Elektrothermische Analyse von planaren PTC-Heizern

Translated title of the contribution: Electro-thermal investigation of planar PTC heaters

Sören Röhrig

Research output: ThesisDoctoral Thesis


Typical materials for Positive Temperatur Coefficient (PTC) thermistor applications are based on properly doped barium titanate, and show a steep increase in the electrical resistivity within a small temperature range, which is the so-called PTC effect. This property is used for self-regulating PTC heating elements. In this work the electro-thermal behaviour of plate-shaped PTC heaters with different electrode designs were investigated theoretically and experimentally. The focus was on an alternative electrode design with co-planar, interdigital electrodes (IDE), which has rarely been studied for PTC devices. Theoretical models with several dimensions were developed in order to work out the essential characteristics of the IDE concept. The most important result for PTC heater was the observation of a locally increased heat generation rate at the edge of the electrodes due to a singularity in the electric field. Consequently, an inhomogeneous temperature evolution was observed with lock-in thermography. It was shown that by adjusting the shape of the electrodes the maximum of temperature at the electrode tip could be reduced. By transforming the mathematical differential equation of the 1- and 2-dimensional model into a dimensionless form and by using a three parameters containing approach for the resistivity characteristics, the number of parameters to be investigated was reduced down to three and five dimensionless quantities, respectively. Theoretical studies provide general guidelines for the design of optimal heaters. Thus, in order to obtain a good performance of the heater, the Biot number has to be smaller than one. Consequently, the thickness of the heater has to be in the range of a few hundred microns, if a high heat output is concerned. Electric and thermographic measurements were carried out on prototypes in air and in oil, respectively. By the use of the full 3-dimensional model and of an appropriate heat transfer coefficient, the measurement results proved to be reproducible. With the results of these general studies, the voltage and the heat output could be predicted in a good agreement compared to service conditions.
Translated title of the contributionElectro-thermal investigation of planar PTC heaters
Original languageGerman
  • Danzer, Robert, Assessor A (internal)
  • Reichmann, Klaus, Assessor B (external), External person
Publication statusPublished - 2013

Bibliographical note

embargoed until 04-02-2018


  • PTC heating elements
  • electrode design

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