Combined `flow and strengthʹ geometric optimization: internal structure in a vertical insulating wall with air cavities and prescribed strength

This paper addresses the fundamental problem of optimizing the internal structure of a vertical wall that must meet two requirements, thermal insulation and mechanical strength. The wall is a composite of solid material (e.g., brick) and parallel air caverns with varying thickness and number. It is shown that the internal structure of the wall (the number of air caverns) can be optimized so that the overall thermal resistance of the wall is maximal, while the mechanical stiffness of the wall is fixed. The maximized thermal resistance increases when the effect of natural convection in the air gaps is weaker, and when the specified wall stiffness decreases. The optimal number of air gaps is larger when the effect of natural convection is stronger, and when the specified wall stiffness is smaller. The optimal structure is such that the volume fraction occupied by air spaces decreases when the natural convection effect (the overall Rayleigh number) increases, and when the prescribed wall stiffness increases. The paper draws attention to a new class of thermal design problems, in which the system architecture is derived from a combination of heat transfer and mechanical strength considerations. This class represents an extension of the constructal design method, which until now has been used for maximizing thermofluid performance subject to size constraints.