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

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

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

Analysis of PDEs 2021-09-28 v1 Fluid Dynamics

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

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 $\rm{Ra}$ , this estimate interpolates between the Whitehead-Doering bound by $\rm{Ra}^{\frac{5}{12}}$ for free-slip conditions [13] and the classical Doering-Constantin $\rm{Ra}^{\frac{1}{2}}$ bound [4].

Keywords

rayleigh-bénard convection nusselt number navier-slip boundary heat flux bounds fixed temperature boundary

Cite

@article{arxiv.2109.13205,
  title  = {Bounds on heat flux for Rayleigh-B\'{e}nard convection between Navier-slip fixed-temperature boundaries},
  author = {Theodore D. Drivas and Huy Q. Nguyen and Camilla Nobili},
  journal= {arXiv preprint arXiv:2109.13205},
  year   = {2021}
}

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15 pages, 1 figure

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

Abstract

Keywords

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