Optimal work flux in sequential systems with complex heat exchange

We extend here our earlier idea of a finite-time exergy [S. Sieniutycz, M. von Spakovsky, Energy & Conversion Management 39 (1998) 1423–1447; S. Sieniutycz, Open Sys. Information Dyn. 5 (1998) 369–390; S. Sieniutycz, Int. J. Heat Mass Transfer 41 (1998) 183–195] to fluids characterized by complex exchange of heat and to those with coupled heat and mass transfer. Functionals are formulated which express work delivered from (or consumed by) a non-equilibrium system composed of a complex fluid, a thermal machine and the environment (acting as an infinite reservoir). The complex fluid constitutes a resource of a finite flow or amount, and work production (consumption) takes place sequentially, in stages of “endoreversible” thermal machines. Boundary layers play the role of resistances for heat and mass transfer, and cause the entropy production at each stage of the operation. For the fluid at flow, total specific work is extremized at constraints which take into account dynamics of heat and mass transport and rate of work generation. Finite-rate model subsumes irreversible production of entropy and losses of classical work potential, caused by the resistances and explains restrictive applicability of classical thermodynamic bounds. Formal analogies between the entropy production expressions for work-assisted and conventional exchange operations help to formulate optimization models of the former. Optimal work potentials, which incorporate a residual minimum of the entropy production, are analyzed in terms of end states, duration and (in discrete processes) number of stages.