The Effect of Insulated Cracks on Heat Transfer of Thermoelectric Plates Using Peridynamics

The Effect of Insulated Cracks on Heat Transfer of Thermoelectric Plates Using Peridynamics

Migbar Assefa Zeleke (University of Botswana, Gaborone, Botswana & Hawassa University, Hawassa, Ethiopia), Lai Xin (Wuhan University of Technology, China) and Liu Lisheng (Wuhan University of Technology, China)
DOI: 10.4018/IJMMME.2020100103
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In this article, peridynamic (PD) theory is applied to analyze two-dimensional heat conduction of thermoelectric plate with discontinuities. It is a well-known fact that heat flux is undefined at the crack tip and causes the temperature field across the crack surface discontinuous. Hence, numerical procedures like finite element method (FEM) became unsuccessful to capture details of moving discontinuities like growing cracks. Therefore, this article proposes a PD theory that is appropriate in resolving moving discontinuities in thermal and electric fields. The PD equations were constructed by writing the continuum-based electrical potentials and temperature fields in the form of their respective non-local integrals that are remarkably powerful in solving continuum problems whether the authors have moving discontinuities or not. To elucidate the trustworthiness of the PD theory, the results in the case of stationary cracks are compared with the one from FEM and witnessed that they were in good agreement.
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Nowadays, the great majority of the energy released from any sector lost in the form of heat to the environment. Hence, it is important to improve the overall efficiency and reduce CO2 emissions through thermoelectric convertors. Thermoelectric convertors are solid state devices that can convert waste heat in to electricity and vice versa. Thermoelectric convertors expected to operate in places where extremely high temperature difference exist. This temperature difference leads the device to expand and contract periodically. Such cyclic thermal load creates cracks at the interface that noticeably affect the service life of the convertor which intern exposes the device to high thermal stresses and strains (Rowe, 1995).

In the analysis of thermoelectric convertors, there exists the coupling of heat and electricity. The equations for a coupled thermoelectric system based on the conventional continuum mechanics are well developed (Liu, 2012; Zhang & Wang, 2013). For homogeneous and isotropic thermoelectric materials, the thermoelectric constitutive equations considered the thermal flux which is related to the gradient of temperature and the charge flux which is related to electric potential gradient. Due to limitation in the manufacturing process of thermoelectric materials (TEMs), flaws like scratches, microcracks and other discontinuities are evident. As a result of these discontinuities there will be thermal flux, thermal stress and electric current concentration near the discontinuities and results interruption of operation or failure. Therefore, it is quite imperative to give a considerable attention to the analysis of thermoelectric materials with discontinuities.

Analysis and modeling of thermoelectric materials (TEMs) with defects using the well-established classical theories results an infinite flux at the discontinuities. One of the widely used and multipurpose numerical techniques that solve engineering problems is Finite Element Method (FEM). Though FEM is quite successful and more versatile in solving engineering problems, the modeling and analysis of moving discontinuities is cumbersome and very rigorous since it requires remeshing at every step of crack propagation.

Recently, a class of non-local theory called peridynamic (PD) theory has been introduced by Stewart Silling (2000) that circumvents the restrictions encountered by classical theories. For the last couple of decades this new theory significantly attracted the attention of researchers in the area of science and engineering due to the fact that it doesn’t demand any other criterion to represent and predict the behavior of discontinuities which is mandatory in the case of classical theories (Belytschko & Black, 1999; Belytschko, et al., 2003; Moes, et al., 1999; Areias & Belytschko, 2005).

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