Generalized mixed-mode, heat-transfer studies to enhance power and work at optimum power in reciprocating regenerative Stirling-like and Carnot heat engines with interactive finite thermal reservoirs

Abstract

This study explores how to enhance both the power and the efficiency (at optimum power) for the family of reciprocating Stirling-like heat engines (including Carnot) with ideal regeneration and either finite or infinite heat reservoirs. To accomplish this, a generalized mixed-mode, heat-transfer approach is developed and employed at cycle thermal ends. Additionally, the difference in the effect on power optimization of operating with either interactive or non-interactive finite reservoirs is examined. The approach developed makes use of a unique time symmetry procedure to minimize cycle time. This procedure ensures the proper allocation of the hot- and cold-end, heat-exchanger capacitance. Furthermore, time symmetry ensures the concurrent employment of the first and second laws of thermodynamics. This in turn guarantees the minimization of internal entropy generation and the maximization of specific cycle work (for a given set of operating temperatures). The general case formulation produces a semi-decoupling of the solution expressions for the upper and lower power-optimized operating temperatures. This semi-decoupling allows the use of various combinations of single and mixed-mode, heat-transfer arrangements at the hot and cold thermal ends of these cycles. Hence, semi-decoupling permits examination of the power and work potentials of different combinations of heat modes under power-optimized conditions. The results point conclusively to the strong preference of using the radiation mode (with or without transfer by the linear mode, but better with as little as possible) in the high-temperature-end, heat-exchange process and of using essentially only linear modes at the low-temperature end of the cycle (i.e. only as small a percentage as possible by radiation). Such cycles are found capable of exceeding the one-half ideal work limit of power-optimized cycles that exclusively employ linear modes at both thermal ends (i.e. Wopt greater than ½Wrev). Also, the efficiency at optimum power of these cycles exceeds the Curzon and Ahlborn efficiency (i.e. opt greater than 1-(TL/TH)0.5). No other combination of heat-transfer modes is found capable of exceeding either the Curzon and Ahlborn efficiency or the ½Wrev limit for power-optimized cycle work for such cycles. Finally, comparing the effects of interactive and non-interactive heat reservoirs on power optimization shows that the heat-exchanger operation (outlet temperatures) should also be included in the overall optimization procedure.