Critical Prandtl number for Heat Transfer Enhancement in Rotating Convection
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914642860703744 |
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| author | Anas, Mohammad Joshi, Pranav |
| author_facet | Anas, Mohammad Joshi, Pranav |
| contents | Rotation, which stabilizes flow, can enhance the heat transfer in Rayleigh-Bénard convection (RBC) through Ekman pumping. In this Letter, we present the results of our direct numerical simulations of rotating RBC, providing a comprehensive analysis of this heat transfer enhancement relative to non-rotating RBC in the parameter space of Rayleigh number ($Ra$), Prandtl number ($Pr$), and Taylor number ($Ta$). We show that for a given $Ra$, there exists a critical Prandtl number ($Pr_{cr}$) below which no significant heat transfer enhancement occurs at any rotation rate, and an optimal Prandtl number ($Pr_{opt}$) at which maximum heat transfer enhancement occurs at an optimal rotation rate ($Ta_{opt}$). Notably, $Pr_{cr}$, $Pr_{opt}$, $Ta_{opt}$, and the maximum heat transfer enhancement all increase with increasing $Ra$. We also demonstrate a significant heat transfer enhancement up to $Ra=2\times 10^{10}$ and predict that the enhancement would become even more pronounced at higher $Ra$, provided $Pr$ is also increased commensurately. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_12525 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Critical Prandtl number for Heat Transfer Enhancement in Rotating Convection Anas, Mohammad Joshi, Pranav Fluid Dynamics Rotation, which stabilizes flow, can enhance the heat transfer in Rayleigh-Bénard convection (RBC) through Ekman pumping. In this Letter, we present the results of our direct numerical simulations of rotating RBC, providing a comprehensive analysis of this heat transfer enhancement relative to non-rotating RBC in the parameter space of Rayleigh number ($Ra$), Prandtl number ($Pr$), and Taylor number ($Ta$). We show that for a given $Ra$, there exists a critical Prandtl number ($Pr_{cr}$) below which no significant heat transfer enhancement occurs at any rotation rate, and an optimal Prandtl number ($Pr_{opt}$) at which maximum heat transfer enhancement occurs at an optimal rotation rate ($Ta_{opt}$). Notably, $Pr_{cr}$, $Pr_{opt}$, $Ta_{opt}$, and the maximum heat transfer enhancement all increase with increasing $Ra$. We also demonstrate a significant heat transfer enhancement up to $Ra=2\times 10^{10}$ and predict that the enhancement would become even more pronounced at higher $Ra$, provided $Pr$ is also increased commensurately. |
| title | Critical Prandtl number for Heat Transfer Enhancement in Rotating Convection |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2307.12525 |