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In this paper, comprehensive governing differential equations of Stirling engines have been developed by coupling the effect of gas leakage through the displacer gap, gas leakage into the crank case and the shuttle heat loss into the traditional model. Instantaneous pressures and temperatures of the working fluid in the engine were evaluated at same time step. The present model was deployed for the thermal simulation of the GPU-3 Stirling engine and the obtained results were robustly compared to experimental data as well as results from previous numerical models. Then, parametric studies were conducted to assess the impact of geometrical and operating parameters on the performance of Stirling engines working with helium or hydrogen. Results suggest that the modifications made in this model led to better accuracy and consistency in predicting the experimental data of the prototype engine at all speeds …