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In many engineering applications one can find periodically variable gas temperatures. Possible examples include the temperature inside the cylinders of Stirling Engines and other reciprocating machines. New methods are proposed and evaluated for the measurement of periodically varying temperature by thermocouples. A Computational Fluid Dynamics model is created to assess the method viability and efficacy in a realistic setting while avoiding measurement errors. The first method is based on matrix analysis, the two others on the particle filter algorithm used to estimate either the heat transfer coefficients with the additional use of other flow information, or to estimate the thermocouple constants without said information. It is shown that the matrix method is sufficient for cases with constant velocities. For variable velocities, the PF algorithm shows promising results as based on measurements generated from the numerical simulation. • Periodic gas temperature measurement is treated as an inverse heat transfer problem. • Two-thermocouple mechanistic solutions are generalized into an overdetermined system. • Application of 'Particle filter', utilizing other heat transfer information. • Methods are tested using CFD generated measurement data. • Particle Filter provides a high quality reconstruction of the actual temperature. [ABSTRACT FROM AUTHOR]

• A zero dimensional model of an α type Stirling engine is created and explained. • Heat transfer models for internal convection in the engine are compared. • Those correlations are implemented in the model and the results are shown. • It is found the models produce starkly different results. In the paper the authors present a zero-dimensional model of an alpha type Stirling engine and special consideration is paid to the problems of the evaluation of internal heat transfer between the heat exchange surfaces and the working fluid. Furthermore, a thermodynamic model of the engine, developed by the authors is shown. The model can be classified as zero-dimensional. Energy and mass conservation equations are written in a differential form, and solved for finite time steps for control volumes, that is the expansion cylinder, the compression cylinder, the regenerator, the regenerator matrix and the engine as a whole, which allows to transform the differential equations into a solvable system of algebraic equations. Unlike most models shown in literature, the one created by the authors evaluates the gas properties based on a real gas model. The impl ementation of a real gas model further helps to evaluate parameters such as viscosity and thermal conductivity of the gas, which is necessary for calculating the heat transfer coefficients. Those are calculated for each volume from known correlations, for a given moment in time. That is, the gas parameters needed are not evaluated as an average for the stroke, rather, they are calculated from instantaneous gas parameters and implemented as variables in the energy equations. The engine working fluid is atmospheric air. The influence of different heat transfer models on the predicted engine performance is shown in the form of engine characteristics for different models, based on variables such as pressure, and rotational. It can be shown, that further research into in-cylinder heat transfer is necessary, as the established models, when implemented into the Stirling engine, predict starkly different engine performance. Furthermore, non-physical results based on those models are shown. [ABSTRACT FROM AUTHOR]