Chapter

Heat Convection and Non-Equilibrium Phase Transitions

Phil Attard

in Non-equilibrium Thermodynamics and Statistical Mechanics

Published in print October 2012 | ISBN: 9780199662760
Published online January 2013 | e-ISBN: 9780191745287 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199662760.003.0006
Heat Convection and Non-Equilibrium Phase Transitions

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Heat convection exemplifies non-equilibrium phase transitions and non-equilibrium pattern formation. For these a new thermodynamic principle is introduced, namely the reduction condition for the second entropy: once maximised with respect to the fluxes, the entropy for convection is then maximised with respect to structure. This distinguishes competing solutions to the hydrodynamic equations, giving the optimum non-equilibrium pattern and phase diagram. Heat convection is characterised numerically by the non-linear Boussinesq hydrodynamic equations. Straight roll solutions are stable over a range of wavelengths for a given supercritical Rayleigh number. The structural entropy is positive with respect to conduction for stable solutions and has a well-defined maximum as a function of wavelength. Quantitative comparison with experimental measurements of straight roll convection shows that the experimentally observed spontaneous transitions correspond to an increase in the structural entropy. It is concluded that this provides a general way to account for non-equilibrium phase transitions.

Keywords: convection; Boussinesq; non-equilibrium pattern; phase diagram; rayleigh number; nusselt number

Chapter.  12565 words.  Illustrated.

Subjects: Condensed Matter Physics

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