Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

On the role of the Prandtl number in convection driven by heat sources and sinks (2006.07109v2)

Published 12 Jun 2020 in physics.flu-dyn

Abstract: We report on a numerical study of turbulent convection driven by a combination of internal heat sources and sinks. Motivated by a recent experimental realisation (Lepot et al. 2018), we focus on the situation where the cooling is uniform, while the internal heating is localised near the bottom boundary, over approximately one tenth of the domain height. We obtain scaling laws $Nu \sim Ra\gamma Pr\chi$ for the heat transfer as measured by the Nusselt number $Nu$ expressed as a function of the Rayleigh number $Ra$ and the Prandtl number $Pr$. After confirming the experimental value $\gamma\approx 1/2$ for the dependence on $Ra$, we identify several regimes of dependence on $Pr$. For a stress-free bottom surface and within a range as broad as $Pr \in [0.003, 10]$, we observe the exponent $\chi\approx 1/2$, in agreement with Spiegel's mixing length theory. For a no-slip bottom surface we observe a transition from $\chi\approx 1/2$ for $Pr \leq 0.04$ to $\chi\approx 1/6$ for $Pr \geq 0.04$, in agreement with scaling predictions by Bouillaut et al. The latter scaling regime stems from heat accumulation in the stagnant layer adjacent to a no-slip bottom boundary, which we characterise by comparing the local contributions of diffusive and convective thermal fluxes.

Summary

We haven't generated a summary for this paper yet.