Multi-index modeling and optimization of thermal performance of shell-and-tube heat accumulator based on MANOVA

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The heat storage process of composite phase change heat accumulators is a complex phenomenon that requires multiple indicators to comprehensively reflect their thermal performance. Current research in this area is not comprehensive enough. There are also limitations in the evaluation indicators used. In this paper, the multi-index modeling, comprehensive evaluation and optimization methods of the heat storage performance of heat accumulators are studied. First, the basic vectors in the vector set of parameters reflecting the heat storage performance are selected as indicator functions, such as heat storage capacity, heat storage time and heat storage residue. Several independent variables are selected from the three aspects of the geometric parameters of the heat accumulator, the operating conditions, and the rib parameters as factors affecting the thermal storage performance. These multi-index dependent variables and independent variables constitute the multi-index form mathematical model group. Second, multivariate analysis of variance (MANOVA) was used to study the constituent terms of the multi-indicator formal mathematical model group. The MANOVA method was used to identify the effects of each independent variable on the thermal performance of the heat accumulators. The MANOVA method was also used to analyze the effect of the interaction between the factors on the multiple indicators of the thermal performance of the thermal storage. Multivariate nonlinear regression analysis was used to construct the multi-indicator mathematical model group reflecting the thermal storage performance based on MANOVA. Finally, the mathematical model group of multiple indicators is normalized and converted into a group of multiple indicator effectiveness functions, and the group of multiple indicator effectiveness functions is mathematically transformed to construct a comprehensive evaluation function that comprehensively responds to the thermal storage performance and seeks an optimization scheme for the thermal storage performance. The maximum value of its comprehensive index is 0.9988, and the corresponding optimal solutions of independent variables are X1 = 24 mm, X2 = 66.7 mm, X3 = 1600 mm, X4 = 0.2 m/s, X5 = 2 mm, X6 = 6.4 mm, and X7 = 46.8 mm.