 Real processing II: Extremal principles of irreversible thermodynamics, relations, generalizations and time dependenceBernhard Reiser Physica A: Statistical Mechanics and its Applications, 1998, vol. 253, issue 1, 223-246 Abstract: We start presenting the extremal principles we will consider: The Statement of Helmholtz 1868 and Rayleigh (SHR) 1913, generalized by Reiser 1996, the Statement of Kelvin (SK) 1849, the Principle of Minimal Entropy Production (PME) of Prigogine 1947 for linear processes, that of Prigogine and Glansdorff 1954 for non-linear processes and finally, the Principle of Maximal Entropy (MEF) of Jaynes, 1957. First we show the relation between SHR and SK. This is a particular example for the property of Irreversible Thermodynamics (TIP) to treat all kinds of movements of fluids, compounds or any type of energy under the engineering term loss, or accurately spoken, entropy production. This possibility to treat different physical effects in the same manner causes by its simplification, considerable economical advantages of treating processes in the frame of TIP. For example, whereas a balance like the momentum balance (Navier–Stokes equation) has to distinguish between inertial, viscous or pressure effects, the PME treats the movements these effects cause with one term, and no pressure coupling or non-linearity is enclosed. Then we generalize the SK from potential velocity fields to general ones and show that it fits into the MEF. We continue with the generalization of the SHR from 1996 to compressible and non-Newtonian fluids. Further, we notice that these principles hold for time-dependent (non-stationary) processes. Therefore, the general fluid dynamical part of the PME 1947 can be generalized from stationary to time-dependent processes. We show that this is possible not only for velocity fields but also for scalar fields using as an example, the temperature in the case of heat conduction. We see that scalar fields need a transformation well known in mathematics. Comparing the PME 1954 with the completely generalized SHR we see that it holds also for non-linear processes. The same holds for the generalized SK. We close the consideration of extremal principles with the formulation of a very general PME which may play the role of a main law of thermodynamics, the fourth one, FML. We compare it with the Evolution Principle of Glansdorff and Prigogine 1964 and show how this may be generalized to time-dependent processes too. The distinction between fixed- and free-process parameters is particularly fruitful. The fixed ones are determined by balances and the free ones by the fourth main law (FML). In data processing this separation allows for drastic simplification in the treatment of processes: Not all process parameters have to be “forced” simultaneously over the balances. They can be calculated separately. Finally, we consider an application of the PME to the improvement of the performance of an evaporator. This improvement is considerable and stands for the meaning of TIP-applications to other ranges of process engineering, in particular to complicated processes, e.g. those with phase changes. Date: 1998 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:253:y:1998:i:1:p:223-246 DOI: 10.1016/S0378-4371(98)00053-3 Access Statistics for this article Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis More articles in Physica A: Statistical Mechanics and its Applications from Elsevier |
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