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[en] Highlights: • A performance analysis is carried out for an irreversible Dual–Atkinson cycle. • A comprehensive numerical analysis is conducted. • The influences of engine design parameters on the performance are examined. • The results obtained could be useful for the engine designers. - Abstract: A comprehensive performance analysis depending on the non-dimensional power output, effective power, non-dimensional power density, effective power density, thermal efficiency, effective efficiency, maximum power output (MP), maximum power density (MPD) and maximum thermal efficiency (MEF) criteria has been conducted for the irreversible Dual–Atkinson cycle engine (DACE) which includes internal irreversibilities by virtue of the irreversible-adiabatic compression process, expansion process, heat transfer and friction losses. In the analyses, Classical Thermodynamics Modeling (CTM) and a new realistic Finite-Time Thermodynamics Modeling (FTTM) have been used. The power output, power density and thermal efficiency are obtained with respect to the variation of the pressure ratio, cut-off ratio, stroke ratio, Atkinson cycle ratio, cycle pressure ratio and cycle temperature ratio. The effects of the engine design and operating parameters on the general and maximum performances of the DACE have been investigated with respect to the variation of the cycle pressure ratio and cycle temperature ratio in the CTM section. The influences of the other engine design and operating parameters such as engine speed, mean piston speed, stroke length, equivalence ratio, compression ratio and bore–stroke length ratio on the engine performance have been investigated in the FTTM section. In addition, the energy losses depending on incomplete combustion, friction, heat transfer and exhaust output have been described as fuel input energy. In order to obtain realistic results, temperature-dependent specific heats for working fluid have been used. The DACE is a new concept for internal combustion engines and just a few studies have been carried out. This study presents new contributions to the analysis of the Dual–Atkinson cycle engines in terms of the effects of engine design and operating parameters on the engine performance. Because CTM, FTTM, energy losses, power density and MPD analyses, for the DACE are newly presented just in this study.