Constructal Design of Cavities Inserted Into a Cylindrical Solid Body

This paper considers the numerical optimization of the shape of cavities that intrude into a cylindrical solid body. The objective is to minimize the global thermal resistance between the solid body and the cavities. Internal heat generating is distributed uniformly throughout the solid body. The cavities are isothermal, while the solid body has adiabatic conditions on the outer surface. The total volume is fixed. The cavities are rectangular, with fixed volume and variable aspect ratio. The number of cavities of the conducting body, N, is a design parameter. The optimized geometry and performance are reported graphically as functions of the ratio between the volume of the cavities and the total volume, $φ0$⁠, and N. The paper shows an example of the application of optimal distribution of imperfections principle. The results indicate that the optimal distribution of the hot spots is affected not only by the complexity of the configuration (larger N) but also by the area of cavities fraction φ₀.