Constructal optimization of a vertical insulating wall based on a complex objective combining heat flow and strength

For a vertical insulating wall, a product function of heat flow and strength with power weight is introduced as the complex optimization objective to compromise between insulating performance and mechanical performance. Under the global constraints of fixed external dimensions and safety requirements, the constructal optimization of the wall is carried out by taking the complex function maximization as the objective. It is shown that the maximum of the complex-objective function and its corresponding optimal internal structure design under a certain environmental condition can be obtained by allowing the internal structure of the wall to vary (evolve) freely. The validity, effectivity and applicability of the complex function are proved by the results and the power weight parameter in the range from 0.4 to 4 can compromise between the requirements of insulating and strength simultaneously and preferably. The constructal optimization with coequal attention to heat flow and strength and the corresponding results are discussed in detail. The optimal structure design and the corresponding performance analyses under various environmental conditions of application are presented. When the change of environment is greater and the total Rayleigh number is bigger, the insulating wall with large number of cavities should be employed. When the total Rayleigh number is small, the better performance can be obtained by reasonably employing the insulating wall with small number of cavities. The complex function has better self-adaptability, and the results in the recent literature are special cases of this paper.

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