Generalized Lagrangian Thermodynamics of Thermorheology
نویسنده
چکیده
The thermodynamic principle of virtual dissipation is given a formulation with variations of the field components freed from any constraints. Application of the principle and the introduction of a new state variable called heat content leads to the integro-differential field equations of thermorheology. Rigorous Lagrangian equations are also obtained which avoid the use of the entropy produced as an auxiliary variable while taking into account the heat generated. Quasi-isothermal and quasi-adiabatic evolutions are considered. Attention is called to the completeness of the generalized coordinate description and to implications in finite-element and bifurcation analysis based on the Lagrangian equations.
منابع مشابه
Structure formation and generalized second law of thermodynamics in some viable f(R)-gravity models
We investigate the growth of matter density perturbations as well as the generalized second law (GSL) of thermodynamics in the framework of f(R)-gravity. We consider a spatially flat FRW universe filled with the pressureless matter and radiation which is enclosed by the dynamical apparent horizon with the Hawking temperature. For some viable f(R) models containing the Starobinsky, Hu-Sawicki, Exp...
متن کاملThermodynamics and Heat-Flow Analysis by Lagrangian Methods
New procedures for the analysis of heat flow are summarized and further applications are presented. The methods may be considered as a special case of a more general formulation of the thermodynamics of irreversible processes. This formulation is based on the introduction of a new thermodynamic potential, the concept of flow field as a state variable, and the use of Lagrangian techniques and ge...
متن کاملGeneralized Einstein's Equations from Wald Entropy
Abstract: We derive the gravitational equations of motion of general theories of gravity from thermodynamics applied to a local Rindler horizon through any point in spacetime. Specifically, for a given theory of gravity, we substitute the corresponding Wald entropy into the Clausius relation. Our approach works for all diffeomorphism-invariant theories of gravity in which the Lagrangian is a po...
متن کاملGeneralized Lagrangian Equations of Nonlinear Reaction-diffusion
The principle of virtual dissipation for irreversible processes in open systems is given a new formulation where variations are unconstrained everywhere including the boundary. As a complementary development a new chemical thermodynamics of open systems initiated earlier is given a simplified derivation and new results are presented. A new evaluation of entropy production for fully nonlinear re...
متن کاملNew variational-Lagrangian thermodynamics of viscous fluid mixtures with thermomolecular diffusion
A principle of virtual dissipation generalizing d’Alembert’s principle to nonlinear irreversible thermodynamics is applied to viscous fluid mixtures with coupled thermomolecular diffusion. Origina,l dynamical field equations are obtained directly from the variational principle. The use of new fundamental concepts and methods in the thermodynamics of open systems avoids the difficulties inherent...
متن کامل