Araştırma Makalesi

### Effective temperature and performance characteristics of heat engines

Yıl 2018, Cilt: 21 Sayı: 3, 158 - 172, 01.09.2018

### Öz

For a heat engine working between
two heat reservoirs, a hot reservoir at high temperature TH
and a cold reservoir at low temperature TL, an effective
temperature and an effective efficiency are introduced.

The effective temperature is defined
as the square root of the ratio between the net work output of the heat engine wnet
The SOT function is defined as the negative of the cyclic
integral of the heat transfer change divided by the square of the temperature.

The effective efficiency of the heat
engine is defined (a novel definition) as one minus the ratio between the low
temperature and the effective temperature.

The effective temperature and the
effective efficiency are worked out in details for the Carnot heat engine and
the air standard cycles (Otto, Brayton, Stirling, and Ericsson).

It was found for the considered
cycles that the effective temperature is given by the expression ()

and the effective
efficiency is given by the expression ()

for all the considered
cycles.

The importance of these two proposed
measures is twofold: educational and they could be used as a quick tool by the
designer.

### Kaynakça

• [1] R. E. Sonntag and G. J. Van Wylen, Introduction to Thermodynamics, Wiley, New York, NY, USA, 3rd edition, 1991. [2] H. B. Callen, Thermodynamics and an Introduction to Thermostatics, Wiley, New York, NY, USA, 2nd edition, 1985. [3] Y. Cengel A., M. A. Boles, Thermodynamics: An Engineering Approach, 5th Ed. Published by McGraw-Hill College, Boston, MA, 2006.[4] F.L. Curzon and B. Ahlborn, "Efficiency of a Carnot Engine at Maximum Power Output," Am. J. Phys. 43, 22, 1975.[5] A. Bejan, “Engineering Advances in Finite-Time Thermodynamics”, Am. J. Phys. Vol.62, pp. 11-12, 1994.[6] I. I., Novikov, “The efficiency of Atomic Power Stations”, J. Nucl. Energy II, Vol. 7, pp 125-128, translated from Novikov, I. I., 1958, Atomnaya Energiya, Vol. 3 (11), pp. 409, 1958.[7] Harvey leff, "Thermal efficiency at maximum work output: New results for old heat engines", American Journal of Physics 55(7):602-610, 1987. [8] B. Andresen, P. Salamon, and R. S. Berry, “Thermodynamics in finite time,” Physics Today, vol. 37, no. 9, pp. 62–70, 1984.[9] B. Andresen, P. Salamon, and R. S. Berry, “Thermodynamics in finite time: extremals for imperfect heat engines,” The Journal of Chemical Physics, vol. 66, no. 4, pp. 1571–1576, 1976. [10] P. Salamon, A. Nitzan, B. Andresen, and R. S. Berry, “Minimum entropy production and the optimization of heat engines,” Physical Review A, vol. 21, no. 6, pp. 2115–2129, 1980. [11] P. Salamon and R. S. Berry, “Thermodynamic length and dissipated availability,” Physical Review Letters, vol. 51, no. 13, pp. 1127–1130, 1983. [12] M. H. Rubin, “Optimal configuration of a class of irreversible heat engines. I,” Physical Review A, vol. 19, no. 3, pp. 1272– 1276, 1979. [13] P. Salamon, Y. B. Band, and O. Kafri, “Maximum power from a cycling working fluid,” Journal of Applied Physics, vol. 53, no. 1, pp. 197–202, 1982. [14] M. Mozurkewich and R. S. Berry, “Optimal paths for thermodynamic systems: the ideal Otto cycle,” Journal of Applied Physics, vol. 53, no. 1, pp. 34–42, 1982. [15] J. M. Gordon and M. Huleihil, “On optimizing maximum power heat engines,” Journal of Applied Physics, vol. 69, no. 1, pp. 1–7, 1991. [16] J. M. Gordon and M. Huleihil, “General performance characteristics of real heat engines,” Journal of Applied Physics, vol. 72, no. 3, pp. 829–837, 1992. [17] J. D. Nulton, P. Salamon, and R. K. Pathria, “Carnot-like processes in finite time. I. Theoretical limits,” American Journal of Physics, vol. 61, no. 10, pp. 911–916, 1993. [18] J. D. Nulton, P. Salamon, and R. K. Pathria, “Carnot-like processes in finite time. II. Applications to model cycles,” American Journal of Physics, vol. 61, no. 10, pp. 916–924, 1993. [19] J. Chen and Z. Yan, “Optimal performance of an endoreversible combined refrigeration cycle,” Journal of Applied Physics, vol. 63, no. 10, pp. 4795–4798, 1988. [20] A. Bejan, “Theory of heat transfer-irreversible refrigeration plants,” International Journal of Heat and Mass Transfer, vol. 32, no. 9, pp. 1631–1639, 1989. [21] J. Chen and Z. Yan, “Equivalent combined systems of threeheat-source heat pumps,” The Journal of Chemical Physics, vol. 90, no. 9, pp. 4951–4955, 1989. [22] Z. Yan and J. Chen, “An optimal endoreversible three-heatsource refrigerator,” Journal of Applied Physics, vol. 65, no. 1, pp. 1–4, 1989. [23] J. M. Gordon and K. C. Ng, “Thermodynamic modeling of reciprocating chillers,” Journal of Applied Physics, vol. 75, no. 6, pp. 2769–2774, 1994. [24] P. K. Bhardwaj, S. C. Kaushik, and S. Jain, “Finite time optimization of an endoreversible and irreversible vapour absorption refrigeration system,” Energy Conversion and Management, vol. 44, no. 7, pp. 1131–1144, 2003. [25] Y. Bi, L. Chen, and F. Sun, “Exergetic efficiency optimization for an irreversible heat pump working on reversed Brayton cycle,” Pramana, vol. 74, no. 3, pp. 351–363, 2010. [26] P. K. Bhardwaj, S. C. Kaushik, and S. Jain, “General performance characteristics of an irreversible vapour absorption refrigeration system using finite time thermodynamic approach,” International Journal of Thermal Sciences, vol. 44, no. 2, pp. 189–196, 2005.[27] SS Hou, "Comparison of performances of air standard Atkinson and Otto cycles with heat transfer considerations", Energy Conversion and Management 48: 1683-1690, 2007.[28] L. Chen, T Zheng ,F Sun , C Wu , "The power and efficiency characteristics for an irreversible Otto cycle", International Journal of Ambient Energy 24: 195- 200, 2003. [29] J. Chen , Y. Zhao , J He , "Optimization criteria for the important parameters of an irreversible Otto heat-engine" Applied Energy 83: 228-238, 2006. [30] YR Zhao , JC Chen, "Irreversible Otto heat engine with friction and heat leak losses and its parametric optimum criteria", Journal of the Energy Institute 81: 54-58, 2008. [31] M. Feidt, "Optimal thermodynamics-New Upperbounds" , Entropy 11: 529- 547, 2009. [32] R Ebrahimi, R, "Effects of gasoline-air equivalence ratio on performance of an Otto engine", J Am Sci 6: 131-135, 2010. [33] R Ebrahimi,"Theoretical study of combustion efficiency in an Otto engine", J Am Sci 6: 113-116, 2010. [34] OA Ozsoysal, "Effects of combustion efficiency on an Otto cycle", International Journal of Exergy 7: 232-242, 2010. [35] R. Ebrahimi , D. Ghanbarian , MR Tadayon, "Performance of an Otto engine with volumetric efficiency", J Am Sci 6: 27-31, 2010. [36] M. Gumus ,M. Atmaca , T. Yilmaz , "Efficiency of an Otto engine under alternative power optimizations", International Journal of Energy and Research 33: 745-752, 2009. [37]Y. Ust , "Ecological performance analysis of irreversible Otto cycle" J Eng Natural Sci 3: 106-117, 2005. [38] HB Mehta, OS Bharti, "Performance analysis of an irreversible Otto cycle using finite time thermodynamics", Proceedings of the World Congress on Engineering, London, UK, 2009. [39] F. Wu, L. Chen, F. Sun, C. Wu, F. Guo F, et al., "Quantum degeneracy effect on performance of irreversible Otto cycle with deal Bose gas", Energy Conversion and Management 47: 3008-3018, 2006. [40] H. Wang, S. Liu, J. He, "Performance analysis and parametric optimum criteria of a quantum Otto heat engine with heat transfer effects", Applied Thermal Engineering 29: 706-711, 2009. [41] H. Wang, S. Liu, J. Du "Performance analysis and parametric optimum criteria of a regeneration Bose-Otto engine", Phys Scr 79: 055004, 2009. [42] W. Nie, Q. Liao, C. Zhang, J. He, "Micro-/nanoscaled irreversible Otto engine cycle with friction loss and boundary effects and its performance characteristics", Energy 35: 4658-4662, 2010.[43] F. Wu, L. Chen, F. Sun, C. Wu, F. Guo, et al "Ecological optimization performance of an irreversible quantum Otto cycle working with an ideal Fermi gas", Open System & Information Dynamics 13: 55-66, 2006. [44] JA Rocha-Martinez, TD Navarrete-Gonzalez, CG Pava-Miller, R. PaezHernandez, F. Angulo-Brown F, "Otto and Diesel engine models with cyclic variability", Revista mexicana de física 48: 228-234, 2002. [45] JA Rocha-Martinez, TD Navarrete-Gonzalez, CG Pavia-Miller, A. Ramirez-Rojas,F. Angulo-Brown, "A simplified irreversible Otto engine model with fluctuations in the combustion heat", International Journal of Ambient Energy 27: 181-192, 2006. [46] Y. Ge, L.Chen, F. Sun, C. Wu, "Thermodynamic simulation of performance of an Otto cycle with heat transfer and variable specific heats of working fluid", Int Journal of Thermal Science 44: 506-511, 2005. [47] Y. Ge, L. Chen, F. Sun, C. Wu, "The effects of variable specific heats of working fluid on the performance of an irreversible Otto cycle", International Journal of Exergy 2: 274-283, 2005. [48] Y. Zhao, B. Lin, J. Chen, "Optimum criteria on the important parameters of an irreversible Otto heat engine with the temperature-dependent heat capacities of the working fluid", ASME Trans J Energy Res Tech 129: 348-354, 2007. [49] JC Lin, SS Hou, "Effects of heat loss as percentage of fuel’s energy, friction and variable specific heats of working fluid on performance of air standard Otto cycle", Energy Conversion and Management 49: 1218-1227, 2008. [50] RM Nejad, IS Marghmaleki, R. Hoseini, P. Alaei, "Effects of irreversible different parameters on performance of air standard Otto cycle", J American Sci 7: 248-254, 2011. [51] Y. Ge, L. Chen, F. Sun, "Finite time thermodynamic modeling and analysis for an irreversible Otto cycle", Applied Energy 85: 618-624, 2008. [52] R. Ebrahimi, "Effects of variable specific heat ratio on performance of an endoreversible Otto cycle", Acta Physica Polonica A 117: 887-891, 2010. [49] R. Ebrahimi, "Engine speed effects on the characteristic performance of Otto engines", J Am Sci 6: 123-128, 2009.[54]. K. H. Hoffmann, "Recent developments in finite time thermodynamics", TechnischeMechanik, Band 22, Heft 1, pp. 14-20, Manuskripeigang:10, Januar, 2002.
Yıl 2018, Cilt: 21 Sayı: 3, 158 - 172, 01.09.2018

### Kaynakça

• [1] R. E. Sonntag and G. J. Van Wylen, Introduction to Thermodynamics, Wiley, New York, NY, USA, 3rd edition, 1991. [2] H. B. Callen, Thermodynamics and an Introduction to Thermostatics, Wiley, New York, NY, USA, 2nd edition, 1985. [3] Y. Cengel A., M. A. Boles, Thermodynamics: An Engineering Approach, 5th Ed. Published by McGraw-Hill College, Boston, MA, 2006.[4] F.L. Curzon and B. Ahlborn, "Efficiency of a Carnot Engine at Maximum Power Output," Am. J. Phys. 43, 22, 1975.[5] A. Bejan, “Engineering Advances in Finite-Time Thermodynamics”, Am. J. Phys. Vol.62, pp. 11-12, 1994.[6] I. I., Novikov, “The efficiency of Atomic Power Stations”, J. Nucl. Energy II, Vol. 7, pp 125-128, translated from Novikov, I. I., 1958, Atomnaya Energiya, Vol. 3 (11), pp. 409, 1958.[7] Harvey leff, "Thermal efficiency at maximum work output: New results for old heat engines", American Journal of Physics 55(7):602-610, 1987. [8] B. Andresen, P. Salamon, and R. S. Berry, “Thermodynamics in finite time,” Physics Today, vol. 37, no. 9, pp. 62–70, 1984.[9] B. Andresen, P. Salamon, and R. S. Berry, “Thermodynamics in finite time: extremals for imperfect heat engines,” The Journal of Chemical Physics, vol. 66, no. 4, pp. 1571–1576, 1976. [10] P. Salamon, A. Nitzan, B. Andresen, and R. S. Berry, “Minimum entropy production and the optimization of heat engines,” Physical Review A, vol. 21, no. 6, pp. 2115–2129, 1980. [11] P. Salamon and R. S. Berry, “Thermodynamic length and dissipated availability,” Physical Review Letters, vol. 51, no. 13, pp. 1127–1130, 1983. [12] M. H. Rubin, “Optimal configuration of a class of irreversible heat engines. I,” Physical Review A, vol. 19, no. 3, pp. 1272– 1276, 1979. [13] P. Salamon, Y. B. Band, and O. Kafri, “Maximum power from a cycling working fluid,” Journal of Applied Physics, vol. 53, no. 1, pp. 197–202, 1982. [14] M. Mozurkewich and R. S. Berry, “Optimal paths for thermodynamic systems: the ideal Otto cycle,” Journal of Applied Physics, vol. 53, no. 1, pp. 34–42, 1982. [15] J. M. Gordon and M. Huleihil, “On optimizing maximum power heat engines,” Journal of Applied Physics, vol. 69, no. 1, pp. 1–7, 1991. [16] J. M. Gordon and M. Huleihil, “General performance characteristics of real heat engines,” Journal of Applied Physics, vol. 72, no. 3, pp. 829–837, 1992. [17] J. D. Nulton, P. Salamon, and R. K. Pathria, “Carnot-like processes in finite time. I. Theoretical limits,” American Journal of Physics, vol. 61, no. 10, pp. 911–916, 1993. [18] J. D. Nulton, P. Salamon, and R. K. Pathria, “Carnot-like processes in finite time. II. Applications to model cycles,” American Journal of Physics, vol. 61, no. 10, pp. 916–924, 1993. [19] J. Chen and Z. Yan, “Optimal performance of an endoreversible combined refrigeration cycle,” Journal of Applied Physics, vol. 63, no. 10, pp. 4795–4798, 1988. [20] A. Bejan, “Theory of heat transfer-irreversible refrigeration plants,” International Journal of Heat and Mass Transfer, vol. 32, no. 9, pp. 1631–1639, 1989. [21] J. Chen and Z. Yan, “Equivalent combined systems of threeheat-source heat pumps,” The Journal of Chemical Physics, vol. 90, no. 9, pp. 4951–4955, 1989. [22] Z. Yan and J. Chen, “An optimal endoreversible three-heatsource refrigerator,” Journal of Applied Physics, vol. 65, no. 1, pp. 1–4, 1989. [23] J. M. Gordon and K. C. Ng, “Thermodynamic modeling of reciprocating chillers,” Journal of Applied Physics, vol. 75, no. 6, pp. 2769–2774, 1994. [24] P. K. Bhardwaj, S. C. Kaushik, and S. Jain, “Finite time optimization of an endoreversible and irreversible vapour absorption refrigeration system,” Energy Conversion and Management, vol. 44, no. 7, pp. 1131–1144, 2003. [25] Y. Bi, L. Chen, and F. Sun, “Exergetic efficiency optimization for an irreversible heat pump working on reversed Brayton cycle,” Pramana, vol. 74, no. 3, pp. 351–363, 2010. [26] P. K. Bhardwaj, S. C. Kaushik, and S. Jain, “General performance characteristics of an irreversible vapour absorption refrigeration system using finite time thermodynamic approach,” International Journal of Thermal Sciences, vol. 44, no. 2, pp. 189–196, 2005.[27] SS Hou, "Comparison of performances of air standard Atkinson and Otto cycles with heat transfer considerations", Energy Conversion and Management 48: 1683-1690, 2007.[28] L. Chen, T Zheng ,F Sun , C Wu , "The power and efficiency characteristics for an irreversible Otto cycle", International Journal of Ambient Energy 24: 195- 200, 2003. [29] J. Chen , Y. Zhao , J He , "Optimization criteria for the important parameters of an irreversible Otto heat-engine" Applied Energy 83: 228-238, 2006. [30] YR Zhao , JC Chen, "Irreversible Otto heat engine with friction and heat leak losses and its parametric optimum criteria", Journal of the Energy Institute 81: 54-58, 2008. [31] M. Feidt, "Optimal thermodynamics-New Upperbounds" , Entropy 11: 529- 547, 2009. [32] R Ebrahimi, R, "Effects of gasoline-air equivalence ratio on performance of an Otto engine", J Am Sci 6: 131-135, 2010. [33] R Ebrahimi,"Theoretical study of combustion efficiency in an Otto engine", J Am Sci 6: 113-116, 2010. [34] OA Ozsoysal, "Effects of combustion efficiency on an Otto cycle", International Journal of Exergy 7: 232-242, 2010. [35] R. Ebrahimi , D. Ghanbarian , MR Tadayon, "Performance of an Otto engine with volumetric efficiency", J Am Sci 6: 27-31, 2010. [36] M. Gumus ,M. Atmaca , T. Yilmaz , "Efficiency of an Otto engine under alternative power optimizations", International Journal of Energy and Research 33: 745-752, 2009. [37]Y. Ust , "Ecological performance analysis of irreversible Otto cycle" J Eng Natural Sci 3: 106-117, 2005. [38] HB Mehta, OS Bharti, "Performance analysis of an irreversible Otto cycle using finite time thermodynamics", Proceedings of the World Congress on Engineering, London, UK, 2009. [39] F. Wu, L. Chen, F. Sun, C. Wu, F. Guo F, et al., "Quantum degeneracy effect on performance of irreversible Otto cycle with deal Bose gas", Energy Conversion and Management 47: 3008-3018, 2006. [40] H. Wang, S. Liu, J. He, "Performance analysis and parametric optimum criteria of a quantum Otto heat engine with heat transfer effects", Applied Thermal Engineering 29: 706-711, 2009. [41] H. Wang, S. Liu, J. Du "Performance analysis and parametric optimum criteria of a regeneration Bose-Otto engine", Phys Scr 79: 055004, 2009. [42] W. Nie, Q. Liao, C. Zhang, J. He, "Micro-/nanoscaled irreversible Otto engine cycle with friction loss and boundary effects and its performance characteristics", Energy 35: 4658-4662, 2010.[43] F. Wu, L. Chen, F. Sun, C. Wu, F. Guo, et al "Ecological optimization performance of an irreversible quantum Otto cycle working with an ideal Fermi gas", Open System & Information Dynamics 13: 55-66, 2006. [44] JA Rocha-Martinez, TD Navarrete-Gonzalez, CG Pava-Miller, R. PaezHernandez, F. Angulo-Brown F, "Otto and Diesel engine models with cyclic variability", Revista mexicana de física 48: 228-234, 2002. [45] JA Rocha-Martinez, TD Navarrete-Gonzalez, CG Pavia-Miller, A. Ramirez-Rojas,F. Angulo-Brown, "A simplified irreversible Otto engine model with fluctuations in the combustion heat", International Journal of Ambient Energy 27: 181-192, 2006. [46] Y. Ge, L.Chen, F. Sun, C. Wu, "Thermodynamic simulation of performance of an Otto cycle with heat transfer and variable specific heats of working fluid", Int Journal of Thermal Science 44: 506-511, 2005. [47] Y. Ge, L. Chen, F. Sun, C. Wu, "The effects of variable specific heats of working fluid on the performance of an irreversible Otto cycle", International Journal of Exergy 2: 274-283, 2005. [48] Y. Zhao, B. Lin, J. Chen, "Optimum criteria on the important parameters of an irreversible Otto heat engine with the temperature-dependent heat capacities of the working fluid", ASME Trans J Energy Res Tech 129: 348-354, 2007. [49] JC Lin, SS Hou, "Effects of heat loss as percentage of fuel’s energy, friction and variable specific heats of working fluid on performance of air standard Otto cycle", Energy Conversion and Management 49: 1218-1227, 2008. [50] RM Nejad, IS Marghmaleki, R. Hoseini, P. Alaei, "Effects of irreversible different parameters on performance of air standard Otto cycle", J American Sci 7: 248-254, 2011. [51] Y. Ge, L. Chen, F. Sun, "Finite time thermodynamic modeling and analysis for an irreversible Otto cycle", Applied Energy 85: 618-624, 2008. [52] R. Ebrahimi, "Effects of variable specific heat ratio on performance of an endoreversible Otto cycle", Acta Physica Polonica A 117: 887-891, 2010. [49] R. Ebrahimi, "Engine speed effects on the characteristic performance of Otto engines", J Am Sci 6: 123-128, 2009.[54]. K. H. Hoffmann, "Recent developments in finite time thermodynamics", TechnischeMechanik, Band 22, Heft 1, pp. 14-20, Manuskripeigang:10, Januar, 2002.

### Ayrıntılar

Birincil Dil İngilizce Mühendislik Regular Original Research Article Mahmoud HULEİHİL Israel 1 Eylül 2018 Yıl 2018 Cilt: 21 Sayı: 3

### Kaynak Göster

 Bibtex @araştırma makalesi { ijot414698, journal = {International Journal of Thermodynamics}, issn = {1301-9724}, eissn = {2146-1511}, address = {}, publisher = {Uluslararası Uygulamalı Termodinamik Derneği İktisadi İşletmesi}, year = {2018}, volume = {21}, number = {3}, pages = {158 - 172}, doi = {10.5541/ijot.414698}, title = {Effective temperature and performance characteristics of heat engines}, key = {cite}, author = {Huleihil, Mahmoud} } APA Huleihil, M. (2018). Effective temperature and performance characteristics of heat engines . International Journal of Thermodynamics , 21 (3) , 158-172 . DOI: 10.5541/ijot.414698 MLA Huleihil, M. "Effective temperature and performance characteristics of heat engines" . International Journal of Thermodynamics 21 (2018 ): 158-172 Chicago Huleihil, M. "Effective temperature and performance characteristics of heat engines". International Journal of Thermodynamics 21 (2018 ): 158-172 RIS TY - JOUR T1 - Effective temperature and performance characteristics of heat engines AU - MahmoudHuleihil Y1 - 2018 PY - 2018 N1 - doi: 10.5541/ijot.414698 DO - 10.5541/ijot.414698 T2 - International Journal of Thermodynamics JF - Journal JO - JOR SP - 158 EP - 172 VL - 21 IS - 3 SN - 1301-9724-2146-1511 M3 - doi: 10.5541/ijot.414698 UR - https://doi.org/10.5541/ijot.414698 Y2 - 2018 ER - EndNote %0 International Journal of Thermodynamics Effective temperature and performance characteristics of heat engines %A Mahmoud Huleihil %T Effective temperature and performance characteristics of heat engines %D 2018 %J International Journal of Thermodynamics %P 1301-9724-2146-1511 %V 21 %N 3 %R doi: 10.5541/ijot.414698 %U 10.5541/ijot.414698 ISNAD Huleihil, Mahmoud . "Effective temperature and performance characteristics of heat engines". International Journal of Thermodynamics 21 / 3 (Eylül 2018): 158-172 . https://doi.org/10.5541/ijot.414698 AMA Huleihil M. Effective temperature and performance characteristics of heat engines. International Journal of Thermodynamics. 2018; 21(3): 158-172. Vancouver Huleihil M. Effective temperature and performance characteristics of heat engines. International Journal of Thermodynamics. 2018; 21(3): 158-172. IEEE M. Huleihil , "Effective temperature and performance characteristics of heat engines", International Journal of Thermodynamics, c. 21, sayı. 3, ss. 158-172, Eyl. 2018, doi:10.5541/ijot.414698