Optimal ratios of the piston speeds for a finite speed irreversible Carnot heat engine cycle

The performance of an irreversible Carnot heat engine cycle is analysed and optimized by using the theory of finite time thermodynamics based on Agrawal's 2009. A finite speed Curzon-Ahlborn engine. European Journal of Physics, 30 (3), 587–592] model of finite piston speed on the four branches and Petrescu et al.’s 2002b. Optimization of the irreversible Carnot cycle engine for maximum efficiency and maximum power through use of finite speed thermodynamic analysis. In: Proceedings of ECOS’2002, 3–5 July, Berlin, Germany, Vol. II, 1361–1368] model of a Carnot cycle engine with the finite rate of heat transfer, heat leakage from heat source to heat sink and irreversibilities caused by finite speed, friction and throttling through the valves. The finite piston speeds on the four branches are further assumed to be different, which is different from the model of constant speed of the piston on the four branches. Expressions of power output and thermal efficiency of the cycle are derived for a fixed cycle period and internal entropy generation rate. Numerical examples show that the curve of power output versus thermal efficiency is loop shaped, and there exist optimal finite piston speeds on the four branches which lead to the maximum power output and maximum thermal efficiency, respectively. The effects of the heat leakage coefficient and internal entropy generation rate on the optimal finite piston speed ratios are discussed.