Multiphysics Simulation of Thermoelectric Systems for Comparison with Experimental Device Performance

Ebling, D.; Jaegle, M.; Bartel, M.; Jacquot, A.; Böttner, H.

doi:10.1007/s11664-009-0825-0

Cited by 89 publications

(47 citation statements)

References 2 publications

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“…These effects describe the direct conversion of the difference in electric potential into a temperature difference within the system (Peltier effect), and vice versa (Seebeck effect). This is typical of thermo-electric cells which could work in two ways: electric generations [1,2] and heat pumps which operate in cool or heat modes [3].…”

Section: Introductionmentioning

confidence: 99%

A coupled electro-thermal Discontinuous Galerkin method

Homsi

Geuzaine

Noels

2017

Journal of Computational Physics

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This paper presents a Discontinuous Galerkin scheme in order to solve the nonlinear elliptic partial differential equations of coupled electro-thermal problems.In this paper we discuss the fundamental equations for the transport of electricity and heat, in terms of macroscopic variables such as temperature and electric potential. A fully coupled nonlinear weak formulation for electro-thermal problems is developed based on continuum mechanics equations expressed in terms of energetically conjugated pair of fluxes and fields gradients. The weak form can thus be formulated as a Discontinuous Galerkin method.The existence and uniqueness of the weak form solution are proved. The numerical properties of the nonlinear elliptic problems i.e., consistency and stability, are demonstrated under specific conditions, i.e. use of high enough stabilization parameter and at least quadratic polynomial approximations. Moreover the prior error estimates in the H 1 -norm and in the L 2 -norm are shown to be optimal in the mesh size with the polynomial approximation degree.

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Section: Introductionmentioning

confidence: 99%

A coupled electro-thermal Discontinuous Galerkin method

Homsi

Geuzaine

Noels

2017

Journal of Computational Physics

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“…The sign of the curvature of the transport properties with respect to temperature has an influence on whether the value of the property at T avg is greater or less than the averaged transport property (Eqs. [6][7][8]. For all other materials studied, the deviation d between the two methods typically increases monotonically with increasing DT.…”

Section: Resultsmentioning

confidence: 99%

“…However, when the temperature gradient is large, and/or one or more of the material properties are strongly temperature-dependent, the central approximation of the abovementioned constant property model is no longer valid. This has motivated the development of a variety of more sophisticated approaches that account for the temperature dependence of material properties, including numerical methods applied to inhomogeneous materials, 6 iterative and finite element techniques, 7,8 and reformulation in terms of reduced variables (thermoelectric compatibility). 9 Calculation of the ''average efficiency'' based on Eq.…”

Section: Introductionmentioning

confidence: 99%

Estimating Energy Conversion Efficiency of Thermoelectric Materials: Constant Property Versus Average Property Models

Armstrong

Boese

Carmichael

et al. 2016

Journal of Elec Materi

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Maximum thermoelectric energy conversion efficiencies are calculated using the conventional ''constant property'' model and the recently proposed ''cumulative/average property'' model (Kim et al. in Proc Natl Acad Sci USA 112:8205, 2015) for 18 high-performance thermoelectric materials. We find that the constant property model generally predicts higher energy conversion efficiency for nearly all materials and temperature differences studied. Although significant deviations are observed in some cases, on average the constant property model predicts an efficiency that is a factor of 1.16 larger than that predicted by the average property model, with even lower deviations for temperature differences typical of energy harvesting applications. Based on our analysis, we conclude that the conventional dimensionless figure of merit ZT obtained from the constant property model, while not applicable for some materials with strongly temperature-dependent thermoelectric properties, remains a simple yet useful metric for initial evaluation and/or comparison of thermoelectric materials, provided the ZT at the average temperature of projected operation, not the peak ZT, is used.

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“…Dynamic thermoelectric elements were implemented into the FEM commercial codes ANSYS and COMSOL in [3], [41], respectively. These implementations did not consider temperature-dependent properties, but included a standard interface element to model heat convection.…”

Section: Thermoelectric Interactionmentioning

confidence: 99%

Multiphysics and Thermodynamic Formulations for Equilibrium and Non-equilibrium Interactions: Non-linear Finite Elements Applied to Multi-coupled Active Materials

Pérez-Aparicio

Palma

Taylor

2015

Arch Computat Methods Eng

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Combining several theories this paper presents a general multiphysics framework applied to the study of coupled and active materials, considering mechanical, electric, magnetic and thermal fields. The framework is based on thermodynamic equilibrium and nonequilibrium interactions, both linked by a two-temperature model.The multi-coupled governing equations are obtained from energy, momentum and entropy balances; the total energy is the sum of thermal, mechanical and electromagnetic parts. The momentum balance considers mechanical plus electromagnetic balances; for the latter the Abraham representation using the Maxwell stress tensor is formulated. This tensor is manipulated to automatically fulfill the angular momentum balance. The entropy balance is formulated using the classical Gibbs equation for equilibrium interactions and non-equilibrium thermodynamics. For the non-linear finite element formulations, this equation requires the transformation of thermoelectric coupling and conductivities into tensorial form.The two-way thermoelastic Biot term introduces damping: thermomechanical, pyromagnetic and pyroelectric converse electromagnetic dynamic interactions. Ponderomotrix and electromagnetic forces are also considered.The governing equations are converted into a variational formulation with the resulting four-field, multicoupled formalism implemented and validated with two custom-made finite elements in the research code FEAP. Standard first-order isoparametric eight-node elements with seven degrees of freedom (dof) per node (three displacements, voltage and magnetic scalar potentials plus two temperatures) are used. Non-linearities and dynamics are solved with Newton-Raphson and Newmark-β algorithms, respectively.Results of thermoelectric, thermoelastic, thermomagnetic, piezoelectric, piezomagnetic, pyroelectric, pyromagnetic and galvanomagnetic interactions are presented, including non-linear dependency on temperature and some second-order interactions.

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Multiphysics Simulation of Thermoelectric Systems for Comparison with Experimental Device Performance

Cited by 89 publications

References 2 publications

A coupled electro-thermal Discontinuous Galerkin method

A coupled electro-thermal Discontinuous Galerkin method

Estimating Energy Conversion Efficiency of Thermoelectric Materials: Constant Property Versus Average Property Models

Multiphysics and Thermodynamic Formulations for Equilibrium and Non-equilibrium Interactions: Non-linear Finite Elements Applied to Multi-coupled Active Materials

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