Time-Dependent Finite-Volume Model of Thermoelectric Devices

Abstract

Thermoelectric modules are an important alternative to heat engines in the harvesting of waste heat. Electrical-thermal analogs are often employed when studying heat conduction and this approach can be extended to develop a model for thermoelectric effects. In this article, the coupled thermoelectric partial differential equations are discretized using the finite-volume method; the discretization respects the coupling between the heat sink and the thermoelectric material. The new model is especially useful when an accurate picture of transients in a thermoelectric device is required. Results from the 1-D finite-volume model are shown to agree with experimental results as well as 3-D simulations using COMSOL.

Time-dependent finite-difference model for transient and steady-state analysis of thermoelectric bulk materials

“…In addition, the model uses several boundary equations to calculate the dynamics at boundaries B and C. Here, P and N thermoelectric materials have separate boundary equations. We employed similar techniques proposed in [15] to develop these boundary equations. All the boundary equations are discretised using the aforementioned differencing schemes.…”

“…The best way to model un-modelled physics is to numerically solve the partial differential equations (PDEs) that describe the thermal and electrical characteristics of thermoelectric materials. So, the third type is the numerical models that have been created in programming platforms using a programming language [14][15][16].…”

“…In this work, a complete formulation and implementation of finite-difference method based thermoelectric model is presented. The model contains the system of PDEs for the typical TE module (figure 1): two heat equations (one for the hot side substrate and the other for the cold side substrate), pair of PDEs for both P and N type thermoelectric materials (one for the heat transport, the other for the electric field), set of boundary equations for boundaries A, B, C, and D. The main advantage of the proposed finite-difference model over the previous implementations [15] is that, in this formulation, electric field and heat transport in both P and N type materials are handled separately, and the temperature dependencies of thermal conductivity, electrical conductivity, and Seebeck coefficient of the P/N materials are addressed directly. PDEs, which are timedependent, are discretised using the finite-difference 'explicit' method, which is particularly well-suited in solving heat-related high-speed dynamic events [17].…”

“…Previous researchers (for e.g. [15]) assumed that the temperature dependent properties such as thermal conductivity, electrical conductivity, and Seebeck coefficient of P and N types of a given bulk material are the same. However, as evident from the material information sheet [20], this is not the case.…”

Thermoelectric cooling for power electronics circuits: Small signal modeling and controller design

“…Because of these two features, the presented TEC analytic circuit model in [8] has been adopted for different purposes, such as steady state and dynamic analysis of TEC system in PCR [6 -7], design evaluation of TEC system for passive heat load [9], temperature control and heat flux measurement by using TEC device as heat flux sensor [10], thermal bilateral control of TEC device for remote palpation [11], frequency response analysis of TEC based temperature and heat inflow control system [12]. Besides the analytic circuit model, Finite Element Analysis (FEA) method has also been used to look at the internal heat distribution and transmission of TEC device in detail [13].…”