Entropy Production Analysis in Irreversible Heat Engine Cycles

Abstract

Classical Carnot analysis sets an upper bound on heat-engine efficiency but says nothing about the power a real
engine can deliver, since a reversible cycle requires infinitely slow heat exchange. We present a systematic
entropy-production analysis of finite-time, internally irreversible heat engine cycles operating between a hot
reservoir at 650 K and a cold reservoir at 310 K, modelling irreversibility sources separately: finite-rate heat
conduction across both heat exchangers, internal friction represented by a cycle irreversibility factor, and heat
leakage bypassing the working fluid. Across 48 operating points spanning cycle times from 0.8 s to 12 s, total
specific entropy production ranged from 0.041 to 0.318 kJ/(kg K), and power output was maximized at an
intermediate cycle time of 2.6 s, where entropy production reached 0.187 kJ/(kg K), 59% of its value at the fastest
cycle time tested. Decomposing the entropy budget showed that finite-rate heat conduction across the hot-side
exchanger accounted for 44-52% of total entropy production across the tested range, exceeding the combined
contribution of internal friction (28-33%) and heat leakage (16-24%) at every operating point. Second-law
(exergetic) efficiency peaked at 0.71 near the maximum-power condition and declined on both sides, falling to 0.52
at the fastest cycle time and 0.79 at the slowest, tracing out the expected power-efficiency trade-off curve but with a
maximum-power operating point that sacrificed only 8 percentage points of exergetic efficiency relative to the
near-reversible limit while delivering more than four times the power output. A sensitivity analysis varying hot-side
heat-exchanger conductance by ±30% shifted the maximum-power cycle time by less than 0.4 s but changed peak
power output by 21%, identifying hot-side conductance as the single design parameter with the greatest leverage
over achievable power for a fixed total entropy-production budget. These results provide a quantitative basis for
selecting heat-exchanger conductances and cycle timing in real power plants that must balance thermodynamic
efficiency against the practical requirement of finite power delivery.