On the basis of introducing the origin and development of finite time thermodynamics (FTT), this paper reviews the progress in FTT optimization for internal combustion engine (ICE) cycles from the following four aspects: the studies on the optimum performances of air standard endoreversible (with only the irreversibility of heat resistance) and irreversible ICE cycles, including Otto, Diesel, Atkinson, Brayton, Dual, Miller, Porous Medium and Universal cycles with constant specific heats, variable specific heats, and variable specific ratio of the conventional and quantum working fluids (WFs); the studies on the optimum piston motion (OPM) trajectories of ICE cycles, including Otto and Diesel cycles with Newtonian and other heat transfer laws; the studies on the performance limits of ICE cycles with non-uniform WF with Newtonian and other heat transfer laws; as well as the studies on the performance simulation of ICE cycles. In the studies, the optimization objectives include work, power, power density, efficiency, entropy generation rate, ecological function, and so on. The further direction for the studies is explored.

An improved irreversible closed modified simple Brayton cycle model with one isothermal heating process is established in this paper by using finite time thermodynamics. The heat reservoirs are variable-temperature ones. The irreversible losses in the compressor, turbine, and heat exchangers are considered. Firstly, the cycle performance is optimized by taking four performance indicators, including the dimensionless power output, thermal efficiency, dimensionless power density, and dimensionless ecological function, as the optimization objectives. The impacts of the irreversible losses on the optimization results are analyzed. The results indicate that four objective functions increase as the compressor and turbine efficiencies increase. The influences of the latter efficiency on the cycle performances are more significant than those of the former efficiency. Then, the NSGA-II algorithm is applied for multi-objective optimization, and three different decision methods are used to select the optimal solution from the Pareto frontier. The results show that the dimensionless power density and dimensionless ecological function compromise dimensionless power output and thermal efficiency. The corresponding deviation index of the Shannon Entropy method is equal to the corresponding deviation index of the maximum ecological function.

A model of a multielement thermoelectric refrigerator with another linear heat transfer law, the linear phenomenological heat transfer law $Q\propto \Delta (1/T)$, is established. The refrigerating capacity and coefficient of performance (COP) are analyzed and optimized. The junction temperature solution equations are derived. The optimum electrical currents and thermal conductance allocation are discussed. The influences of thermoelectric element quantity and refrigerating temperature difference on the optimum performances and optimum electrical currents are analyzed. The results show that different optimization objectives have different requirements for the distribution of electrical current and thermal conductance. The refrigeration capacity is not proportional to the number of thermoelectric elements. It is found that the refrigerating capacity can be achieved only when the number of thermoelectric elements is matched for fixed external heat exchangers. The input electrical current and the allocation of the thermal conductance between the two heat exchangers can be optimized synchronously to achieve maximum refrigerating capacity or maximum COP. Performance is compared with that with a Newtonian heat transfer law. The influences of the Thomson effect are also examined. Performance of the refrigerator with Newtonian heat transfer law is higher than that of the refrigerator with linear phenomenological heat transfer law. The Thomson effect can improve the performance of the refrigerator.

Variation trends of dimensionless power density (PD) with a compression ratio and thermal efficiency (TE) are discussed according to the irreversible Atkinson cycle (AC) model established in previous literature. Then, for the fixed cycle temperature ratio, the maximum specific volume ratios, the maximum pressure ratios, and the TEs corresponding to the maximum power output (PO) and the maximum PD are compared. Finally, multi-objective optimization (MOO) of cycle performance with dimensionless PO, TE, dimensionless PD, and dimensionless ecological function (EF) as the optimization objectives and compression ratio as the optimization variable are performed by applying the non-dominated sorting genetic algorithm-II (NSGA-II). The results show that there is an optimal compression ratio which will maximize the dimensionless PD. The relation curve of the dimensionless PD and compression ratio is a parabolic-like one, and the dimensionless PD and TE is a loop-shaped one. The AC engine has smaller size and higher TE under the maximum PD condition than those of under the maximum PO condition. With the increase of TE, the dimensionless PO will decrease, the dimensionless PD will increase, and the dimensionless EF will first increase and then decrease. There is no positive ideal point in Pareto frontier. The optimal solutions by using three decision-making methods are compared. This paper analyzes the performance of the PD of the AC with three losses, and performs MOO of dimensionless PO, TE, dimensionless PD, and dimensionless EF. The new conclusions obtained have theoretical guideline value for the optimal design of actual Atkinson heat engine.

Constructal optimization of a plate condenser with fixed heat transfer rate and effective volume in ocean thermal energy conversion (OTEC) system is performed based on constructal theory. Optimizations of entropy generation rate ( ${\dot{S}}_{\mathrm{g}}$ ) in heat transfer process and total pumping power ( $P_{\mathrm{sum}}$ ) due to friction loss are two conflicting objectives for a plate condenser. With the conventional optimization method, the plate condenser is designed by taking a composite function (CF) considering both ${\dot{S}}_{\mathrm{g}}$ and $P_{\mathrm{sum}}$ as optimization objectives, and employing effective length, width, and effective number of heat transfer plates as design variables. Effects of structural parameters of the plate condenser and weighting coefficient of CF on design results are investigated. With a multi-objective genetic algorithm, the plate condenser is designed by simultaneously optimizing ${\dot{S}}_{\mathrm{g}}$ and $P_{\mathrm{sum}}$ , and the Pareto optimal set is obtained. The results demonstrate that CFs after primary and twice-constructal optimizations are respectively reduced by 7.8% and 9.9% compared with the initial CF, and the effective volume of the plate condenser has a positive impact on the twice minimum CF. Furthermore, the Pareto optimal set can provide better selections for performance optimizations of plate condensers.

One or more isothermal heating process was introduced to modify single and regenerative Brayton cycles by some scholars, which effectively improved the thermal efficiency and significantly reduced the emissions. To analyze and optimize the performance of this type of Brayton cycle, a regenerative modified Brayton cycle with an isothermal heating process is established in this paper based on finite time thermodynamics. The isothermal pressure drop ratio is variable. The irreversibilities of the compressor, turbine and all heat exchangers are considered in the cycle, and the heat reservoirs are variable-temperature ones. The function expressions of four performance indexes; that is, dimensionless power output, thermal efficiency, dimensionless power density and dimensionless ecological function are obtained. With the dimensionless power density as the optimization objective, the heat conductance distributions among all heat exchangers and the thermal capacitance rate matching among the working fluid and heat reservoir are optimized. Based on the NSGA-II algorithm, the cycle’s double-, triple- and quadruple-objective optimization are conducted with the total pressure ratio and the heat conductance distributions among heat exchangers as design variables. The optimal value is chosen from the Pareto frontier by applying the LINMAP, TOPSIS and Shannon entropy methods. The results show that when the pressure ratio in the compressor is less than 12.0, it is beneficial to add the regenerator to improve the cycle performance; when the pressure ratio is greater than 12.0, adding the regenerator will reduce the cycle performance. For single-objective optimization, the four performance indexes could be maximized under the optimal pressure ratios, respectively. When the pressure ratio is greater than 9.2, the cycle is simplified to a closed irreversible simple modified Brayton cycle with one isothermal heating process and coupled to variable-temperature heat reservoirs. Therefore, when the regenerator is used, the range of pressure ratio is limited, and a suitable pressure ratio should be selected. The triple objective (dimensionless power output, dimensionless power density and dimensionless ecological function) optimization’ deviation index gained by LINMAP or TOPSIS method is the smallest. The optimization results gained in this paper could offer some new pointers for the regenerative Brayton cycles’ optimal designs.