Curzon-Ahlborn engine

It was pointed out very early [3] that the natural way to find such optima is through the application of optimal control theory. In fact the first such application was carried out by Rubin [6,7], specifically to find the pathways and optimal performance so obtained for a cyclic engine of the sort described above, Rubin found the conditions for optimum power and for optimum efficiency, which of course are normally different. It was in these works that he introduced the term endoreversible to describe a process that could have irreversible interactions with its environment but would be describable internally in terms of the thermodynamic variables of a system at equilibrium. An endoreversible system comes to equilibrium internally very rapidly compared, whatever heat or work exchange it incurs with the outside. It was here that one first saw the comparison of the efficiency for maximum power of the Curzon-Ahlborn engine compared graphically with the maximum efficiency, in terms of a curve of power vs. heat flow. Figure 14.1 is an example of this. 

In the present paper, the performance of a non-endoreversible heat engine modeled as a Curzon-Ahlborn cycle is analyzed. The procedure in [5] is combined with the procedure in [16], arriving to linear approaches of the efficiency as a function of a parameter that contains the compression ratio in both regimens maximum power output and maximum ecological function. From the limit values of the non-endoreversibility parameter and the compression... 

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],... 

SO that the ecological function for Curzon and Ahlborn engine takes the form. 

Ladino-Luna, D. (2003). Efficiency of a Curzon and Ahlborn engine with Dulong-Petit heat transfer law. Rev. Mex. Eis., Vol. 49, pp. 97-91... 

The T-s diagram and schematic diagram of the Curzon and Ahlborn (endoreversible Carnot) cycle are shown in Figs. 7.5 and 7.6, respectively (Cuzon, F.L. and Ahlborn, B., Efficiency of a Carnot engine at maximum... 

Curzon, F.L. Ahlborn, B. Efficiency of a Camot engine at maximum power output. Am.. Phys. 1975, 43, 22. 

Suppose a thermal engine working like a Curzon and Ahlborn cycle, in which an internal heat by internal processes of working fluid appears, assuming ideal gas as working fluid. The Clausius inequality with the parameter of non-endoreversibility becomes... 

On other hand, Angulo-Brown et al (1999) showed that a general property of endoreversible Curzon and Ahlborn cycle demostrated previously (Arias-Hernandez Angulo-Brown, 1997) can be extended for a non-endoreversible Curzon and Ahlborn cycle. Besides, Velasco et. al. (2000) follow the idea in Chen (1994, 1996), and they found expressions to measure possible reductions of non-desired effects in heat engines operation. They pointed out that Is is not depending of e and re-wrote Equation (6) as. 

So we can use the Newton s heat transfe law, and also we can assume the same thermal conductance a in two isothermal processes of Curzon and Ahlborn cycle. The heat exchanged between the engine and its surroundings can be expressed as. 

With the previous ideas, to make the present paper self-contained we include in this section a brief explanation and some results of model used by Gutkowicz-Krusin et al (1978), and others that we need for our present purposes. In their model Gutkowicz-Kru et al. consider a working substance inside of a cylinder with a movable piston as engine, and also they considered an ideal gas as working fluid, contained in the cylinder and the mass of piston not negligible. The inertia of the movable piston does not affect the endoreversible character of Curzon and Ahlborn cycle to consider the expansion of gas, and because the volume occupied by the gas in the expansion and compression can be written as... 

In real compressors, named alternative compressors with dead space, percent of volume in the total displacement of a piston into a cylinder is named dead space ratio, defined as c = volume of dead space) / (volume of displacement), (Burghardt, 1982). In case of a Curzon and Ahlborn cycle c = (minimum volume) / (maximum volume) is the reciprocal of. Experimentally it is found that 3%r< >100/10, or 33>r(->10. Compression ratio is a useful parameter to model the behavior of a thermal engines, but it is not easy to include this parameter in design of power plants, would be interesting find a model in which could be explicitly incorporated in design power plants. 

In the case of a Curzon and Ahlborn cycle (Figure 1), for the heat exchange between the engine and the reservoirs. Equation (93) leads to the time of the isothermal processes by taking its integration. Moreover in the case of adiabatic processes dQ / dt = 0, so that Equation (87) reduces to... 

Curzon and Ahlborn [2], in their original work on this subject, argue that the power output on this plot must have a maximum for an explanation see the caption to Fig. 13.2. The efficiency of the engine is defined as WjQi and thus we have... 

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