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The weak solvability of the steady problem modelling the flow of a viscous incompressible heat-conductive fluid through the profile cascade

Tomáš Neustupa (Czech Technical University in Prague, Faculty of Mechanical Engineering, Institute of Technical Mathematics, Prague, Czech Republic)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 3 July 2017

Abstract

Purpose

The paper aims to theoretically study the mathematical model of a steady flow of a heat-conductive incompressible viscous fluid through a spatially periodic plane profile cascade.

Design/methodology/approach

Reduction of the infinite periodical problem to one period. Leray-Schauder fixed point principle was used.

Findings

This study proves the existence of a weak solution for arbitrarily large given data (i.e. the inflow velocity and the acting specific body force).

Practical implications

The author proposed a special boundary condition on the outflow of the domain not only for the velocity and pressure but also for the temperature.

Originality/value

To the author’s knowledge, the problem has not been studied earlier. More detailed overview is given in the paper in the first part.

Keywords

Acknowledgements

The research was supported by the Grant Agency of the Czech Rep., grant No. 13-00522S. A short version of this paper was presented at the 10th International Symposium on Numerical Analysis of Fluid Flow and Heat Transfer Numerical Fluids 2015.

Citation

Neustupa, T. (2017), "The weak solvability of the steady problem modelling the flow of a viscous incompressible heat-conductive fluid through the profile cascade", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 27 No. 7, pp. 1451-1466. https://doi.org/10.1108/HFF-03-2016-0104

Publisher

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Emerald Publishing Limited

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