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 [Formula: see text] terms of the series. The formula for calculating the value of [Formula: see text] 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 [Formula: see text] 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 [Formula: see text] 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.
Various designs have been introduced to build heat pumps using the electrocaloric effect (ECE). Each of all the current designs uses at least one moving part, which significantly reduces the reliability of the pump and adds complexities. In this work, a new all-solid design is introduced, in which two layers of an electrocaloric material (ECM) are permanently sandwiched in the source and sink, which would significantly increase the device’s reliability since nothing moves and all are permanently bound together. More importantly, the electric fields applied on two ECM layers are independently controlled. A special sequence for the electric fields on two ECM layers is introduced. Numerical calculation was used to simulate the device’s performance by using the newly introduced analytical solutions for the heat conduction in the system. It is concluded that a continuous heat transformation from the source to sink at the same temperature can be achieved when the contacting coefficient, [Formula: see text], is very small, where [Formula: see text], [Formula: see text], and [Formula: see text] are thermal conductivity, density, and heat capacity, respectively, while the superscript [Formula: see text] and [Formula: see text] represent the ECM and source/sink, respectively.
Most of electrocaloric devices reported so far 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.
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