Abstract
The extensive quantities of a global system may change due to a flux over the boundary or due to production and supply within the volume, resulting in balance equations for the conserved quantities of mass, momentum, angular momentum, and energy. We start with the global balance equations and derive the local form in regular points of the continuum (where the field quantities are continuously differentiable) as well as at surfaces of discontinuity. In addition to one-component systems, we consider mixtures of different chemical components.
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
References
J. Altenbach, H. Altenbach, Einführung in die Kontinuumsmechanik. Studienbücher. (Teubner-Verlag, Stuttgart, 1994)
A. Bertram, Axiomatische Einführung in die Kontinuumsmechanik (B.I. Wissenschaftsverlag, Mannheim, Wien, Zürich, 1989)
E. Becker, W. Bürger, Kontinuumsmechanik (Teubner Studienbücher, Stuttgart, 1975)
W. Schottky, Thermodynamik (Springer, Berlin, 1929)
T. Alts, K. Hutter, I: surface balance laws and their interpretation in terms of three dimensional balance laws averaged over the phase change boundary layer, II: Thermodynamics, III: thermostatics and its consequences, IV: on thermostatic stability and well-posedness. J. Non-Equilib. Thermodyn. 13, 221–301 (1988)
W. Muschik, Fundamentals of nonequilibrium thermodynamics, in Non-equilibrium Thermodynamics with Applications to Solids, ed. by W. Muschik. CISM Courses and Lectures, vol. 336 (Springer, Wien, New York, 1993), pp. 1–63
J.W. Gibbs, Collected Works (Yale University Press, New Haven, 1948)
C. Papenfuss, Contribution to a Continuum Theory of Two Dimensional Liquid Crystals (Wissenschaft- und Technik Verlag, Berlin, 1995)
R. Prud’homme, Fluides hétérogènes et réactifs: écoulements et transferts, Lecture Notes in Physics (Springer, Berlin, Heidelberg, New York, 1988)
D. Ronis, D. Bedeaux, I. Oppenheim, On the derivation of dynamical equations for a system with an interface I: General theory. Phys. A 90A, 487–506 (1978)
D. Ronis, I. Oppenheim, On the derivation of dynamical equations for a system with an interface: II The gas-liquid interface. Physica 117A, 317–354 (1983)
A. Grauel, Feldtheoretische Beschreibung von Grenzflächen (Springer, Berlin, New York, London, 1989)
W.H. Müller, W. Muschik, Bilanzgleichungen offener mehrkomponentiger Systeme I Massen- und Impulsbilanzen. J. Non-Equilib. Thermodyn. 8, 29–46 (1983)
W. Muschik, W.H. Müller, Bilanzgleichungen offener mehrkomponentiger Systeme II. Energie- und Entropiebilanz. J. Non-Equilib. Thermodyn. 8, 47–66 (1983)
W. Muschik, C. Papenfuss, H. Ehrentraut, Concepts of Continuum Thermodynamics (Kielce University of Technology, Technische Universität, Berlin, 1996). ISBN 83-905132-7-7
I. Müller, Thermodynamics (Pitman Advanced Publishing Program, Boston, 1985)
I. Müller, Grundzüge der Thermodynamik (Springer, Berlin, 1994)
J. Verhas, C. Papenfuss, W. Muschik, A simplified thermodynamic theory for biaxial nematics using Gyarmati’s principle. Mol. Cryst. Liq. Cryst. 215, 313–321 (1992)
C. Papenfuss, J. Verhas, W. Muschik, A simplified thermodynamic theory for biaxial nematics. Z. Naturforsch. 50a, 795–804 (1994)
K. Wilmański, Thermomechanics of Continua (Springer, Berlin, 1998)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Papenfuß, C. (2020). Balance Equations. In: Continuum Thermodynamics and Constitutive Theory. Springer, Cham. https://doi.org/10.1007/978-3-030-43989-7_3
Download citation
DOI: https://doi.org/10.1007/978-3-030-43989-7_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-43988-0
Online ISBN: 978-3-030-43989-7
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)