Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effect of Prandtl number on heat transport enhancement in
  Rayleigh-B\'enard convection under geometrical confinement   We study, using direct numerical simulations, the effect of geometrical
confinement on heat transport and flow structure in Rayleigh-B\'enard
convection in fluids with different Prandtl numbers. Our simulations span over
two decades of Prandtl number $Pr$, $0.1 \leq Pr \leq 40$, with the Rayleigh
number $Ra$ fixed at $10^8$. The width-to-height aspect ratio $\Gamma$ spans
between $0.025$ and $0.25$ while the length-to-height aspect ratio is fixed at
one. We first find that for $Pr \geq 0.5$, geometrical confinement can lead to
a significant enhancement in heat transport as characterized by the Nusselt
number $Nu$. For those cases, $Nu$ is maximal at a certain $\Gamma =
\Gamma_{opt}$. It is found that $\Gamma_{opt}$ exhibits a power-law relation
with $Pr$ as $\Gamma_{opt}=0.11Pr^{-0.06}$, and the maximal relative
enhancement generally increases with $Pr$ over the explored parameter range. As
opposed to the situation of $Pr \geq 0.5$, confinement-induced enhancement in
$Nu$ is not realized for smaller values of $Pr$, such as $0.1$ and $0.2$. The
$Pr$ dependence of the heat transport enhancement can be understood in its
relation to the coverage area of the thermal plumes over the thermal boundary
layer (BL) where larger coverage is observed for larger $Pr$ due to a smaller
thermal diffusivity. We further show that $\Gamma_{opt}$ is closely related to
the crossing of thermal and momentum BLs, and find that $Nu$ declines sharply
when the thickness ratio of the thermal and momentum BLs exceeds a certain
value of about one. In addition, through examining the temporally averaged flow
fields and 2D mode decomposition, it is found that for smaller $Pr$ the
large-scale circulation is robust against the geometrical confinement of the
convection cell.

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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org