Thermodynamics for non-equilibrium pattern formation

The second entropy theory for non-equilibrium thermodynamics is used to show that the optimum structure or pattern of a time-dependent system corresponds to the maximum entropy. A formula for the total entropy of convective heat flow is derived. The Navier-Stokes equations in Boussinesq approximatio...

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Main Author:	Phil Attard
Format:	Article
Language:	English
Published:	AIP Publishing LLC 2011-09-01
Series:	AIP Advances
Online Access:	http://dx.doi.org/10.1063/1.3632033

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spelling	doaj-69871ca503464744ae2273550c10082a2020-11-25T00:54:15ZengAIP Publishing LLCAIP Advances2158-32262011-09-0113032146032146-2010.1063/1.3632033046103ADVThermodynamics for non-equilibrium pattern formationPhil Attard02/52-56 Auburn st, Sutherland NSW 2232 AustraliaThe second entropy theory for non-equilibrium thermodynamics is used to show that the optimum structure or pattern of a time-dependent system corresponds to the maximum entropy. A formula for the total entropy of convective heat flow is derived. The Navier-Stokes equations in Boussinesq approximation for straight roll convection are solved by a Fourier expansion technique. Results for the velocity amplitude are in good agreement with previous computations and experimental measurements. For the spontaneous transitions between straight roll states reported in the literature, it is shown that the measured change in convective pattern wave length corresponds to an increase in the entropy.http://dx.doi.org/10.1063/1.3632033
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Phil Attard
spellingShingle	Phil Attard Thermodynamics for non-equilibrium pattern formation AIP Advances
author_facet	Phil Attard
author_sort	Phil Attard
title	Thermodynamics for non-equilibrium pattern formation
title_short	Thermodynamics for non-equilibrium pattern formation
title_full	Thermodynamics for non-equilibrium pattern formation
title_fullStr	Thermodynamics for non-equilibrium pattern formation
title_full_unstemmed	Thermodynamics for non-equilibrium pattern formation
title_sort	thermodynamics for non-equilibrium pattern formation
publisher	AIP Publishing LLC
series	AIP Advances
issn	2158-3226
publishDate	2011-09-01
description	The second entropy theory for non-equilibrium thermodynamics is used to show that the optimum structure or pattern of a time-dependent system corresponds to the maximum entropy. A formula for the total entropy of convective heat flow is derived. The Navier-Stokes equations in Boussinesq approximation for straight roll convection are solved by a Fourier expansion technique. Results for the velocity amplitude are in good agreement with previous computations and experimental measurements. For the spontaneous transitions between straight roll states reported in the literature, it is shown that the measured change in convective pattern wave length corresponds to an increase in the entropy.
url	http://dx.doi.org/10.1063/1.3632033
work_keys_str_mv	AT philattard thermodynamicsfornonequilibriumpatternformation
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Thermodynamics for non-equilibrium pattern formation

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