Electrocaloric devices part I: Analytical solution of one-dimensional transient heat conduction in a multilayer electrocaloric system

Abstract

The analytical solution is reported for one-dimensional (1D) dynamic conduction heat transfer within a multilayer system that is the typical structure of electrocaloric devices. Here, the multilayer structure of typical electrocaloric devices is simplified as four layers in which two layers of electrocaloric materials (ECMs) are sandwiched between two semi-infinite bodies representing the thermal sink and source. The temperature of electrocaloric layers can be instantaneously changed by external electric field to establish the initial temperature profile. The analytical solution includes the temperatures in four bodies as a function of both time and location and heat flux through each of the three interfaces as a function of time. Each of these analytical solutions includes five infinite series. It is proved that each of these series is convergent so that the sum of each series can be calculated using the first N terms of the series. The formula for calculating the value of N is presented so that the simulation of an electrocaloric device, such as the temperature distribution and heat transferred from one body to another can be performed. The value of N is dependent on the thickness of electrocaloric material layers, the time of heat conduction, and thermal properties of the materials used. Based on a case study, it is concluded that the N is mostly less than 20 and barely reaches more than 70. The application of the analytical solutions for the simulation of real electrocaloric devices is discussed.