Abstract
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 610<SUP>o</SUP>C, 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.
Highlights
The Carnot engine constitutes the basic heat engine model having reversible processes and yields upper bound of thermal efficiency for heat engines working between two heat reservoirs at constant temperatures
When the power output is limited by the heat transfer rates between the heat reservoirs and the working substance, the heat engine is defined as endo-reversible
The physical solution of Eq 2 gives the efficiency of golden section Carnot heat engine for the case that the heat rejection is larger than the work output
Summary
The Carnot engine constitutes the basic heat engine model having reversible processes and yields upper bound of thermal efficiency for heat engines working between two heat reservoirs at constant temperatures. The main purpose of their paper was to point out and find some applications of the golden ratio and of Fibonacci numbers in differential geometry They studied a structure defined on a class of Riemannian manifolds, called by them a golden structure. More ever he claims that Eggs, an apple blossom, a human face, a seashell—all embody golden section proportions He believes that the golden section is a simple tool that may be used to enhance the meaning and beauty of an architectural work. Lefebvre and Efremov considered the problem of double geometric progression and golden section in the decay profiles of bursts [32] They found that for bursts lasting less than 25sec and if two significant peaks are observed in the power spectrum, the ratio of their centroid frequencies is approximately constant and equal to 1.59.
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