Bounds on heat flux for Rayleigh-Bénard convection between Navier-slip fixed-temperature boundaries

Theodore D. Drivas; Huy Q. Nguyen; Camilla Nobili

doi:10.1098/rsta.2021.0025

Bounds on heat flux for Rayleigh-Bénard convection between Navier-slip fixed-temperature boundaries

Theodore D. Drivas
, Huy Q. Nguyen
, Camilla Nobili

Mathematics

University of Maryland, College Park
University of Hamburg

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

We study two-dimensional Rayleigh-Bénard convection with Navier-slip, fixed temperature boundary conditions and establish bounds on the Nusselt number. As the slip-length varies with Rayleigh number Ra, this estimate interpolates between the Whitehead-Doering bound by Ra 5/12 for free-slip conditions (Whitehead & Doering. 2011 Ultimate state of two-dimensional Rayleigh-Bénard convection between free-slip fixed-temperature boundaries. Phys. Rev. Lett. 106, 244501) and the classical Doering-Constantin Ra 1/2 bound (Doering & Constantin. 1996 Variational bounds on energy dissipation in incompressible flows. III. Convection. Phys. Rev. E 53, 5957-5981). This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 1)'.

Original language	English
Article number	20210025
Journal	Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	380
Issue number	2225
DOIs	https://doi.org/10.1098/rsta.2021.0025
State	Published - 2022

Keywords

Navier-slip boundary conditions
Nusselt number
Rayleigh-Bénard convection
background field method
scaling laws

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10.1098/rsta.2021.0025

Cite this

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title = "Bounds on heat flux for Rayleigh-B{\'e}nard convection between Navier-slip fixed-temperature boundaries",

abstract = "We study two-dimensional Rayleigh-B{\'e}nard convection with Navier-slip, fixed temperature boundary conditions and establish bounds on the Nusselt number. As the slip-length varies with Rayleigh number Ra, this estimate interpolates between the Whitehead-Doering bound by Ra 5/12 for free-slip conditions (Whitehead \& Doering. 2011 Ultimate state of two-dimensional Rayleigh-B{\'e}nard convection between free-slip fixed-temperature boundaries. Phys. Rev. Lett. 106, 244501) and the classical Doering-Constantin Ra 1/2 bound (Doering \& Constantin. 1996 Variational bounds on energy dissipation in incompressible flows. III. Convection. Phys. Rev. E 53, 5957-5981). This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 1)'.",

keywords = "Navier-slip boundary conditions, Nusselt number, Rayleigh-B{\'e}nard convection, background field method, scaling laws",

author = "Drivas, \{Theodore D.\} and Nguyen, \{Huy Q.\} and Camilla Nobili",

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doi = "10.1098/rsta.2021.0025",

language = "English",

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T1 - Bounds on heat flux for Rayleigh-Bénard convection between Navier-slip fixed-temperature boundaries

AU - Drivas, Theodore D.

AU - Nguyen, Huy Q.

AU - Nobili, Camilla

PY - 2022

Y1 - 2022

N2 - We study two-dimensional Rayleigh-Bénard convection with Navier-slip, fixed temperature boundary conditions and establish bounds on the Nusselt number. As the slip-length varies with Rayleigh number Ra, this estimate interpolates between the Whitehead-Doering bound by Ra 5/12 for free-slip conditions (Whitehead & Doering. 2011 Ultimate state of two-dimensional Rayleigh-Bénard convection between free-slip fixed-temperature boundaries. Phys. Rev. Lett. 106, 244501) and the classical Doering-Constantin Ra 1/2 bound (Doering & Constantin. 1996 Variational bounds on energy dissipation in incompressible flows. III. Convection. Phys. Rev. E 53, 5957-5981). This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 1)'.

AB - We study two-dimensional Rayleigh-Bénard convection with Navier-slip, fixed temperature boundary conditions and establish bounds on the Nusselt number. As the slip-length varies with Rayleigh number Ra, this estimate interpolates between the Whitehead-Doering bound by Ra 5/12 for free-slip conditions (Whitehead & Doering. 2011 Ultimate state of two-dimensional Rayleigh-Bénard convection between free-slip fixed-temperature boundaries. Phys. Rev. Lett. 106, 244501) and the classical Doering-Constantin Ra 1/2 bound (Doering & Constantin. 1996 Variational bounds on energy dissipation in incompressible flows. III. Convection. Phys. Rev. E 53, 5957-5981). This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 1)'.

KW - Navier-slip boundary conditions

KW - Nusselt number

KW - Rayleigh-Bénard convection

KW - background field method

KW - scaling laws

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ER -

Bounds on heat flux for Rayleigh-Bénard convection between Navier-slip fixed-temperature boundaries

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Keywords

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