In the paper, a second order thermodynamic analysis of a small scale alpha-type Stirling engine is presented. The developed mathematical model is based on the Finite Time Thermodynamics (FFT) approach and it is derived from the differential time dependent equations of energy and mass conservation. The engine model consists of three spaces: compression, expansion and regenerator. In contrast to available models, the model presented in this paper assumes polytropic processes in the compression and expansion spaces, which corresponds to the non-ideal heat transfer in these spaces. The results, obtained using the developed second order model, were compared with the results obtained using the Computational Fluid Dynamics (CFD) analysis of the same engine. A very good agreement between the second order model and the CFD model was achieved. Finally, the developed model was applied to analyse potential to recover cryogenic exergy of the Liquefied Natural Gas (LNG). The paper presents the results of the dimensional upscaling of the engine and the influence of the average working pressure. It was revealed that increasing the size of the engine or the average working pressure moves the engine to practically unachievable working conditions. (C) 2017 Elsevier Ltd. All rights reserved.