Finite-Time Thermodynamics

The second step historically in the approach discussed here was a sort of test case, the analysis of a simple model system that consisted of a Carnot cycle that operated in short, finite-time steps [2]. In this work, the system operates through a series of small, discrete steps in which the pressure changes discontinuously and the system is connected to its heat reservoirs by finite heat conductances. The results gave the values and conditions for maximum effectiveness, the ratio of the work actually done, per cycle, to the total change of 

---

Durmayaz, A. Sogut, S. Sahin, B., and Yavuz, H., 2004, Optimization of thermal systems based on finite-time thermodynamics and thermoeconomics, Progress in Energy and Comb. Sci. 30 175-217. 

Szargut, I, 1990, In Finite-Time Thermodynamics and Thermoeconomics, eds. By S. Sieniut-cyz, P. Salamon, Taylor Francis, New York. 

Classical thermodynamics is based on the concept of equilibrium. Time is not involved in conventional engineering thermodynamic textbooks. Heat transfer deals with rate of energy transfer, but does not cover cycles. There is a gap between thermodynamics and heat transfer. The chapter Finite-Time Thermodynamics bridges the gap between thermodynamics and heat transfer. 

Finite-time thermodynamics is an extension to traditional thermodynamics in order to obtain more realistic limits to the performance of real processes, and to deal with processes or devices with finitetime characteristics. Finite-time thermodynamics is a method for the modeling and optimization of real devices that owe their thermodynamic imperfection to heat transfer, mass transfer, and fluid flow irreversibility. 

A literature survey of finite-time thermodynamics is given by Wu, Chen, and Chen (Wu, C., Chen, L., and Chen, J., Recent Advances in Finite-Time Thermodynamics, Nova Science Publ. Inc., New York, 1999). 

Engineering thermodynamic cycle analysis is based on the concept of equilibrium and does not deal with time. Heat transfer does deal with time but not cycle analysis. Finite-time thermodynamics fills in a gap that has long existed between equilibrium thermodynamics and heat transfer. 

Finite-time thermodynamies is one of the newest and most challenging areas in thermodynamics. A book entitled Recent Advances in Finite Time Thermodynamics (editors Chih Wu, Lingen Chen, and Jincan Chen, Nova Science Publishers, Inc., New York, USA, 1999, ISBN 1-56072-644-4) provides results from research, which continues at an impressive rate. The book contains many academic and industrial papers that are relevant to current problems and practice. The numerous contributions from the international thermodynamic community are indicative of the continuing global interest in finite-time thermodynamics. 

The readers should find the papers listed in the Bibliography informative and useful for analysis and design of various finite-time thermodynamic cycles. It is hoped that these papers will provide interest and encouragement for further study in the area of finite-time thermodynamics. 

Wu, C. and Kiang, R.L., Finite time thermodynamic analysis of a Carnot engine with internal irreversibility. Energy The International Journal, 17(12),... 

Chen, L., Sun, F., and Wu, C., Performance analysis for a real closed regenerated Brayton cycle via methods of finite-time thermodynamics. International Journal of Ambient Energy, 20(2), 95-104, 1999. 

Other finite-time thermodynamic cycle literature including Atkinson, combined and cascaded, Diesel, dual, Ericsson, Otto, Rallis, and Stirling cycles are provided in the following ... 

Wu, C., Finite-time thermodynamic analysis of a two-stage combined heat pump system. International Journal of Ambient Energy, 16(4), 205-208, 1995. 

Blank, D.A. and Wu, C., Performance potential of a terrestrial solar-radiant Ericsson power cycle from finite-time thermodynamics. International Power and Energy Systems, 15(2), 78-84, 1995. 

Geometrical tools prove useful in addressing various problems of finite-time thermodynamics and optimal control theory. These methods also have potential applicability to thermodynamic-type applications in subjects ranging from the chemical, biological, and materials sciences to information theory. Efficient vector-algebraic tools allow such applications to be extended to systems of virtually unlimited complexity, beyond realistic reach of classical methods. 

B. Andresen. Finite-time thermodynamics and simulated annealing. In J. S. Shiner (ed.). Entropy and Entropy Generation (Springer, New York, 2002), pp. 111-28. 

B. Andresen. Minimizing losses—tools of finite-time thermodynamics. In A. Bejan and E. Mamut (eds). Thermodynamic Optimization of Complex Energy Systems (Springer, New York, 1999), p. 411. 

S. Sieniutycz and P. Salamon, Eds., Finite Time Thermodynamics and Thermoeconomics, Advances in Thermodynamics, Vol. 4, Taylor and Francis, 1991. 

One of the important definitions in finite-time thermodynamics is the definition of finite-time availability A given by... 

Keywords finite time thermodynamics, power output, ecological function, efficiency... 

A more realistic cycle than the Carnot cycle is a modified cycle taking into account the processes time of heat transfer between the system and its surroundings, in which the working temperatures are different of those its reservoirs [1], obtaining the efficiency t]CAN =1 Jtc / TH, first found in references [2] and [3], and known as Curzon-Ahlbom-Novikov-Chambadal efficiency. At present, the duration of heat transfer processes is important. Based on this model, at the end of the last century, a theory was developed as an extension of classical equilibrium thermodynamics, the finite time thermodynamics, in which the duration of the exchange processes heat becomes important. 

Since the pioneer paper [1], the so-called finite time thermodynamics has been development. They proposed a model of thermal engine shown in Figure 1, which has the mentioned Curzon-Ahlborn-Novikov-Chambadal efficiency, as a function of the cold reservoir temperature Tc and the hot reservoir temperature TH, as follows ... 

By contrast, in finite time, thermodynamics is usually considered an endoreversible Curzon-Ahlborn cycle, but in nature, there is no endoreversible engine. Thus, some authors have analyzed the non-endoreversible Curzon and Ahlborn cycle. Particularly in [16] has been analyzed the effect of thermal resistances, heat leakage, and internal irreversibility by a non-endoreversibility parameter, advanced in [14],... 

The existence of a finite heat transfer in the isothermal processes is affected with the assumption of a non-endoreversible cycle with ideal gas as working substance. Power output and ecological function have also an issue that shows direct dependence on the temperature of the working substance. Expressions obtained with the changes of variables have the virtue of leading directly to the shape of the efficiency through Z, function. Thus, in classical equilibrium thermodynamics, the Stirling cycle has its efficiency like the Carnot cycle efficiency in finite time thermodynamics, this cycle has an efficiency in their limit cases as the Curzon-Ahlborn cycle efficiency. 

Tlili, I. (2012). Finite time thermodynamics evaluation of endoreversible Stirling heat engine at maximum power conditions. Renew. Sust. Energy Rev., Vol. 16, pp 2234— 2241. 

A comparison of values obtained with the previous expressions of efficiency, for some plants reported in the literature of finite time thermodynamics, is shown in Table 1. 

In the next Chap. 14, there is a presentation of Finite Time Thermodynamics , by R.S. Berry, which is another way of formulating thermodynamics for systems not at equilibrium. 

---