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Fabian Kock
Technische Thermodynamik, TU Hamburg-Harburg, 21073 Hamburg, Germany

Heinz Herwig
Institute of Thermodynamics, Hamburg University of Technology, Hamburg, D-21073, Germany


Entropy production in turbulent shear flows with heat transfer is calculated locally and afterwards integrated over the whole flow domain. This quantity may serve as an efficiency parameter for turbulent heat transfer processes. Based on the time averaged entropy balance equation, four different mechanisms of entropy production can be identified and cast into mathematical equations. They are: dissipation in the mean and the fluctuating velocity field and heat flux due to the mean and the fluctuating temperature field.
It turns out that no additional balance equation has to be solved, provided the turbulent dissipation rate is known in the flow field together with the mean velocity and temperature distribution. Since all four entropy production rates show very steep gradients close to a wall numerical solutions are far more effective with wall functions for the production terms. These wall functions are mandatory when high Reynolds number turbulent models are used, as for example the high Reynolds number k − ε model, like in our case. As an example flow through a heated pipe with a spiral insert is calculated in detail including the local entropy production rate. For this configuration experimental results show an increase in heat transfer as well as in pressure drop when the spiral slope is increased. Therefore, no optimum of the spiral slope can be found in the experiments. An analysis based on entropy production, however, reveals that there is a distinct optimum for a certain slope of the spiral. Thus, entropy production can be used as an efficiency parameter with respect to minimizing the loss of available work in a process.

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