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ISSN Online: 2377-424X

ISBN Print: 978-1-56700-474-8

ISBN Online: 978-1-56700-473-1

International Heat Transfer Conference 16
August, 10-15, 2018, Beijing, China

CHARACTERIZING THE IRREVERSIBILITY OF HEAT CONDUCTION PROCESS BY ENTRANSY AND ITS DISSIPATION RATE AS LYAPUNOV FUNCTIONS

Get access (open in a dialog) DOI: 10.1615/IHTC16.cip.022994
pages 2569-2574

Abstract

Prigogine established the relation between the irreversibility (i.e. one-sidedness) of an irreversible process and Lyapunov function in the modern theory of stability. For heat conduction in a compressible isolated system, thermodynamic equilibrium is an attractor of non-equilibrium states and the entropy production rate is its Lyapunov function. However, for heat conduction in an incompressible isolated system that only involves heat conduction process, except for the entropy production rate, the entransy dissipation rate (the dot product of heat flux and negative temperature gradient), even other quantity being the function of temperature, can also serve as its Lyapunov function. This implies that the Lyapunov function or the dissipation function of heat conduction process in an incompressible isolated system is not unique. What the difference is that only the variation of the entransy dissipation rate can lead to Fourier's heat conduction law and the corresponding differential equation of heat conduction, while other dissipation functions cannot. This indicates that the entransy dissipation rate as the action of heat conduction process is unique. Therefore, compared with other dissipation functions, the entransy dissipation rate should be more proper to handle the heat conduction problems, such as the entransy dissipation rate based element method for the approximate solution of heat conduction problems and the optimization of heat conduction systems.