An analytical study of the endoreversible Curzon–Ahlborn cycle for a non-linear heat transfer law

Abstract

Abstract In the present article, an endoreversible Curzon–Ahlborn engine is studied by considering a non-linear heat transfer law, particularly the Dulong–Petit heat transfer law, using the `componendo and dividendo' rule as well as a simple differentiation to obtain the Curzon–Ahlborn efficiency as proposed by Agrawal in 2009. This rule is actually a change of variable that simplifies a two-variable problem to a one-variable problem. From elemental calculus, we obtain an analytical expression of efficiency and the power output. The efficiency is given only in terms of the temperatures of the reservoirs, such as both Carnot and Curzon–Ahlborn cycles. We make a comparison between efficiencies measured in real power plants and theoretical values from analytical expressions obtained in this article and others found in literature from several other authors. This comparison shows that the theoretical values of efficiency are close to real efficiency, and in some cases, they are exactly the same. Therefore, we can say that the Agrawal method is good in calculating thermal engine efficiencies approximately.