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Total energy balance in a natural convection flow

Hector Barrios-Piña (Escuela de Ingenieria y Ciencias, Tecnologico de Monterrey, Zapopan, Mexico)
Stéphane Viazzo (CNRS Ecole Centrale de Marseille, Aix-Marseille Université, Marseille, France)
Claude Rey (CNRS Ecole Centrale de Marseille, Aix-Marseille Université, Marseille, France)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 7 August 2017

Abstract

Purpose

The purpose of this paper is to show a thermodynamic analysis to determine the contribution of each term of the total energy balance.

Design/methodology/approach

The thermodynamic analysis comprises a number of numerical simulations where some terms, typically ignored by the commonly used approximations, are removed from the total energy equation to quantify the effects in the flow and heat transfer fields. The case study is the differentially heated square cavity flow, in which the effects of work done by the pressure forces contribute significantly to the energy balance. Because local magnitudes are computed here for discussion, the dimensional form of the governing equations is preferred and a numerical model without any restrictive approximation about the role of the pressure is used.

Findings

The results show that the work of gravity forces term is in perfect balance with the work of pressure forces term, and thus, ignoring the contribution of one of them yields an incorrect solution. In addition, it is shown that the assumption of zero divergence of the Boussinesq approximation can be erroneous, even for a natural convection flow case where the temperature difference is very small.

Research limitations/implications

As the flow and heat transfer governing equations are complex, simplifying assumptions are generally used; that is, the Boussinesq and low Mach number approximations. These assumptions are systematically adopted without any validation process and without considering that they modify the physical meaning of one or more of the thermodynamic quantities, particularly the pressure. This fact results in inconsistencies of the different forms of energy.

Originality/value

This is the first time that the terms of the total energy balance are quantified in such a way, in a differentially heated square cavity flow, which is a case study addressed by several authors.

Keywords

Acknowledgements

This research was partially supported by the Consejo Nacional de Ciencia y Tecnología of Mexico, Grant Fellowship 205881. The support and technical contribution of the Laboratoire de Mécanique, Modélisation & Procédés Propres is greatly appreciated.

Citation

Barrios-Piña, H., Viazzo, S. and Rey, C. (2017), "Total energy balance in a natural convection flow", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 27 No. 8, pp. 1735-1747. https://doi.org/10.1108/HFF-03-2016-0093

Publisher

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Emerald Publishing Limited

Copyright © 2017, Emerald Publishing Limited