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ISSN Online: 2377-424X

ISBN CD: 1-56700-226-9

ISBN Online: 1-56700-225-0

International Heat Transfer Conference 13
August, 13-18, 2006, Sydney, Australia

INFLUENCE OF THE PRESSURE STRESS WORK ON HEAT TRANSFER AND FLOW IN THE DIFFERENTIALLY HEATED CAVITY

Get access (open in a dialog) DOI: 10.1615/IHTC13.p6.320
12 pages

Resumo

The Boussinesq equations are extensively used in the field on natural convection. However, for sake of consistency with thermodynamics, especially the second law, the terms accounting for the work of pressure field and for the heat released by viscous friction should be maintained in the heat equation. This is the thermodynamic Boussinesq model. With those effects, the flow now depends on the size of cavity. An example of comparison between a small square cavity and a large one, also square, is given for Ra = 108 . In the large cavity, the pressure-field work is so significant that convection is strongly reduced while heat transfer is significantly increased due to a process similar to the piston effect. Similarly, the contribution of viscous friction to the total irreversibility is strongly increased. With those two cavities of fixed size, the Rayleigh number is increased via the temperature difference. In the large cavity, the flow remains steady up to Ra = 4×108 (the highest value investigated herein). In the small cavity, the flow destabilizes around Ra = 1.82×108 like in the usual Boussinesq calculations. The onset of unsteadiness offers the opportunity to address the relations between instability and thermodynamics: are steady-states characterized by minimal irreversibility? Is there any topological relationship between fluctuations and irreversibility?