REAL PROCESSING II - EXTREMAL PRINCIPLES OF IRREVERSIBLE THERMODYNAMICS, RELATIONS, GENERALIZATIONS AND TIME-DEPENDENCE

We start presenting the extremal principles we will consider: The Stat ement of Helmholtz 1868 and Rayleigh (SHR) 1913, generalized by Reiser 1996, the Statement of Kelvin (SK) 1849, the Principle of Minimal Ent ropy Production (PME) of Prigogine 1947 for linear processes, that of Prigogine and Glansdorff 1954 for non-linear processes and finally, th e Principle of Maximal Entropy (MEF) of Jaynes, 1957. First we show th e relation between SHR and SK. This is a particular example for the pr operty of Irreversible Thermodynamics (TIP) to treat all kinds of move ments 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 process es in the frame of TIP. For example, whereas a balance like the moment um balance (Navier-Stokes equation) has to distinguish between inertia l, viscous or pressure effects, the PME treats the movements these eff ects cause with one term, and no pressure coupling or nonlinearity 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 rime-depende nt processes. Therefore, the general fluid dynamical part of the PME 1 947 can be generalized from stationary to time-dependent (non-stationa ry) processes. We;how that this is possible not only for velocity fiel ds but also for scalar fields using as an example, the temperature in the case of heat conduction. We see that scalar fields need a transfor mation well known in mathematics. Comparing the PME 1954 with the comp letely generalized SHR we see that it holds also for non-linear proces ses. The same holds for the generalized SK. We close the consideration of extremal principles with the formulation of a very general PME whi ch may play the role of a main law of thermodynamics, the fourth one, FML. We compare it with the Evolution Principle of Glansdorff and Prig ogine 1964 and show how this may be generalized to time-dependent proc esses too. The distinction between fixed- and free-process parameters is particularly fruitful. The fixed ones are determined by balances an d the free ones by the fourth main law (FML), In data processing this separation allows for drastic simplification in the treatment of proce sses: Not all process parameters have to be ''forced'' simultaneously over the balances. They can be calculated separately. Finally, we cons ider an application of the PME to the improvement of the performance o f an evaporator. This improvement is considerable and stands for the m eaning of TIP-applications to other ranges of process engineering, in particular to complicated processes: e.g, those with phase changes. (C ) 1998 Elsevier Science B.V. All rights reserved.