiabatic conditions on the outer surface. There are six degrees of freedom which are free to vary. The H-cavity is optimized completely, i.e. it is optimized with respect to all its degrees of freedom. The ratio between the volume of the H-shaped cavity and the total volume (ϕ) is a problem constraint, which is evaluated here. Numerical results show that the optimal H-shaped configuration is the one that distributes better the hot spots in agreement with the optimal imperfections principle. The H-shaped cavity has its worst performance when the ratio between its height and length is set equal to two. The performance improves as this ratio is larger or smaller than two. An important finding is that the dimensionless maximum excess temperature calculated for the best H-shaped cavity with ratio between the height and the length of the cavity equal to 0.1 is approximately only 30% of the maximum excess temperature calculated for the elemental C-shaped cavity under the same thermal conditions.