Abstract
In this chapter we investigate the mathematical properties of thermodynamic functions and chemistry source terms. We first specify the mathematical assumptions associated with thermodynamics and investigate smoothness, convexity and differentials of various functionals. A fundamental alternative arises, however, concerning the mathematical thermodynamic formalism to be used.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
E. Boillat, Existence and Uniqueness of the Solution to the Edge Problem in a Two-Dimensional Reactive Boundary Layer, Math. Mod. Meth. Appl. Sci., 5, (1995), pp. 1–27.
M. W. Chase, Jr., C. A. Davies, J. R. Downey, Jr., D. J. Frurip, R. A. McDonald, and A. N. Syverud, JANAF Thermochemical Tables, Third Edition, J. Phys. Chem. Ref. Data, 14, Suppl. 1, (1985), pp. 1–1856.
S. R. de Groot and P. Mazur, Non-Equilibrium Thermodynamics, Dover, New York, (1984).
A. Ern and V. Giovangigli, Multicomponent Transport Algorithms, Lecture Notes in Physics, New Series “Monographs”, m 24, Springer-Verlag, Berlin, 1994.
M. Feinberg, The Existence and Uniqueness of Steady States for a Class of Chemical Reaction Networks, Arkiv Rat. Mech. Anal, 132, (1995), pp. 311–370.
M. Feinberg, Multiple Steady States for Chemical Reaction Networks of Deficiency One, Arkiv Rat. Mech. Anal, 132, (1995), pp. 371–406.
V. Giovangigli, Plane Flames with Multicomponent Transport and Complex Chemistry, Math. Mod. Meth. Appl. Sci., 9, (1999), pp. 337–378.
V. Giovangigli and M. Massot, Asymptotic Stability of Equilibrium States for Multicomponent Reactive Flows, Math. Mod. Meth. Appl. Sci., 8, (1998), pp. 251–297.
V. Giovangigli and M. Smooke, Extinction Limits of Strained Premixed Laminar Flames with Complex Chemistry, Comb. Sci. Tech., 53, (1987), pp. 23–49.
E. A. Guggenheim, Thermodynamics, Interscience, New York, (1957).
F. J. M. Horn, Necessary and Sufficient Conditions for Complex Balancing in Chemical Kinetics, Arch. Rational Mech. Anal., 49, (1972), pp. 172–186.
F. J. M. Horn and R. Jackson, General Mass Action Kinetics, Arch. Rational Mech. Anal, 47, (1972), pp. 81–116.
F. J. Krambeck, The Mathematical Structure of Chemical Kinetics, Arch. Rational Mech. Anal., 38, (1970), pp. 317–347.
J. Meixnier, Zur Thermodynamik der Irreversiblen Prozesse in Gases mit Chemish Reagierenden, Dissoziierenden und Anregbaren Komponent, Annalen der Physik, 5, (1943), pp. 244–270.
J. Pousin, Modélisation et Analyse Numérique de Couches Limites Réactives d’Air, Doctorat es Sciences, Ecole Polytechnique Fédérale de Lausanne, 1112, (1993).
N. Z. Shapiro and L. S. Shapley, Mass Action Law and the Gibbs Free Energy Function, SIAM J. Appl. Math., 13, (1965), pp. 353–375.
D. R. Stull and H. Prophet, JANAF Thermochemicai Tables, Second ed., Washington, NBS NSRDS-NBS37, (1971).
A. Vol’pert and S. Hudjaev, Analysis in Classes of Discontinuous Functions and Equations of Mathematical Physics, Mechanics: Analysis 8, Martinus Nijhoff Publishers, Dordrecht, (1985).
F. A. Williams, Combustion Theory, Second ed., The Benjamin/Cummings Publishing Company, Inc., Menlo Park, (1985).
L. C. Woods, The Thermodynamics of Fluid Systems, Oxford Eng. Sci. Series, 2, (1986).
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1999 Springer Science+Business Media New York
About this chapter
Cite this chapter
Giovangigli, V. (1999). Mathematics of Thermochemistry. In: Multicomponent Flow Modeling. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1580-6_6
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1580-6_6
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7202-1
Online ISBN: 978-1-4612-1580-6
eBook Packages: Springer Book Archive