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1D modelling of thermogenerator elements with linear material profiles

Zabrocki, Knud and Müller, Eckhard and Seifert, Wolfgang (2009) 1D modelling of thermogenerator elements with linear material profiles. 28th International / 7th European Conference on Thermoelectrics, 26.-30. Juli 2009, Freiburg.

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Abstract

Graded and segmented thermoelectric elements have been studied for a long time with the aim of improving the performance of thermogenerators that are exposed to a large temperature difference. However, it has been shown that simply adjusting maximum figure of merit Z T in each segment of a stacked or graded thermoelectric (TE) element is not a sufficient rule to maximize thermoelectric device performance. Global optimization of a performance parameter is commonly based on a one-dimensional continua-theoretical model. Following the proposal by Müller et al., the temperature profile T(x) can be calculated within a model-free setup directly from the 1D thermal energy balance e. g. based on continuous monotonous gradient functions for all material profiles, and independent and free variability of the material parameters S(x), sigma(x) and kappa(x) is assumed primarily, where S is the Seebeck coefficient, sigma and kappa are the electrical and thermal conductivities, respectively. Thus the optimum current density can be determined from the maximum of the global performance parameter. This has been done up to now by means of numerical procedures as a 1D thermoelectric finite element method code (1D TE FEM) or the algorithm of multi-segmented elements. Here, an analytical solution of the 1D thermal energy balance has been found for constant gradients based on Bessel functions. For a constant electric conductivity but linear profiles S(x) and kappa(x), the authors present first results for the electrical power output of a thermogenerator.

Document Type:Conference or Workshop Item (Speech)
Title:1D modelling of thermogenerator elements with linear material profiles
Authors:
AuthorsInstitution or Email of Authors
Zabrocki, KnudInstitute of Physics, Martin Luther University Halle-Wittenberg, Germany
Müller, EckhardGerman Aerospace Center, Institute of Materials Research, Köln, Germany
Seifert, WolfgangInstitute of Physics, Martin Luther University Halle-Wittenberg, Germany
Date:27 July 2009
Status:Accepted
Keywords:modelling thermoelectric elements - performance - thermogenerator - functionally graded materials - spatial dependent material properties
Event Title:28th International / 7th European Conference on Thermoelectrics
Event Location:Freiburg
Event Type:international Conference
Event Dates:26.-30. Juli 2009
Organizer:International Thermoelectric Society (ITS) organized by Fraunhofer IPM Freiburg
HGF - Research field:Aeronautics, Space and Transport (old)
HGF - Program:Transport
HGF - Program Themes:Terrestrial Vehicles
DLR - Research area:Transport
DLR - Program:V BF - Bodengebundene Fahrzeuge
DLR - Research theme (Project):V - Fahrzeugenergiesysteme (old)
Location: Köln-Porz
Institutes and Institutions:Institute of Materials Research > Thermoelectric Materials and Systems
Deposited By: Dr. Knud Zabrocki
Deposited On:25 Nov 2009 14:14
Last Modified:25 Nov 2009 14:14

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