Analytical Solution of Heat Exchange in Typical Electrocaloric Devices

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.

On wave propagation and free vibration of piezoelectric sandwich plates with perfect and porous functionally graded substrates

This paper aims to develop analytical solutions for wave propagation and free vibration of perfect and porous functionally graded (FG) plate structures integrated with piezoelectric layers. The effect of porosities, which occur in FG materials, is rarely reported in the literature of smart FG plates but included in the present modeling. The modified rule of mixture is therefore considered for variation of effective material properties within the FG substrate. Based on a four-variable higher-order theory, the electromechanical model of the system is established through the use of Hamilton’s principle, and Maxwell’s equation. This theory drops the need of any shear correction factor, and results in less governing equations compared to the conventional higher-order theories. Analytical solutions are applied to the obtained equations to extract the results for two investigations: (I) the plane wave propagation of infinite smart plates and (II) the free vibration of smart rectangular plates with different boundary conditions. After verifying the model, extensive numerical results are presented. Numerical results demonstrate that the wave characteristics of the system, including wave frequency and phase velocity along with the natural frequencies of its bounded counterpart, are highly influenced by the plate parameters such as power-law index, porosity, and piezoelectric characteristics.

Analytical Solutions of a Class of Fluids Models with the Caputo Fractional Derivative

This paper studies the analytical solutions of the fractional fluid models described by the Caputo derivative. We combine the Fourier sine and the Laplace transforms. We analyze the influence of the order of the Caputo derivative the Prandtl number, the Grashof numbers, and the Casson parameter on the dynamics of the fractional diffusion equation with reaction term and the fractional heat equation. In this paper, we notice that the order of the Caputo fractional derivative plays the retardation effect or the acceleration. The physical interpretations of the influence of the parameters of the model have been proposed. The graphical representations illustrate the main findings of the present paper. This paper contributes to answering the open problem of finding analytical solutions to the fluid models described by the fractional operators.