Open AccessThe role of boundary conditions in scaling laws for turbulent heat transport
Author(s) -
Camilla Nobili,
AUTHOR_ID
Publication year - 2022
Publication title -
mathematics in engineering
Language(s) - English
Resource type - Journals
ISSN - 2640-3501
DOI - 10.3934/mine.2023013
Subject(s) - boundary value problem , nusselt number , mechanics , slip (aerodynamics) , boundary conditions in cfd , no slip condition , turbulence , convection , boundary (topology) , physics , classical mechanics , mathematics , neumann boundary condition , thermodynamics , robin boundary condition , boundary layer thickness , mathematical analysis , reynolds number
In most results concerning bounds on the heat transport in the Rayleigh-Bénard convection problem no-slip boundary conditions for the velocity field are assumed. Nevertheless it is debatable, whether these boundary conditions reflect the behavior of the fluid at the boundary. This problem is important in theoretical fluid mechanics as well as in industrial applications, as the choice of boundary conditions has effects in the description of the boundary layers and its properties. In this review we want to explore the relation between boundary conditions and heat transport properties in turbulent convection. For this purpose, we present a selection of contributions in the theory of rigorous bounds on the Nusselt number, distinguishing and comparing results for no-slip, free-slip and Navier-slip boundary conditions.