Local Stability of Curzon-Ahlborn Cycle with Non-Linear Heat Transfer for Maximum Power Output Regime

Delfino Ladino-Luna, Pedro Portillo-Díaz, Ricardo T. Páez-Hernández

Universidad Autónoma Metropolitana-Atzcapotzalco, Física de Procesos Irreversibles, Cd. México, México.

DOI: 10.4236/jmp.2013.47A2004                

Abstract

The study of local stability of thermal engines modeled as an endoreversible Curzon and Ahlborn cycle is shown. It is assumed a non-linear heat transfer for heat fluxes in the system (engine + environments). A semisum of two expressions of the efficiency found in the literature of finite time thermodynamics for the maximum power output regime is considered in order to make the analysis. Expression of variables for local stability and power output is found even graphic results for important parameters in the analysis of stability, and a phase plane portrait is shown.

Keywords

Local Stability; Thermal Engines; Non-Linear Heat Transfer

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	S. Carnot, “Réflexions sur la Puissance Motrice du feu et sur les Machines Propres à Développer Cette Puissanc,” Spanish Translation, IPN Press, México, 1998.
[2]	R. Clausius, “Théorie Mécanique de la Chaleur, 1ére Partie,” Lacroix, 1868.
[3]	E. Fermi, “Thermodynamics,” Columbia University Press, New York, 1936.
[4]	R. C. Tolman and P. C. Fine, Reviews of Modern Physics, Vol. 20, 1948, pp. 51-77. doi:10.1103/RevModPhys.20.51
[5]	I. I. Novikov, Journal of Nuclear Energy II, Vol. 7, 1958, pp. 125-128.
[6]	P. Chambadal, “Les Centrales Nucleares,” Armand Colin, 1957.
[7]	F. L. Curzon and B. Ahlborn, American Journal of Physics, Vol. 43, 1975, pp. 22-24. doi:10.1119/1.10023
[8]	D. Gutkowics-Krusin, I. Procaccia and J. Ross, Journal of Chemical Physics, Vol. 69, 1978, pp. 3898-3906. doi:10.1063/1.437127
[9]	M. Rubin, Physical Review A, Vol. 19, 1979, pp. 1272-1276. doi:10.1103/PhysRevA.19.1272
[10]	M. Rubin, Physical Review A, Vol. 19, 1979, pp. 1277-1289. doi:10.1103/PhysRevA.19.1277
[11]	P. Salamon, A. Nitzan, B. Andresen and R. S. Berry, Physical Review A, Vol. 21, 1980, pp. 2115-2129. doi:10.1103/PhysRevA.21.2115
[12]	J. L. Torres, Revista Mexicana de Física, Vol. 34, 1988, pp. 18-24.
[13]	F. Angulo-Brown, Revista Mexicana de Física, Vol. 37, 1991, pp. 87-96.
[14]	F. Angulo-Brown, Journal of Applied Physics, Vol. 69, 1991, pp. 7465-7469. doi:10.1063/1.347562
[15]	F. Angulo-Brown and R. T. Páez-Hernández, Journal of Applied Physics, Vol. 74, 1993, pp. 2216-2219. doi:10.1063/1.354728
[16]	D. Ladino-Luna, Revista Mexicana de Física, Vol. 48, 2003, pp. 87-91.
[17]	L. A. Arias-Hernández, G. Ares and F. Angulo-Brown, Open Systems & Information Dynamics, Vol. 10, 2003, pp. 351-375. doi:10.1023/B:OPSY.0000009556.27759.11
[18]	D. Ladino-Luna, Journal of the Energy Institute, Vol. 81, 2008, pp. 114-117. doi:10.1179/174602208X301961
[19]	A. Lifschitz and E. Hameiri, Physical Fluids A, Vol. 3, 1991, pp. 2644-2651. doi:10.1063/1.858153
[20]	G. Gallavotti, “New Methods in Noequilibrium Gases and Fluids,” arXiv:chao-dyn/9610018v1 [accesed 30.10.1996].
[21]	M. Santillán, G. Maya and F. Angulo-Brown, Journal of Physics D, Vol. 34, 2001, pp. 2068-2072. doi:10.1088/0022-3727/34/13/318
[22]	R. T. Páez-Hernández, F. Angulo-Brown and M. Santillán, The Journal of Non-Equilibrium Thermodynamics, Vol. 31, 2006, pp. 173-188.
[23]	Y. Huang and D. Sun, The Journal of Non-Equilibrium Thermodynamics, Vol. 33, 2008, pp. 61-74.
[24]	Y. Huang, D. Sun and Y. Kang, Journal of Applied Physics, Vol. 102, 2007, pp. 349051-349056. doi:10.1063/1.2767622
[25]	L. Guzmán-Vargas, I. Reyes-Ramírez and N. Sánchez, Journal of Physics D: Applied Physics, Vol. 38, 2005, pp. 1282-1295. doi:10.1088/0022-3727/38/8/028
[26]	R. T. Páez-Hernández, D. Ladino-Luna and P. Portillo-Díaz, Physica A, Vol. 390, 2011, pp. 3275-3282. doi:10.1016/j.physa.2011.05.019
[27]	L. W. Taylor, “Manual of Advanced Undergraduate Experiments in Physics,” Addison-Wesley, 1959, p. 115.
[28]	M. Nelson and P. Parker, “Advanced Level Physics,” 4th Edition, Heinemann, New Orleans, 1977, p. 194.