Optimal configuration of a class of endoreversible heat engines for maximum efficiency with radiative heat transfer law

Abstract

Optimal configuration of a class of endoreversible heat engines with fixed duration, input energy and radiative heat transfer law (q ∝ Δ(T 4 )) is determined. The optimal cycle that maximizes the efficiency of the heat engine is obtained by using optimal-control theory, and the differential equations are solved by the Taylor series expansion. It is shown that the optimal cycle has eight branches including two isothermal branches, four maximum-efficiency branches, and two adiabatic branches. The interval of each branch is obtained, as well as the solutions of the temperatures of the heat reservoirs and the working fluid. A numerical example is given. The obtained results are compared with those obtained with the Newton's heat transfer law for the maximum efficiency objective, those with linear phenomenological heat transfer law for the maximum efficiency objective, and those with radiative heat transfer law for the maximum power output objective. radiative heat transfer law, endoreversible heat engine, optimal control theory, optimal configuration, generalized thermodynamic optimization There are two standard problems in finite time thermodynamics: one is to determine the objective function limits and the relations between objective functions for the given thermodynamic system, and the other is to determine the optimal thermodynamic process for the given optimization objectives [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] . Procaccia and Ross [21] proved that in all acceptable cycles, an endoreversible Carnot cycle with a larger compression ratio can produce maximum power, i.e., the Curzon-Ahlborn cycle [22] is the optimal configuration with only First and Second Law constraints. Rubin [23,24] found the optimal configurations of endoreversible heat engines with Newton's heat transfer law and different constraints. The optimal configuration with fixed duration for maximum power output is a six-branch cycle, and the optimal configuration with fixed energy input for maximum efficiency is an eight-branch cycle [23] . The results were extended to a class of heat engines with a fixed com-

Entransy dissipation minimization for a class of one-way isothermal mass transfer processes

“…There are two standard problems in finite time thermodynamics: one is to determine the objective function limits and the relations between objective functions for the given thermodynamic system, and another is to determine the optimal thermodynamic process for the given optimization objectives [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. The latter belongs to functional extremum problems and needs to use optimal control theory.…”

Constructal optimization of discrete and continuous-variable cross-section conducting path based on entransy dissipation rate minimization

“…Based on irreversible thermodynamics, some scholars used finite-time thermodynamics (FTT) or entropy generation minimization (EGM) [18][19][20][21][22][23][24][25][26][27][28][29][30] to optimize the heat transfer process, which was also called thermodynamic optimization. The entropy generation minimization is a heat transfer optimization aiming at exergy lost minimization, but the heat transfer mostly focuses on the heat transfer regularity and its transfer speed, not the exergy lost.…”

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 [ ( )…”