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Analytical properties of Graetz modes in parallel and concentric configurations

Pierre, Charles and Plouraboué, Franck Analytical properties of Graetz modes in parallel and concentric configurations. (2020) Meccanica, 55. 1545-1559. ISSN 0025-6455

(Document in English)

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Official URL: https://doi.org/10.1007/s11012-020-01192-4


The generalized Graetz problem refers to stationary convection–diffusion in uni-directional flows. In this contribution we demonstrate the analyt- icity of generalized Graetz solutions associated with layered domains: either cylindrical (possibly concen- tric) or parallel. Such configurations are considered as prototypes for heat exchangers devices and appear in numerous applications involving heat or mass transfer. The established framework of Graetz modes allows to recast the 3D resolution of the heat transfer into a 2D or even 1D spectral problem. The associated eigen- functions (called Graetz modes) are obtained with the help of a sequence of closure functions that are recursively computed. The spectrum is given by the zeros of an explicit analytical series, the truncation of which allows to approximate the eigenvalues by solving a polynomial equation. Graetz mode compu- tation is henceforth made explicit and can be per- formed using standard software of formal calculus. It permits a direct and mesh-less computation of the resulting solutions for a broad range of configurations. Some solutions are illustrated to showcase the interest of mesh-less analytical derivation of the Graetz solutions, useful to validate other numerical approaches.

Item Type:Article
HAL Id:hal-02943171
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Other partners > Université de Pau et des Pays de l'Adour - UPPA (FRANCE)
Laboratory name:
Deposited On:18 Sep 2020 14:40

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