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Thermal boundary-layer structure in laminar horizontal convection

Published online by Cambridge University Press:  31 March 2021

Bo Yan Open the ORCID record for Bo Yan [Opens in a new window] ,
Olga Shishkina Open the ORCID record for Olga Shishkina [Opens in a new window]  and
Xiaozhou He Open the ORCID record for Xiaozhou He [Opens in a new window]
Bo Yan
Affiliation:
School of Mechanical Engineering and Automation, Harbin Institute of Technology, Shenzhen, 518055 China
Olga Shishkina
Affiliation:
Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany
Xiaozhou He*
Affiliation:
School of Mechanical Engineering and Automation, Harbin Institute of Technology, Shenzhen, 518055 China Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen, Germany
*
†Email address for correspondence: hexiaozhou@hit.edu.cn
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Abstract

We present experimentally obtained time-averaged vertical temperature profiles $\theta (z)$ in horizontal convection (HC) in water (Prandtl number $Pr \simeq 6$), which were measured near the heating and cooling plates that are embedded in the bottom of HC samples. Three HC rectangular samples of different sizes but the same aspect ratio $\varGamma \equiv L:W:H = 10:1:1$ ($L$, $W$ and $H$ are the length, width and height of the sample, respectively) were used in the experiments, which allowed us to study HC in a Rayleigh-number range $2 \times 10^{10} \lesssim {Ra} \lesssim 9 \times 10^{12}$. The measurements revealed that above the cooling plate, the mean temperature profiles have a universal scaling form $\theta (z/\lambda _c)$ with $\lambda _c$ being a $Ra$-dependent thickness of the cold thermal boundary layer (BL). The $\theta (z/\lambda _c)$-profiles agree well with solutions to a laminar BL equation in HC, which is derived under assumption that the large-scale horizontal velocity achieves its maximum near the plate and vanishes in the bulk. Above the heating plate, the mean temperature field has a double-layer structure: in the lower layer, the $\theta$ profiles scale with the hot thermal BL thickness $\lambda _h$, while in the upper layer, they again scale with $\lambda _c$. Both scaling forms are in good agreement with the solutions to the BL equation with a proper parameter choice.

JFM classification

Boundary Layers: Boundary layer structure

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JFM Rapids
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Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , R5
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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