Abstract
We revisit the problem of optimal power extraction in four-step cycles (two adiabatic and two heat-transfer branches) when the finite-rate heat transfer obeys a linear law and the heat reservoirs have finite heat capacities. The heat-transfer branch follows a polytropic process in which the heat capacity of the working fluid stays constant. For the case of ideal gas as working fluid and a given switching time, it is shown that maximum work is obtained at Curzon-Ahlborn efficiency. Our expressions clearly show the dependence on the relative magnitudes of heat capacities of the fluid and the reservoirs. Many previous formulae, including infinite reservoirs, infinite-time cycles, and Carnot-like and non-Carnot-like cycles, are recovered as special cases of our model.
Highlights
Curzon-Ahlborn efficiency, ηCA = 1 − T2/T1, where T1 and T2 are the reservoir temperatures [1], is regarded as a landmark result of finite-time thermodynamics
The heat cycle has two adiabatic steps and in the remaining two steps the working fluid follows a polytropic process with a constant heat capacity
It is observed that some common heat cycles such as Otto cycle, Joule-Brayton cycle, and Carnot cycle can be incorporated as special cases of this model
Summary
Curzon-Ahlborn efficiency, ηCA = 1 − T2/T1, where T1 and T2 are the reservoir temperatures [1], is regarded as a landmark result of finite-time thermodynamics It models the effect of irreversibilities due to finite rate of heat transfer on the performance of heat engines. We revisit the problem of optimal performance with “linear” irreversibilities of finite time and finite heat reservoirs in classical models of engines This question was addressed in [7] using a Lagrangian formalism, for a one-component working fluid without assuming an equation of state. Gordon [8] used an ancillary device of intermediate reservoirs to arrive at a closed form solution It was shown [8] that for Carnot-like engines, finiteness of reservoirs has no effect on the efficiency at maximum power, and it is still at Curzon-Ahlborn efficiency. The explicit expressions of work for these special cases clearly show that the irreversibilities of finite time and/or finite reservoirs reduce the maximum amount of work extracted as compared with infinite time and infinite reservoirs cases
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