A numerical approach to a very fast thermal transient in an air cooling evaporator

According to some international standards, some products, developed for use under heavy thermal conditions, have to be tested by subjecting them for a short time to a particular heating and cooling thermal stress to allow them an acceptable future operative life. It is possible to obtain these fast thermal gradients in con"ned environments, called climatic chambers where the air is heated by an electrical resistance and is cooled with a "nned evaporator which is linked to a vapour compression system subjected to a particular control system of the refrigerating power. In particular, in this paper the air and object tested thermal transients are studied from an analytical and experimental point of view. The study of the mathematical model is realized assuming simpli"ed hypotheses about the air, the object and the air cooled evaporator temperature. The most complex circumstances are related to a very fast temperature decrease because under this working condition the mathematical model is characterized by a nonlinear di!erential system. The nonlinear term is represented by the refrigerating power that varies in a de"nite range with the evaporator temperature according to a sinusoid trend. For this power a suitable analytical expression, derived by the control system performance and by the compressor characteristic, has been found. The analytical}experimental comparison during a cooling thermal stress of typical products subjected to international standard tests as the electronic boards, has been carried out showing acceptable results. The model presented is useful to foresee the climatic chamber performances in the presence of a speci"c refrigerating power trend; this is the start-point for the design of the vapour compression plant and its control system