Optimal configuration of a class of endoreversible heat engines with linear phenomenological heat transfer law [q∝Δ(T−1)]

Abstract

Optimal configuration of a class of endoreversible heat engines with fixed duration, input energy, and linear phenomenological heat transfer law [q∝Δ(T−1)] has been determined. The optimal cycles that maximize the efficiency and the power output of the engine have been obtained using optimal-control theory, and the differential equations are solved by using Taylor series expansion. It is shown that the optimal cycle for maximum efficiency has eight branches including two isothermal branches, four maximum-efficiency branches, and two adiabatic branches, and that the optimal cycle for maximum-power output has six branches including two isothermal branches, four maximum-power branches, and without an adiabatic branch. The interval of each branch has been obtained, as well as the solutions of the temperatures of heat reservoirs and working fluid. Numerical examples are given. The obtained results are compared with those obtained with Newton’s heat transfer law [q∝Δ(T)] for maximum-efficiency and maximum-power output objectives.

The optimal path of piston motion for Otto cycle with linear phenomenological heat transfer law

“…(33), (34) and (36), the same set of differential equations as that obtained for the case of without acceleration constraint is obtained. On this basis one can conclude that the optimal trajectory with acceleration constraint on the power stroke is a three-branch path, i.e.…”

“…Song et al [33][34][35] determined the optimal configurations of endoreversible heat engines for maximum efficiency objective and maximum power output objective with linear phenomenological heat transfer law [ 1 ( ) q T − ∝ Δ ] [33] and those for maximum power output with fixed duration and radiative heat transfer law [ [34,35] , and derived the results different from those obtained by Rubin [13] . Chen et al [36] and Song et al [37] determined the optimal configurations of expansion process of a heated working fluid in the piston cylinder with linear…”

Optimal paths for a light-driven engine with a linear phenomenological heat transfer law

“…Heat transfer laws not only have significant influences on the performance of given thermodynamic processes [31][32][33][34][35][36][37], but also influence the optimal configurations of thermodynamic processes for the given optimization objectives. Song et al [38][39][40][41] and Chen et al [42] determined the optimal configurations of endoreversible heat engines for maximum power output objective and maximum efficiency objective with linear phenomenological heat transfer law [ ( ) [38], and those for maximum power output objective [39] and maximum efficiency objective [40] with the radiative heat transfer law [ ( )…”

Non-Instantaneous Adiabats in Finite Time

“…Particularly, the optimal configuration of heat engines was studied (Rubin, 1979a), and it was introduced a procedure in which the power output of cycle is taken as a function of the compression ratio by using the parameter ~ , where max V and min V are the maximum and the minimum volumes spanned in the cycle, respectively (Gutkowicz-Krusin et al, 1978). More recently, this subject has been also studied by other authors (Badescu, 2004;Amelkin, et al, 2004Amelkin, et al, , 2005Song et al, 2006Song et al, , 2007. Even more Angulo-Brown (1991) introduced an optimization criterion of merit for the Curzon and Ahlborn cycle taking into account entropy production, the ecological criterion, through the function,…”