In this manuscript, a beta type Stirling engine is numerically modulated. The flow and heat transfer characteristics are finely considered in each engine compartment. The PV diagram is plotted to determine the produced work by the engine. The instantaneous temperature in compression and expansion spaces present a larger variations that recorded in all treated heat exchangers. It is observed that the porous media dumps the oscillations. The temperature evolution is plotted for 100 successive Stirling cycles in order to observe its stability in each Stirling compartments. During the first 10 cycles, the regenerator temperature is influenced by the cold flow pumped by the cooler. It reaches thermal equilibrium after only 10 cycles. From this point, the regenerator temperature undergoes a slight increase to stabilize at 1.05 * Ta.

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