Abstract
In this article a Novikov engine with fluctuating hot heat bath temperature is presented. Based on this model, the performance measure maximum expected power as well as the corresponding efficiency and entropy production rate is investigated for four different stationary distributions: continuous uniform, normal, triangle, quadratic, and Pareto. It is found that the performance measures increase monotonously with increasing expectation value and increasing standard deviation of the distributions. Additionally, we show that the distribution has only little influence on the performance measures for small standard deviations. For larger values of the standard deviation, the performance measures in the case of the Pareto distribution are significantly different compared to the other distributions. These observations are explained by a comparison of the Taylor expansions in terms of the distributions’ standard deviations. For the considered symmetric distributions, an extension of the well known Curzon–Ahlborn efficiency to a stochastic Novikov engine is given.
Highlights
Power stations that use heat to produce electricity can be understood in principle as heat engines receiving heat from a hot reservoir with temperature TH and releasing heat to a cold reservoir with temperature TL
That turned out to be more realistic than the Carnot one. This term is often referred to as Curzon–Ahlborn efficiency, as Curzon and Ahlborn got the same expression for a slightly different irreversible engine a few years later [5]. These pioneer articles led to Endoreversible Thermodynamics [6,7,8]
Thermodynamics point of view, the Novikov engine can be considered as a reversible Carnot engine working in a steady state mode and transforming an incoming heat flux qH into usable power P
Summary
In 1957, the Russian scientist Novikov took those irreversibilities in his model of a heat engine into account by considering a linear heat transport law between the hot heat reservoir and the energy transformation process [3,4] In this way, he could derive an expression for the r. That turned out to be more realistic than the Carnot one This term is often referred to as Curzon–Ahlborn efficiency, as Curzon and Ahlborn got the same expression for a slightly different irreversible engine a few years later [5]. These pioneer articles led to Endoreversible Thermodynamics [6,7,8].
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