The expansion of a gas within a piston-cylinder arrangement is studied in order to obtain a better understanding of the heat transfer which occurs during this process. While the situation of heat transfer during the expansion of a gas has received considerable attention, the process is still not very well understood. In particular, the time dependence of heat transfer has not been well studied, with many researchers instead focused on average heat transfer rates. Additionally, many of the proposed models are not in agreement with each other and are usually dependent on experimentally determined coefficients which have been found to vary widely between test geometries and operating conditions. Therefore, the expansion process is analyzed in order to determine a model for the time dependence of heat transfer during the expansion. A model is developed for the transient heat transfer by assuming that the expansion behaves in a polytropic manner. This leads to a heat transfer model written in terms of an unknown polytropic exponent, n. By examining the physical significance of this parameter, it is proposed that the polytropic exponent can be related to a ratio of the time scales associated with the expansion process, such as a characteristic Peclet number.
Experiments are conducted to test the proposed heat transfer model and to establish a relationship for the polytropic exponent. The tests are performed using an apparatus that consists of a single piston-cylinder, which allows for pressure-volume data to be collected during the expansion of a hot gas. These experiments justify the polytropic expansion assumption, and from these results models are developed for the polytropic exponent. Heat transfer data are also collected from these experiments through applying an energy balance on the gas during expansion. These heat transfer data are used to compare the Nusselt number predicted by the proposed model with the experimentally determined Nusselt number. It is found that the proposed model agrees very well with the experimental data, and accurately captures the time dependence of the heat transfer characteristics. The proposed model also accurately handles variations in the heat transfer characteristics due to the different test conditions studied. By capturing the transient effects of heat transfer during the expansion process, the proposed model should be a more accurate tool in determining heat loss during the expansion of a gas than previously developed models
