Entropy Change through Rayleigh-B\'enard Convective Transition with Rigid Boundaries

TL;DR

This study extends previous work on Rayleigh-Bénard convection to include rigid boundaries, analyzing entropy changes during convective transitions and finding similar qualitative behavior to stress-free boundary cases.

Contribution

It introduces a calculation of entropy change for convective transitions with rigid boundaries, expanding understanding of entropy behavior in different boundary conditions.

Findings

Roll convection occurs above the critical Rayleigh number.

Convection states with periodic structures have maximum entropy.

Results are qualitatively similar to stress-free boundary cases.

Abstract

The previous investigation on Rayleigh-B\'enard convection of a dilute classical gas [T. Kita: J. Phys. Soc. Jpn. {\bf 75} (2006) 124005] is extended to calculate entropy change of the convective transition with the rigid boundaries. We obtain results qualitatively similar to those of the stress-free boundaries. Above the critical Rayleigh number, the roll convection is realized among possible steady states with periodic structures, carrying the highest entropy as a function of macroscopic mechanical variables.