Work optimization in continuous and discrete systems with complex fluids
Optimization of work in fluid systems is an important problem in thermodynamics. In classical equilibrium thermodynamics, the extremal work delivered by the system is related to changes in availability. If work must be delivered in a finite time, the problem becomes much more involved, and the transport equations of the system are required, besides its equations of state. Optimization under finite time constraints is an active topic of current research [\textit{R. S. Berry} et al, Thermodynamic optimization of finite time processes (2000); \textit{A. Bejan}, Entropy generation minimization. The methods of thermodynamic optimization of finite-size systems and finite-time processes. Mechanical Engineering Series. Boca Raton, FL: CRC Press (1996; Zbl 0864.76001)]. In this paper, the author extends previous research on finite-time optimization of work to the realm of complex fluids, mainly flowing polymeric fluids (for instance, in processes involving solving or separating polymers from their solution). At each stage of the process, heat and mass transfer through boundary layers play the role of thermal and mechanical resistances in the system model. Total specific work is then extremized at constraints which take into account the dynamics of heat and mass transfer and the rate of work generation. Finite rate limits are then obtained for the work production and consumption, which provide stronger and more realistic bounds than those predicted by classical thermodynamics. Here, optimal work functions are found in terms of initial and final states, of the duration of the process, and (in discrete systems) of the number of stages, for the case of heat transfer coupled with transfer of mass. Finally, it is shown how formal analogies between the entropy production expressions for work assisted and conventional mass transfer operations help in formulating optimization models.
scientific article; zbMATH DE number 1567185