Entropic model and optimization of a refrigeration machine

The refrigeration machines are operating upon various reverse cycles. However, Blanchard, then Goth and Feidt have shown in the 1980s that unlike engines, there is no natural optimum in working fluid temperature, since these temperatures are not bounded in principle. This paper adds complements to the modeling of refrigeration machines on examples of machines derived from the Carnot one, endoreversible or not (model according to Chambadal; model according to Curzon – Ahlborn). The consequences on the machine operation optimization in the presence or absence of additional constraints are reported. The main constraints observed in the literature are (1) imposed refrigeration load, (2) imposed energy consumption, or (3) imposed coefficient of performance (COP). The present work reveals that while Chambadal model does not provide an optimal solution when constraints are not considered, the Curzon-Ahlborn model shows that working fluid temperatures depend on the heat transfer laws at the source and sink, but also on the extensity transfer entropy at the source, ΔS, taken as reference and accounting for the existence of the cycle. The results emphasize an optimal distribution of the physical properties of finite dimensions at the source and sink, as function of ΔS. This new result is the outcome of a sensitivity study. Extensions are under development. (paper)