Optimal path of piston motion of irreversible Otto cycle for minimum entropy generation with radiative heat transfer law

The performance of an Otto cycle heat engine with internal and external irreversibilities of heat transfer and friction, in which the heat transfer between the working fluid and the environment obeys radiative heat transfer law [q∝Δ(T4)], is studied in this paper using finite time thermodynamics. The optimal piston motion trajectory for minimising entropy generation per cycle is derived for the fixed total cycle time and fuel consumed per cycle. Optimal control theory is applied to determine the optimal piston trajectories for the cases with and without piston acceleration constraint on each stroke and the optimal distribution of the total cycle time among the strokes. The optimal piston motion with acceleration constraint for each stroke consists of three segments, including initial maximum acceleration and final maximum deceleration boundary segments respectively. Numerical examples for optimal configuration are provided, and the obtained results are compared with those obtained with Newton’s heat transfer law [q∝Δ(T)] and linear phenomenological heat transfer law q∝Δ(T−1). The results also show that optimising the piston motion can reduce the entropy generation of the engine by >28%. This is primarily due to the decrease in entropy generation that arised from heat transfer loss on the initial portion of the power stroke.