In the present study, the design of experiments (DOE) methodology is employed to statistically model and optimize the thermal performance of a forced circulation solar water heating system (FSWHS) with various budget constraints using a small number of simulation trails. The simulation trails are implemented using a model developed in TRNSYS 17 software, and climate conditions of Cairo, Egypt. A sequential approach is used to obtain the optimum system configuration with respect to the budget constraint. The definitive screening design is first utilized to eliminate the insignificant factors and investigate the effect of the quadratic terms. Then, the Box-Behnken design (BBD) is used for developing mathematical models based on multiple regression analysis. Finally, the optimization problem is formulated and solved using the desirability function. The developed mathematical models for the thermal performance responses showed a good agreement with the results obtained in TRNSYS for various budget constraints. This agreement proved the ability of the mathematical models to predict the performance of FSWHS precisely. Furthermore, the optimization methodology can be applied for various types of solar water heating systems, and different renewable energy applications.

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