Real processing III. The generalized statement of Helmholtz and Rayleigh and its meaning for process engineering

Abstract

Entropy production defines the process losses. Because it is a fundamental state function like entropy its neglect in process engineering can cause only more effort and worse results. Because of this scientific and economic importance of the entropy production we show on the basis of the last two publications of the author Real Processing I and Real Processing II, see the literature citation, a complete and closed mathematical–physical derivation of the generalised Principle of Minimal Entropy Production on the basis of the statement of Helmholtz and Rayleigh. Therefore, we talk of Helmholtz-Thermodynamics of Irreversible Processes. We introduce entropy production into balances, apply the Principle of Minimal Entropy Production and obtain in this way considerable simplifications. In an example we first derive the Principle of Minimal Entropy Production for the momentum transport in the case of stationary, Newtonian and density conserving flow and treat with this Principle a typical calculation in process engineering, the flow through a filter in a simple difference scheme with neither the non-linear convection terms nor that of the pressure. In this example, we see that the physics changes from that of general processes, reversible and irreversible, to that of only irreversible ones and therefore simplifies, becomes more accurate, transparent and economic. As a by-product it turns out that the Principle of Minimal Entropy Production may be derived directly from balances generally and special expressions of entropy production may be derived from balances. In many cases we obtain analytic representations, at least to a large extent. So we do in a treatment of the general tube flow which may be transformed on channel flow with arbitrary geometry by conformal mapping. We treat the Hagen–Poiseuille and Couette flow by the Principle of Minimal Entropy Production in the case of multiple phase flow and show that the Principle of Minimal Entropy Production is irreplaceable particularly for complicated processes. Reversible cycle processes, well known from motor processes, are generalised to irreversibility and optimised by the Principle of Minimal Entropy Production. Astonishingly, we find that well-known effects turn out to be simple consequences of the Principle of Minimal Entropy Production.