Modelling cascaded caloric refrigeration systems that are based on thermal diodes or switches

Solid state cooling based on caloric materials has a large potential, because there is no need for fluid refrigerants. The state of the art system approach relies on a heat transfer fluid, which is pumped back and forth through a regenerator of caloric material. This system approach has fundamental limitations regarding the cycle frequency. Different system approaches are considered. One is the utilization of fast thermal diodes or switches. The aim of this work is to provide a universal model to describe a cooling system based on caloric materials using thermal diodes or switches. The heat capacitance of the caloric material is defined to be constant, allowing a lumped elements representation. An analytical model based on an analogy to an electrical low pass filter is introduced. The analytical model is compared with good agreement to lumped elements simulations and measurement data from the literature. It is shown, that the newly introduced cut-off frequency as merit for the potential cycle frequency is proportional to the heat transfer coefficient of the diodes/switches in flux direction and inverse proportional to the length scale of the caloric material in heat flux direction. Different heat transfer mechanisms are discussed as basis for such thermal diodes and switches in combination with different caloric effects. To increase the cycle frequency compared to state of the art systems, latent heat transfer is a promising candidate for all caloric effects, whereas for example a dry press contact for a magnetocaloric system presents many challenges.