Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rayleigh-B\'enard convection in a creeping solid with melting and
  freezing at either or both its horizontal boundaries   Solid state convection can take place in the rocky or icy mantles of
planetary objects and these mantles can be surrounded above or below or both by
molten layers of similar composition. A flow toward the interface can proceed
through it by changing phase. This behaviour is modeled by a boundary condition
taking into account the competition between viscous stress in the solid, that
builds topography of the interface with a timescale $\tau_\eta$, and convective
transfer of the latent heat in the liquid from places of the boundary where
freezing occurs to places of melting, which acts to erase topography, with a
timescale $\tau_\phi$. The ratio $\Phi=\tau_\phi/\tau_\eta$ controls whether
the boundary condition is the classical non-penetrative one ($\Phi\rightarrow
\infty$) or allows for a finite flow through the boundary (small $\Phi$). We
study Rayleigh-B\'enard convection in a plane layer subject to this boundary
condition at either or both its boundaries using linear and weakly non-linear
analyses. When both boundaries are phase change interfaces with equal values of
$\Phi$, a non-deforming translation mode is possible with a critical Rayleigh
number equal to $24\Phi$. At small values of $\Phi$, this mode competes with a
weakly deforming mode having a slightly lower critical Rayleigh number and a
very long wavelength, $\lambda_c\sim 8\sqrt{2}\pi/ 3\sqrt{\Phi}$. Both modes
lead to very efficient heat transfer, as expressed by the relationship between
the Nusselt and Rayleigh numbers. When only one boundary is subject to a phase
change condition, the critical Rayleigh number is $\Ray_c=153$ and the critical
wavelength is $\lambda_c=5$. The Nusselt number increases about twice faster
with Rayleigh number than in the classical case with non-penetrative conditions
when the bottom boundary is a phase change interface.

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The categories of this paper are: hep-ph
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The categories of this paper are: math
30
The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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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: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: funct-an