Golden Section Heat Engines and Heat Pumps

In this study the efficiency of heat engines and the coefficient of performance of heat pumps are reconsidered following the idea of the golden section ratio. Two models are analyzed: the golden section Carnot cycle and the golden section endo-reversible cycle. The observed expressions for efficiency and coefficient of performance are cast in terms of the golden section ratio. Single (steam turbines[40Wilfried, U., OMMI, vol. 2, issue 3, pp. 1-9, 2003]) and double (combined cycles[Ishikawa, M., Terauchi, M., Komori, T., Yasuraoka, J., Mitsubishi Heavy Industries, Ltd., Technical Review Vol. 45 No. 1, pp. 15-17, 2008]) heat engine cycles are considered. Expressions for the working fluid temperatures at the hot and cold sides are derived. Calculations performed on steam parameters, with the supercritical temperature of 610oC, show that the relative differences of the golden section single heat engine, when compared to the endo-reversible results, fell within the 2- 4% range, with relative power reductions of 15% from the maximum power point. Finally, it was shown that system efficiency differs by approximately 3.6% from the efficiency derived based on the golden section.