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• The 1D model is in good agreement with the CFD model. • Regenerators perform effectively at high speeds. • Heat transfer mechanisms are enhanced at high speeds. • Expressions for the heat transfer coefficient vs Reynolds number were generated. • The efficiency of the designed Vuilleumier machine increases with the speed. A one-dimensional analytical model and a three-dimensional CFD numerical model were used for the investigation of the effect that the rotational speed has on several thermodynamic quantities and the performance of a Vuilleumier machine. The machine, was designed as a combination of two opposing Stirling engines. The one-dimensional program was based on the energy balance at each control volume in order to calculate the energy flow inside the machine and then losses were added. On the other hand, the CFD model utilized fundamental conservation equations at each of the numerous computational cells which resulted to accurate calculations at every dimension. It was able to provide the heat transfer coefficients inside the heat exchangers that were in turn utilized by the analytical model. The pressure drop was computed directly at each space by the numerical model and with equations for flow losses from the bibliography by the analytical model. Pressure drop increased significantly with the speed. The effectiveness of the regenerators was evaluated by an existing analytical model and resulted to reduce drastically with the drop of speed. The effectiveness plays very important role on the efficiency of the machine. Furthermore, there appears to be a discrepancy between the heat flow in the heat exchangers and the wall-gas temperature difference at high speeds which has to be examined according to the oscillatory nature of the gas flow. Heat transfer coefficients were generated in relationship with the Reynolds number for each speed investigated, yielding less thermal resistance when the speed is high. Finally, the change of heat amounts through the four heat exchangers and change of the efficiency of the Vuilleumier machine with the speed, resulted to be similar with experimental data. [ABSTRACT FROM AUTHOR]