Multiobjective constructal optimization of an insulating wall combining heat flow, strength and weight

For a vertical insulating wall, it is pursued in engineering design that taking the three requirements of heat insulation, mechanical strength and weight into account simultaneously, so we further develop the pioneer study of multidisciplinary constructal optimization presented in the previous paper [S. Lorente, A. Bejan, Combined 'flow and strength' geometric optimization: internal structure in a vertical insulating wall with air cavities and prescribed strength, Int. J. Heat Mass Transfer, 2002, 45(16): 3313-3320]. In this paper, thermal resistance per unit mass is introduced as the optimization objective, and a multidisciplinary and multiobjective constructal optimization is carried out based on the maximization of thermal resistance per unit mass with the global constraints, i.e. fixed external dimensions and prescribed mechanical strength. The results show that, the thermal resistance per unit mass of the insulating wall can approach its maximum with the corresponding optimal number of cavity under specified environmental condition (i.e. with specified natural convection effect). The bigger the strength is, the smaller the thermal resistance per unit mass is. For specified strength, the maximum thermal resistance per unit mass is insensitive to the change of the overall Rayleigh number group when the overall Rayleigh number group is much small; and then decreases monotonically with the increase of the overall Rayleigh number group when the overall Rayleigh number group is big, however, its decreasing amplitude decreases gradually. When heat flow, strength and weight are all taken into account, the 3-way optimization and selection (the maximization of thermal resistance per unit mass) of wall architecture requires higher degree of accuracy compared with the 2-way optimization and selection (the maximization of overall thermal resistance). This paper gives out an alternative scheme for the practical design of insulating wall, especially for the application case in which the weight of wall is limited strictly.