A variational principle for transport processes in continuous systems: Derivation and application

Document Type

Syllabus

Publication Date

12-1-2005

Abstract

This chapter emphasizes the routine procedure for derivation of variational equations that represents a wide range of continuous systems. The procedure involves the use of the generalized variables and fluxes for system description. The application of this procedure is demonstrated by constructing the variational equations for both dissipative and reversible processes. A variational equation describing heat, mass, and momentum transfer in a moving, chemically reactive continuous media is constructed using the proposed routine. The Euler-Lagrange equations following from the constructed variational equation are identical to the balance equations for entropy, momentum, and mass. A Lagrangian density, relating the rate of the energy change in the system with energy dissipation, work, and entropy production, is constructed. The use of this Lagrangian is demonstrated by its application to the formation of a solid structure in the course of a eutectic solidification. Therefore, the chapter focuses on simple procedure for the conversion of the available information about a system into a variational equation. The form of the variational equation and the feasibility to derive this equation depends on the system characteristics. If the fluxes are functions of the time derivatives of the generalized coordinates, the application of the proposed technique results in construction of a genuine variational principle. If the fluxes are determined by the space derivatives of the generalized variables the proposed technique brings about formation of restricted variational equations. © 2005 Elsevier B.V.

Identifier

84882528788 (Scopus)

ISBN

[9780080444888]

Publication Title

Variational and Extremum Principles in Macroscopic Systems

External Full Text Location

https://doi.org/10.1016/B978-008044488-8/50029-1

First Page

543

Last Page

559

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