Analytical Solution of Heat Exchange in Typical Electrocaloric Devices

Abstract

To date, most of electrocaloric devices reported can be simplified as a multilayer structure in which thermal source and sink are different materials at two ends. The thermal conduction in the multilayer structure is the key for the performance of the devices. In this paper, the analytical solutions for the thermal conduction in a multilayer structure with four layers are introduced. The middle two layers are electrocaloric materials. The analytical solutions are also simplified for a hot/cold plate with two sides being different media—a typical case for thermal treatment of materials. The analytical solutions include series with infinite terms. It is proved that these series are convergent so the sum of a series can be calculated using the first N terms. The equation for calculating the N is introduced. Based on the case study, it is found that the N is usually a small number, mostly less than 40 and rarely more than 100. The issues related to the application of the analytical solutions for the simulation of real electrocaloric devices are discussed, which includes the usage of multilayer ceramic capacitor, influence of electrodes, and characterization of thin film.