Analytical closed-form model for predicting the power and efficiency of Stirling engines based on a comprehensive numerical model and the genetic programming

• A previous model was modified based non-isothermal heat exchangers.
• The numerical model was validated with experimental data.
• The numerical model was employed to generate data required by GP tool.
• GP tool was used to obtain analytical expressions.
• Accuracy of model and effects of parameters were studied.

High accuracy and simplicity in use are two important required features of thermal models of Stirling engines. A new numerical second-order thermal model was presented through the improvement of our previous modified-PSVL model in order to have an elevated accuracy. The modified-PSVL model was modified by considering a non-isothermal model for heater and cooler. Then, the model called as CPMS-Comprehensive Polytropic Model of Stirling engine, was used to simulate the GPU-3 Stirling engine, and the obtained results were compared with those of the previous thermal models as well as the experimental data. For the sack of the simplicity, the combination of the CPMS model and genetic programming was employed to generate analytical closed-form correlation. In this regards, a comprehensive data bank of results of the CPMS was constructed and exported to the GP tool and analytical expressions of the power, efficiency, and polytropic indexes were obtained. It was shown that the analytical correlations not only had the same accuracy as the CPMS model, but also, it can be simply used without difficulties of numerical models. The CPMS and its out coming analytical expressions, predicted the power and efficiency of the GPU-3 Stirling with +1.13% and +0.45 (as difference), respectively.