An Unified Approach to Thermodynamics of Power Yield in Thermal, Chemical and Electrochemical Systems
This paper unifies power optimization approaches in
various energy converters, such as: thermal, solar, chemical, and
electrochemical engines, in particular fuel cells. Thermodynamics
leads to converter-s efficiency and limiting power. Efficiency
equations serve to solve problems of upgrading and downgrading of
resources. While optimization of steady systems applies the
differential calculus and Lagrange multipliers, dynamic optimization
involves variational calculus and dynamic programming. In reacting
systems chemical affinity constitutes a prevailing component of an
overall efficiency, thus the power is analyzed in terms of an active
part of chemical affinity. The main novelty of the present paper in the
energy yield context consists in showing that the generalized heat
flux Q (involving the traditional heat flux q plus the product of
temperature and the sum products of partial entropies and fluxes of
species) plays in complex cases (solar, chemical and electrochemical)
the same role as the traditional heat q in pure heat engines.
The presented methodology is also applied to power limits in fuel
cells as to systems which are electrochemical flow engines propelled
by chemical reactions. The performance of fuel cells is determined by
magnitudes and directions of participating streams and mechanism of
electric current generation. Voltage lowering below the reversible
voltage is a proper measure of cells imperfection. The voltage losses,
called polarization, include the contributions of three main sources:
activation, ohmic and concentration. Examples show power maxima
in fuel cells and prove the relevance of the extension of the thermal
machine theory to chemical and electrochemical systems. The main
novelty of the present paper in the FC context consists in introducing
an effective or reduced Gibbs free energy change between products p
and reactants s which take into account the decrease of voltage and
power caused by the incomplete conversion of the overall reaction.
[1] S. Sieniutycz, "A synthesis of thermodynamic models unifying
traditional and work-driven operations with heat and mass exchange".
Open Sys. & Information Dynamics, vol. 10, no.1, pp. 31-49, 2003.
[2] F..L. Curzon and B. Ahlborn, "Efficiency of Carnot engine at maximum
power output". American J. Phys., vol. 43, no.1, pp. 22-24, 1975.
[3] A. De Vos, Endoreversible Thermodynamics of Solar Energy
Conversion, Oxford University Press, pp. 30-41, 1994.
[4] S. Sieniutycz and P. Kuran, "Nonlinear models for mechanical energy
production in imperfect generators driven by thermal or solar energy",
Intern. J. Heat Mass Transfer, vol. 48, no. 3-4, pp. 719-730, 2005.
[5] S. Sieniutycz and P. Kuran, "Modeling thermal behavior and work flux
in finite-rate systems with radiation". Intern. J. Heat and Mass Transfer,
vol. 49, no. 17-18, pp. 3264-3283, 2006.
[6] S. Sieniutycz, "Dynamic programming and Lagrange multipliers for
active relaxation of resources in non-equilibrium systems", Applied
Mathematical Modeling, vol. 33, no. 3, pp. 1457-1478, 2009.
[7] P. Kuran, Nonlinear Models of Production of Mechanical Energy in
Non-Ideal Generators Driven by Thermal or Solar Energy, PhD Thesis,
Warsaw University of Technology, 2006.
[8] R. S. Berry, V. A. Kazakov, S. Sieniutycz, Z. Szwast, and A. M. Tsirlin,
Thermodynamic Optimization of Finite Time Processes, Chichester,
Wiley, 2000, p.197, 200.
[9] S. Sieniutycz, "Thermodynamic Limits on Production or Consumption
of Mechanical Energy in Practical and Industrial Systems", Progress in
Energy and Combustion Science, vol. 29, pp. 193-246, 2003.
[10] S. Sieniutycz, "Carnot controls to unify traditional and work-assisted
operations with heat & mass transfer", International Journal of Applied
Thermodynamics, vol. 6, np. 2, pp. 59-67, 2003.
[11] S. Sieniutycz and J. JeŜowski, Energy Optimization in Process Systems,
Oxford, Elsevier, 2009.
[12] S. Sieniutycz, "An analysis of power and entropy generation in a
chemical engine", Intern. J. of Heat and Mass Transfer, vol. 51, no. 25-
26, pp. 5859-5871, 2008.
[13] R. Bellman, Adaptive Control Processes: a Guided Tour, Princeton
University Press, 1961.
[14] R. Petela, "Exergy of heat radiation", J. Heat Transfer, vol. 86, no.2,
pp.187-192, 1964.
[15] J. Jeter, J., "Maximum conversion efficiency for the utilization of direct
solar radiation", Solar Energy, vol. 26, no. 3, pp. 231-236, 1981.
[16] A.M. Tsirlin, V. Kazakov, V.A. Mironova, and S.A. Amelkin, "Finitetime
thermodynamics: conditions of minimal dissipation for
thermodynamic process", Physical Review E, vol. 58, no. 1, pp. 215-
223, 1998.
[17] S. Sieniutycz, "Complex chemical systems with power production
driven by mass transfer", Intern. J. of Heat and Mass Transfer, vol. 52,
no.10, pp. 2453-2465, 2009.
[18] Y. Zhao, C. Ou, and J. Chen. "A new analytical approach to model and
evaluate the performance of a class of irreversible fuel cells".
International Journal of Hydrogen Energy, vol. 33, no.1, pp. 4161-
4170, 2008.
[19] M. Wierzbicki, Optimization of SOFC based energy system using Aspen
PlusTM, MsD Thesis supervised by S. Sieniutycz (Faculty of Chemical
and Process Engineering, Warsaw TU) and J. Jewulski (Laboratory of
Fuel Cells, Warsaw Institute of Energetics), Warsaw, 2009.
[20] T. J. Kotas, Exergy Method of Thermal Plant Analysis, Butterworths,
Borough Green, 1985, pp. 2-19.
[21] M. M. Mench, Fuel Cell Engines, Hoboken (N.J), Wiley, 2008.
[22] J.T. Pukrushpan, A.G., Stefanopoulou and H. Peng, Control of Fuel Cell
Power Systems, London, Springer, 2004
[23] S. Sieniutycz, "Dynamical converters with power-producing relaxation
of solar radiation", Intern. Journal of Thermal Sciences, vol. 66, pp.
219-231, 2007.
[24] Y. Zhao, J. Chen, "Modeling and optimization of a typical fuel cell-heat
engine hybrid system and its parametric design criteria", Journal of
Power Sources, vol. 186, pp. 96-103, 2009.
[1] S. Sieniutycz, "A synthesis of thermodynamic models unifying
traditional and work-driven operations with heat and mass exchange".
Open Sys. & Information Dynamics, vol. 10, no.1, pp. 31-49, 2003.
[2] F..L. Curzon and B. Ahlborn, "Efficiency of Carnot engine at maximum
power output". American J. Phys., vol. 43, no.1, pp. 22-24, 1975.
[3] A. De Vos, Endoreversible Thermodynamics of Solar Energy
Conversion, Oxford University Press, pp. 30-41, 1994.
[4] S. Sieniutycz and P. Kuran, "Nonlinear models for mechanical energy
production in imperfect generators driven by thermal or solar energy",
Intern. J. Heat Mass Transfer, vol. 48, no. 3-4, pp. 719-730, 2005.
[5] S. Sieniutycz and P. Kuran, "Modeling thermal behavior and work flux
in finite-rate systems with radiation". Intern. J. Heat and Mass Transfer,
vol. 49, no. 17-18, pp. 3264-3283, 2006.
[6] S. Sieniutycz, "Dynamic programming and Lagrange multipliers for
active relaxation of resources in non-equilibrium systems", Applied
Mathematical Modeling, vol. 33, no. 3, pp. 1457-1478, 2009.
[7] P. Kuran, Nonlinear Models of Production of Mechanical Energy in
Non-Ideal Generators Driven by Thermal or Solar Energy, PhD Thesis,
Warsaw University of Technology, 2006.
[8] R. S. Berry, V. A. Kazakov, S. Sieniutycz, Z. Szwast, and A. M. Tsirlin,
Thermodynamic Optimization of Finite Time Processes, Chichester,
Wiley, 2000, p.197, 200.
[9] S. Sieniutycz, "Thermodynamic Limits on Production or Consumption
of Mechanical Energy in Practical and Industrial Systems", Progress in
Energy and Combustion Science, vol. 29, pp. 193-246, 2003.
[10] S. Sieniutycz, "Carnot controls to unify traditional and work-assisted
operations with heat & mass transfer", International Journal of Applied
Thermodynamics, vol. 6, np. 2, pp. 59-67, 2003.
[11] S. Sieniutycz and J. JeŜowski, Energy Optimization in Process Systems,
Oxford, Elsevier, 2009.
[12] S. Sieniutycz, "An analysis of power and entropy generation in a
chemical engine", Intern. J. of Heat and Mass Transfer, vol. 51, no. 25-
26, pp. 5859-5871, 2008.
[13] R. Bellman, Adaptive Control Processes: a Guided Tour, Princeton
University Press, 1961.
[14] R. Petela, "Exergy of heat radiation", J. Heat Transfer, vol. 86, no.2,
pp.187-192, 1964.
[15] J. Jeter, J., "Maximum conversion efficiency for the utilization of direct
solar radiation", Solar Energy, vol. 26, no. 3, pp. 231-236, 1981.
[16] A.M. Tsirlin, V. Kazakov, V.A. Mironova, and S.A. Amelkin, "Finitetime
thermodynamics: conditions of minimal dissipation for
thermodynamic process", Physical Review E, vol. 58, no. 1, pp. 215-
223, 1998.
[17] S. Sieniutycz, "Complex chemical systems with power production
driven by mass transfer", Intern. J. of Heat and Mass Transfer, vol. 52,
no.10, pp. 2453-2465, 2009.
[18] Y. Zhao, C. Ou, and J. Chen. "A new analytical approach to model and
evaluate the performance of a class of irreversible fuel cells".
International Journal of Hydrogen Energy, vol. 33, no.1, pp. 4161-
4170, 2008.
[19] M. Wierzbicki, Optimization of SOFC based energy system using Aspen
PlusTM, MsD Thesis supervised by S. Sieniutycz (Faculty of Chemical
and Process Engineering, Warsaw TU) and J. Jewulski (Laboratory of
Fuel Cells, Warsaw Institute of Energetics), Warsaw, 2009.
[20] T. J. Kotas, Exergy Method of Thermal Plant Analysis, Butterworths,
Borough Green, 1985, pp. 2-19.
[21] M. M. Mench, Fuel Cell Engines, Hoboken (N.J), Wiley, 2008.
[22] J.T. Pukrushpan, A.G., Stefanopoulou and H. Peng, Control of Fuel Cell
Power Systems, London, Springer, 2004
[23] S. Sieniutycz, "Dynamical converters with power-producing relaxation
of solar radiation", Intern. Journal of Thermal Sciences, vol. 66, pp.
219-231, 2007.
[24] Y. Zhao, J. Chen, "Modeling and optimization of a typical fuel cell-heat
engine hybrid system and its parametric design criteria", Journal of
Power Sources, vol. 186, pp. 96-103, 2009.
@article{"International Journal of Chemical, Materials and Biomolecular Sciences:53927", author = "S. Sieniutycz", title = "An Unified Approach to Thermodynamics of Power Yield in Thermal, Chemical and Electrochemical Systems", abstract = "This paper unifies power optimization approaches in
various energy converters, such as: thermal, solar, chemical, and
electrochemical engines, in particular fuel cells. Thermodynamics
leads to converter-s efficiency and limiting power. Efficiency
equations serve to solve problems of upgrading and downgrading of
resources. While optimization of steady systems applies the
differential calculus and Lagrange multipliers, dynamic optimization
involves variational calculus and dynamic programming. In reacting
systems chemical affinity constitutes a prevailing component of an
overall efficiency, thus the power is analyzed in terms of an active
part of chemical affinity. The main novelty of the present paper in the
energy yield context consists in showing that the generalized heat
flux Q (involving the traditional heat flux q plus the product of
temperature and the sum products of partial entropies and fluxes of
species) plays in complex cases (solar, chemical and electrochemical)
the same role as the traditional heat q in pure heat engines.
The presented methodology is also applied to power limits in fuel
cells as to systems which are electrochemical flow engines propelled
by chemical reactions. The performance of fuel cells is determined by
magnitudes and directions of participating streams and mechanism of
electric current generation. Voltage lowering below the reversible
voltage is a proper measure of cells imperfection. The voltage losses,
called polarization, include the contributions of three main sources:
activation, ohmic and concentration. Examples show power maxima
in fuel cells and prove the relevance of the extension of the thermal
machine theory to chemical and electrochemical systems. The main
novelty of the present paper in the FC context consists in introducing
an effective or reduced Gibbs free energy change between products p
and reactants s which take into account the decrease of voltage and
power caused by the incomplete conversion of the overall reaction.", keywords = "Power yield, entropy production, chemical engines, fuel cells, exergy.", volume = "4", number = "6", pages = "402-16", }