Geometric optimization of shapes on the basis of Bejan's Constructal theory

This paper documents the optimization of architecture in accordance with Bejan's Constructal theory. For illustration, we consider the optimization of a cavity that intrudes into a solid conducting wall, having internal heat generation and adiabatic conditions on the outer surfaces. The cavity is rectangular, with fixed volume and variable aspect ratio, and the solid is trapezoidal. The objective is to minimize the global thermal resistance between the volume of the entire system (cavity and solid) and the surroundings. The performance improves as the cavity becomes slender. The geometry is optimal when the cavity penetrates the conducting wall completely.