Equipartitioning thermodynamic optimization

This principle has been confirmed by Bejan and Tondeur (Bejan, A. Tondeur, D. Equipartition, optimal allocation, and the constructal approach to predicting organization in nature. Rev. Gen. Therm. 1998,37,165-180.) in a highly original approach using the principle of equiparti-tioning in finite-time, finite-size thermodynamics. We refer for this treatment to Sections 5.3 and 5.4 in this book. 

This chapter establishes a direct relation between lost work and the fluxes and driving forces of a process. The Carnot cycle is revisited to investigate how the Carnot efficiency is affected by the irreversibilities in the process. We show to what extent the constraints of finite size and finite time reduce the efficiency of the process, but we also show that these constraints still allow a most favorable operation mode, the thermodynamic optimum, where the entropy generation and thus the lost work are at a minimum. Attention is given to the equipartitioning principle, which seems to be a universal characteristic of optimal operation in both animate and inanimate dynamic systems. 

Bejan and Tondeur [9] make a number of other observations in their paper. One is that the relation between j and x is not necessarily linear. Another observation is that a similar analysis can show that the force x should be equipartitioned in time, which is another way of saying that the steady state is optimal. Prigogine gave an earlier proof of this principle [11]. The steady state is common in nature and often the favored state in industrial operation. It can be considered to be the "stable state" of nonequilibrium thermodynamics, comparable to the equilibrium state of reversible thermodynamics (see Figure 4.2). Of course, the latter is characterized by Sgen = 0, whereas the former is characterized by a minimum value , larger than zero. 

Tondeur, D., 1990. Equipartition of entropy production a design and optimization criterion in chemical engineering. In Finite-Time Thermodynamics and Thermoeconomics. Taylor Francis, New York. 

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