Constructal optimization for an insulating wall combining heat flow, strength and volume

Volume is pursued smaller and smaller in engineering fields with various scales. Constructal optimization of a vertical insulating wall is carried out to meet three engineering requirements of heat insulation, mechanical strength and volume simultaneously in this paper. The optimization objective is the thermal resistance per unit volume, the global constraint is the fixed total mass (solid material) of the insulating wall, and the intersection of asymptotes method is employed. The results show that, for the specified number of air gaps, the maximal thermal resistance per unit volume decreases monotonically with the increase of the global Rayleigh number group, and the smaller the global Rayleigh number group, the quicker the decrease of the maximal thermal resistance per unit volume. For the specified global Rayleigh number group, the maximal thermal resistance per unit volume increases monotonically with the increase of the number of air gaps, but the increase of the maximal thermal resistance per unit volume is not obvious in small regions of the global Rayleigh number group. The optimal spacing of the air gap increases slowly with the increase of the number of air gaps. For the engineering case in which the volume of the insulating wall is limited strictly, this paper can provide some theoretical guidelines.