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2016 | OriginalPaper | Chapter

1. A Family of Convective Models

Author : David Goluskin

Published in: Internally Heated Convection and Rayleigh-Bénard Convection

Publisher: Springer International Publishing

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Abstract

Six canonical models of convection are described: three configurations of internally heated (IH) convection driven by constant and uniform volumetric heating, and three configurations of Rayleigh–Bénard (RB) convection driven by the boundary conditions. The IH models are distinguished by differing pairs of thermal boundary conditions: top and bottom boundaries of equal temperature, an insulating bottom with heat flux fixed at the top, and an insulating bottom with temperature fixed at the top. The RB models too are distinguished by whether temperatures or heat fluxes are fixed at the top and bottom boundaries. Integral quantities important to heat transport are examined, including the mean fluid temperature, the mean temperature difference between the boundaries, and the mean convective heat flux. Integral relations and bounds are presented, and further bounds are conjectured for the IH cases. Similarities and differences between the six configurations are emphasized.

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next chapter Stabilities and Bounds
Appendix
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Metadata
Title
A Family of Convective Models
Author
David Goluskin
Copyright Year
2016
Book
Internally Heated Convection and Rayleigh-Bénard Convection

Print ISBN: 978-3-319-23939-2

Electronic ISBN: 978-3-319-23941-5

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-23941-5_1

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