A universal expression for optimum specific work of reciprocating heat engines having endoreversible carnot efficiencies

Irreversible heat transfer (finite time) analysis is used to obtain the optimum thermodynamic specific work potential at maximum power for various practical reciprocating cycles having endoreversible Carnot efficiencies. The theory of finite‐time thermodynamics for reciprocating endoreversible cycles with heat transfer irreversibilities gives rise to an optimum efficiency at maximum power output, of η=1−(T_L/T_H)^0·5 for Carnot‐like cycles in contrast to the upper limit for Carnot‐like cycles of η=1−(T_L/T_H) obtained from infinite‐time thermodynamics. It is shown here that, additionally, for this same general family of regenerative reciprocating cycles which includes the Stirling, the Ericsson and the reciprocating Carnot cycle, the finite‐time optimum specific work output at maximum power, (w_opt), is exactly half of that obtained for infinite‐time reversible cycles (Carnot work, w_rev) operating between the same temperature limits (i.e., w_opt=½w_rev). To accomplish this, the analysis makes use of time symmetry to minimize overall cycle time and to thus optimize net cycle power. Based on linear heat transfer laws, the expression for optimum specific work is shown to be independent of heat conductances. Moreover, this optimum specific work output is the same expression for all of the members of this family of cycles. This analysis makes use of the ideal gas model with constant specific heats, though the results are shown to be universal for the Carnot cycle for vapours and real gases. A sample calculation is given which shows that while operating under the same optimized conditions, the endoreversible Stirling engine will have the same thermal efficiency as the endoreversible Ericsson, but will have a higher optimum power output. The optimum power of the reciprocating endoreversible Carnot engine will be superior to both. Copyright © 1999 John Wiley & Sons, Ltd.     

Effects of unequal finite piston speeds on the optimal performances of endoreversible Carnot refrigeration and heat pump cycles

The performances of endoreversible Carnot refrigeration and heat pump cycles with loss of heat resistance and finite piston speeds are analysed and optimized by using the combination of finite time thermodynamics, finite speed thermodynamics and direct method. The unequal finite piston speed model on four branches is adopted. Expressions of cooling load of endoreversible Carnot refrigeration cycle and of heating load of endoreversible Carnot heat pump cycle are derived with a fixed cycle period and unequal finite piston speeds on the four branches. Numerical examples show that there exist optimal expansion ratios, which lead to maximum cooling load and maximum heating load for the fixed coefficient of performance (COP), respectively. The maximum cooling load, maximum heating load, optimal ratios of finite piston speeds and optimal hot- and cold-side working fluid temperatures versus COP characteristics for the endoreversible Carnot refrigeration and heat pump cycles are obtained. Moreover, the effects of design parameters on the performances of the two cycles are discussed.     

Cogeneration of power and heat by using endoreversible Carnot engine

The annual worth for production of heat and power of an endoreversible Carnot engine is analyzed by using the methods of finite time thermodynamics. It was found that, in order to obtain the maximum annual worth of production of heat and power, in the design of such systems, the heat exchangers on the hot and cold sides of the Carnot engine must have equal products of their size and heat transfer coefficient. Also, for the maximum annual worth, the ratio of the lower and higher temperatures of the Carnot engine should have its optimal value.     

Exergoeconomic performance of an endoreversible Carnot heat pump with complex heat transfer law

The finite-time exergoeconomic performance of an endoreversible Carnot heat pump with a complex heat transfer law, including generalized convective heat transfer law and generalized radiative heat transfer law q∝ (Δ T ⁿ ) ^m , is investigated in this paper. The focus of this paper is to obtain the compromised optimization between economics (profit) and the energy utilization factor (coefficient of performance, COP) for the endoreversible Carnot heat pump, by searching the optimum COP at maximum profit, which is termed as the finite-time exergoeconomic performance bound. The obtained results include those obtained in much of the literature and can provide some theoretical guidance for the design of practical heat pumps.     

Finite-time thermodynamic analysis of a Carnot engine with internal irreversibility

This paper extends Curzon and Ahlborn's result which gives a thermodynamic efficiency of an endoreversible Carnot engine. It is shown that the internal irreversibilities of a Carnot engine can be characterized by a single parameter representing the ratio of two entropy differences. Named the cycle irreversibility parameter, the presence of this parameter in the equations for maximum power and efficiency clearly shows that an engine with internal irreversibilities delivers less power and has a lower efficiency than an endoreversible engine.     

A variational optimization of a finite-time thermal cycle with a nonlinear heat transfer law

In this paper we use a variational approach to study an endoreversible Curzon–Ahlborn–Novikov (CAN) heat engine under both maximum power and maximum ecological function conditions. By means of this procedure we analyze the performance of a CANheat engine with a nonlinear heat transfer law (the Dulong–Petit law) to describe the heat exchanges between the working substance and its thermal reservoirs. Our results are consistent with previous ones obtained by means of other procedures. In addition, we obtain expressions for the temperatures of the isothermal branches of the working fluid under maximum power conditions. Finally, we present an expression for a kind of nonendoreversible Carnot efficiency.     

Study on optimal performance and working temperatures of endoreversible forward and reverse carnot cycles

The connection between the expressions of optimization performances of Carnot heat engines, refrigerators and heat pumps, which operate subject to irreversible heat flow, is studied. We consider the endoreversible forward and reverse Carnot cycles and analyse the expressions which relate efficiency, refrigeration and heating coefficients to power, refrigeration and heating rates, respectively. It is found and proved that when one of the optimal relations is derived the others are also determined, and give the unified formulation of the related optimal working temperatures of the forward and reverse Carnot cycles by isentropic temperature ratio exponent. Finally, several new optimal performance relations are derived for forward and reverse Carnot cycles under nonlinear heat transfer, and some major results in the references are easily deduced and unified in this paper.     

Model of optimized solar heat engine operating on Mars

An endoreversible Carnot cycle is used to describe heat engine operation. This provides upper limits for real performance. The output power is maximized. Meteorological and actinometric data provided by the Viking Lander 1 are used as inputs. Four strategies of collecting solar energy are considered. Results concerning the following three parameters are briefly reported: (1) optimum solar collector surface area, (2) optimum solar collector temperature and (3) maximum output power.     

Effect of heat transfer law on the finite-time exergoeconomic performance of a Carnot refrigerator

The operation of a Carnot refrigerator is viewed as a production process with exergy as its output. The economic optimization of the endoreversible refrigerator is carried out in this paper. The Coefficient of Performance (COP) of the refrigerator is a secondary consideration of the practical engineering effort of maximizing cooling rate and exergy whose goodness is constrained by economical considerations. Therefore, the profit of the refrigerator is taken as the optimization objective. Using the method of finite-time exergoeconomic analysis, which emphasizes the compromise optimization between economics (profit) and the appropriate energy utilization factor (Coefficient of Performance, COP) for finite-time (endoreversible) thermodynamic cycles, this paper derives the relation between optimal profit and COP of an endoreversible Carnot refrigerator based on a relatively general heat transfer law q∝Δ(Tⁿ). The COP at the maximum profit is also obtained. The results obtained involve those for three common heat transfer laws: Newton's law (n=1), the linear phenomenological law in irreversible thermodynamics (n=−1), and the radiative heat transfer law (n=4).     

Effect of the heat transfer law on the finite-time, exergoeconomic performance of heat engines

The efficiency bounds at maximum profit are obtained from finite-time exergoeconomic analysis for three common heat transfer laws: Newton's law (n = 1), a linear pheomenological law in irreversible thermodynamics (n = 1), and the radiative heat law (n = 4). The relation between optimal profit and efficiency of an endoreversible Carnot engine is derived on the basis of the general heat-transfer law q∝Δ(Tⁿ).     

包含6种热机模型的普适内可逆热机循环(火用)经济性能优化

用有限时间热力学方法分析了工作在恒温热源TH、TL之间的普适定常流内可逆热机循环模型的炯经济性能，导出了循环利润率与工质温比、热效率与工质温比的关系式，以及利润率和效率的特性关系，并由数值计算分析了循环过程对循环性能的影响特点。所得结果包含了内可逆Carnot、Diesel、Otto、Atkinson、Brayton和Dual循环的有限时间炯经济性能。     

Optimal performance of a spin quantum Carnot heat engine with multi-irreversibilities

By using quantum master equation, semi-group approach and finite time thermodynamics (FTT), this paper derives the expressions of cycle period, power and efficiency of an irreversible quantum Carnot heat engine with irreversibilities of heat resistance, internal friction and bypass heat leakage, and provides detailed numerical examples. The irreversible quantum Carnot heat engine uses working medium consisting of many non-interacting spin-1/2 systems and its cycle is composed of two isothermal processes and two irreversible adiabatic processes. The optimal performance of the quantum heat engine at high temperature limit is deduced and analyzed by numerical examples. Effects of internal friction and bypass heat leakage on the optimal performance are discussed. The endoreversible case, frictionless case and the case without bypass heat leakage are also briefly discussed.     

Maximum power of an endoreversible intercooled Brayton cycle

This paper describes an application of finite‐time thermodynamics to optimize the power output of endoreversible intercooled Brayton cycles coupled to two heat reservoirs with infinite thermal capacitance rates. The effects of intercooling on the maximum power and maximum‐power efficiency of an endoreversible Brayton cycle are examined. With appropriate temperature ratios of turbines and compressors being used, the maximum power output of an endoreversible intercooled Brayton cycle can be higher than that of an endoreversible simple Brayton cycle without lowering the thermal efficiency. New diagrams for maximum power, maximum‐power thermal efficiency, and optimum temperature ratios of turbines and compressors are reported. Copyright © 2000 John Wiley & Sons, Ltd.     

Performance optimization of a solar driven heat engine with finite-rate heat transfer

An optimal performance analysis for an equivalent Carnot-like cycle heat engine of a parabolic-trough direct-steam-generation solar driven Rankine cycle power plant at maximum power and maximum power density conditions is performed. Simultaneous radiation-convection and only radiation heat transfer mechanisms from solar concentrating collector, which is the high temperature thermal reservoir, are considered separately. Heat rejection to the low temperature thermal reservoir is assumed to be convection dominated. Irreversibilities are taken into account through the finite-rate heat transfer between the fixed temperature thermal reservoirs and the internally reversible heat engine. Comparisons proved that the performance of a solar driven Carnot-like heat engine at maximum power density conditions, which receives thermal energy by either radiation-convection or only radiation heat transfer mechanism and rejects its unavailable portion to surroundings by convective heat transfer through heat exchangers, has the characteristics of (1) a solar driven Carnot heat engine at maximum power conditions, having radiation heat transfer at high and convective heat transfer at low temperature heat exchangers respectively, as the allocation parameter takes small values, and of (2) a Carnot heat engine at maximum power density conditions, having convective heat transfer at both heat exchangers, as the allocation parameter takes large values. Comprehensive discussions on the effect of heat transfer mechanisms are provided.     

考虑热漏影响的热泵装置有限时间热力学性能

本文研究热漏对热泵装置最优性能的影响,导出存在热阻和热漏损失的定常态流不可逆卡诺热泵最佳供热系数与供热率关系,所得结果与仅存在热阻损失时的内可逆卡诺热泵供热系数供热率特性关系有量和质的区别。     

Power optimization of a finite-time Carnot heat engine

The power output of a simple, finite-time Carnot heat engine is studied. The model adopted is a reversible Carnot cycle coupled to a heat source and a heat sink by heat transfer. Both the heat source and the heat sink have finite heat-capacity rates. A mathematical expression is derived for the power output of the irreversible heat engine. The maximum power output is found. The maximum bound provides the basis for designing a real heat engine and for a performance comparison with existing power plants.     

变温热源内可逆中冷回热布雷顿循环功率密度分析

用有限时间热力学方法分析内可逆变温热源中冷回热布雷顿循环,导出了无因次功率密度的解析式,由数值计算给出了燃气轮机功率密度特性,分析了循环中各热力参数对功率密度的影响,并对最大功率工况与最大功率密度工况下的主要参数进行了比较,得出了最大功率密度设计的优点和不足。     

A New Realistic Characteristics of Real Energy Conversion Process: A Contribution of Finite Size Thermodynamics

The perfection of the energy conversion process is currently gauged through a kind of quality indicator that compares the real performance of the process to that of the ideal reversible Carnot process. The criteria resulting from this commonly used approach give a false idea as to the real quality of the energy conversion process. Indeed, the real energy conversion process that generates true energetic power levels is compared to the ideal associated Carnot process, which generates a zero-output power level. The real conversion process implementing finite heat exchanger areas is then compared to the ideal process that needs an infinite heat exchanger area to fulfill the same power requirements. This paper presents a new thermo-economic approach, based on Finite Size Thermodynamics, that is more suitable for qualifying real energy conversion processes. This approach takes into account the external thermodynamic irreversibilities relative to the heat transfer rate through a finite size heat exchanger surface between the external heat sources or sinks and an ideal process without internal thermodynamic irreversibilities. This new approach enables a more realistical evaluation of ideal performances of real energy conversion processes. It makes possible the definition of new criteria that characterize more reasonably the quality of a real thermal process compared with the corresponding endoreversible process the same power duty (performance criterion) or the same involved total heat exchanger surface (technical criterion).     

Exergy optimization for an endoreversible cogeneration cycle

Exergy optimization has been carried out for an endoreversible cogeneration cycle using finite-time thermodynamics. The optimum values of the design parameters of the cogeneration cycle at maximum exergy output were determined. Our model is more general than the endoreversible power cycle found in the literature. The effects of design parameters on exergetic performance are investigated and the results discussed.     

Finite time thermodynamic evaluation of endoreversible Stirling heat engine at maximum power conditions

Maximum power and efficiency at the maximum power point of an endoreversible Stirling heat engine with finite heat capacitance rate of external fluids in the heat source/sink reservoirs with regenerative losses are treated. It was found that the thermal efficiency depends on the regenerator effectiveness and the internal irreversibility resulting from the working fluid for a given value of reservoir temperature. It was also concluded that it is desirable to have larger heat capacity of the heat sink in comparison to the heat source reservoir for higher maximum power output and lower heat input.