Constructal design of an elliptical cavity into a solid conducting wall

This work reports, according to Bejan’s Constructal theory, the geometric optimization of an elliptical cavity that intrudes into a solid conducting wall. The objective is to minimize the global thermal resistance between the solid and the cavity. There is uniform heat generation on the solid wall. The cavity is isothermal and the solid conducting wall is isolated on the external perimeter. The total volume and the elliptical cavity volume are fixed while the geometry of the cavity is free to vary. The cavity shape is optimal when penetrates the conducting wall completely.