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Thermofluiddynamics: Do We Solve the Right Kind of Equations?

DOI: 10.1615/ICHMT.2006.TurbulHeatMassTransf.10
pages 3-18

Franz Durst
FMP TECHNOLOGY GMBH, Am Weichselgarten 34, 91058 Erlangen, Germany

J. Gomes
Lehrstuhl für Strömungsmechanik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstrasse 4, D-91058 Erlangen, Germany

R. Sambasivam
TATA Steel, Jamshedpur 831001, Jharkhand State, India

Аннотация

The present paper reconsiders the Navier-Stokes equations for flows of ideal gases. The authors stress that for these fluids the molecular transport of mass, heat and momentum is physically well understood. Hence the molecular transport terms mi, qi and τij can be reconsidered with a clear understanding of their causes, at least for ideal gases. Such considerations are carried out in the present paper. A methodology is adopted to derive the relationships for qi and τij under the usually applied assumption of mi = 0:
...
It is stressed that the assumption mi = 0 contradicts those introduced to derive the relationship for qi, i.e. the Fourier law. The major part of the paper concerns derivations that are carried out for ideal gases adopting the suggested methodology for the derivations in a more general form. This yields for the mass diffusion mi ≠ 0 and results in additional terms in relationships for qi and τij. These are presented and discussed and the significance of the terms is demonstrated by comparisons of first numerical computations. These were carried out for internal flows with heated walls employing the conventional and extended forms of the fluid flow equations. Significant differences between the predicted flow fields resulted. Some of the results are presented in this paper.

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