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Limiting power in imperfect systems with fluid flow

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We develop a simple formula for the efficiency of imperfect energy converters and then apply it to the irreversible extension of the classical problem of maximum mechanical work. The work is the cumulative effect obtained from a system composed of: a resource fluid at flow, a set of sequentially arranged engines, and an infinite bath. In the engine mode the fluid's temperature T decreases along the path, thus tending to the bath temperature [T^e]. In the heat-pump mode the process direction is inverted and the fluid is heated (thermal utilization). In a related classical problem the process rates vanish due to the reversibility; here, however, finite rates und unavoidable losses of the work potential are admitted. The method of variational calculus leads to a finite-rate generalization of the maximum-work potential called the finite-rate exergy. This finite-rate exergy is a function of the usual thermal coordinates and the overall number of transfer units tau. The resulting bounds onthe work delivered or supplied are stronger than the reversible bounds predicted by the classical thermodynamics.
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