Time, entropy generation, and optimization in low-dissipation heat devices

Abstract

We present new results obtained from the Carnot-like low-dissipation model of heat devices when size-and time-constraints are taken into account, in particular those obtained from the total cycle time and the contact times of the working system with the external heat reservoirs. The influence of these constraints and of the characteristic time scale of the model on the entropy generation allows for a clear and unified interpretation of different energetic properties for both heat engines and refrigerators (REs). Some conceptual subtleties with regard to different optimization criteria, especially for REs, are discussed. So, the different status of power input, cooling power, and the unified figure of merit χ are analyzed on the basis of their absolute or local role as optimization criteria.

Maximum efficiency of low-dissipation heat engines at arbitrary power

“…With decreasing α, the partially optimised power (8) monotonously interpolates between 0 (attained for α = 1, t * i,α = ∞ and ε * α = ε C /(2 + ε C ), note that this process is not reversible even-though the cycle duration diverges) and its maximum, reached for α = α * = 0 [61]. The resulting maximum power and the corresponding duration of the isothermal branches thus read…”

“…A natural starting point for calculating maximum COP at fixed power is thus determination of P for LD refrigerators, which was done in Ref. [61]. Since peculiarities of the derivation strongly affect qualitative behavior of maximum COP at fixed power, we review it in detail.…”

“…and thus it exhibits a discontinuity at σ = 0 [61]. It is caused by the requirement α * = 0, which means that the duration of the hot isotherm is negligible compared to that of the cold one.…”

Carnot-Like Heat Engines Versus Low-Dissipation Models

“…The signs −(+) take into account the direction of the heat fluxes from (toward) the hot (cold) reservoir in such a way that Q c and Q h are positive quantities. Then, the total entropy generation is given by At this point, it is helpful to use the dimensionless variables defined in [40]: α ≡ t c /t, Σ c ≡ Σ c /Σ T and t ≡ (t ∆S)/Σ T , where t = t h + t c and Σ T ≡ Σ h + Σ c . In this way, it is possible to define a characteristic total entropy production per unit time for the LD-model aṡ…”

“…In particular, the CA-efficiency is recovered in the LD-model under the assumption of symmetric dissipation. Recently, a description of the LD model in terms of characteristic dimensionless variables was proposed in [40][41][42]. From this treatment, it is possible to separate efficiency-power behaviors typical of CA-endoreversible engines as well as irreversible engines according to the imposed time constraints.…”