Constructal design of non-uniform x-shaped cavity

Abstract

This paper applies constructal design to study a non-uniform X-shaped cavity that penetrates a conductive solid wall. The goal is to minimize the maximal dimensionless excess of temperature between the solid body and cavity. There is a uniform heat generation on the solid body. The total volume and the volume of the cavity are fixed, but the angle formed between the stems of the cavity may vary. The cavity surfaces are isothermal while the solid body has adiabatic conditions in the outer surface. Results indicate that the optimal X-cavity performs 60.1% better than the Cshaped cavity and 44% better than the T-shaped cavity. However, it has a performance approximately 38% inferior than the performance of the optimized H-shaped cavity.