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Main Author: Seis, Christian
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2504.11051
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author Seis, Christian
author_facet Seis, Christian
contents We are concerned with infinite Prandtl number Rayleigh--Bénard convection with Navier-slip boundary conditions. The goal of this work is to estimate the average upward heat flux measured by the nondimensional Nusselt number $Nu$ in terms of the Rayleigh number $Ra$, which is a nondimensional quantity measuring the imposed temperature gradient. We derive bounds on the Nusselt number that coincide for relatively small slip lengths with the optimal Nusselt number scaling for no-slip boundaries, $Nu\lesssim Ra^{1/3}$; for relatively large slip lengths, we recover scaling estimates for free-slip boundaries, $Nu\lesssim Ra^{5/12}$.
format Preprint
id arxiv_https___arxiv_org_abs_2504_11051
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Infinite Prandtl number convection with Navier-slip boundary conditions
Seis, Christian
Analysis of PDEs
We are concerned with infinite Prandtl number Rayleigh--Bénard convection with Navier-slip boundary conditions. The goal of this work is to estimate the average upward heat flux measured by the nondimensional Nusselt number $Nu$ in terms of the Rayleigh number $Ra$, which is a nondimensional quantity measuring the imposed temperature gradient. We derive bounds on the Nusselt number that coincide for relatively small slip lengths with the optimal Nusselt number scaling for no-slip boundaries, $Nu\lesssim Ra^{1/3}$; for relatively large slip lengths, we recover scaling estimates for free-slip boundaries, $Nu\lesssim Ra^{5/12}$.
title Infinite Prandtl number convection with Navier-slip boundary conditions
topic Analysis of PDEs
url https://arxiv.org/abs/2504.11051