•In this paper we give a general thermodynamic theory of coupled chemical reaction-thermal diffusion-elastic systems, including complete energy conservation equation, an entropy equation, evolution ...equations of the heat conduction and the mass diffusion, and the complete governing equations of these coupled general heterogeneous systems. This complete governing equation system is the foundation for solving coupling problems including chemical engineering.•This general theory gives a unified method to discuss the heterogeneous chemical reaction-thermal diffusion-elastic systems and the results obtained by this method are consistent with some previous correct theories in special cases.•This paper clarifies some concepts and formulas published in previous papers.
Many transport and rate processes in chemical, physical and biological systems, are controlled by the coupled chemical reaction-thermal diffusion process. Though many literatures, including the literatures of engineering of chemical reactions, discussed this coupled problem, but a unified rigorous theory and a unified method based on the chemical thermodynamics are lacked. In this paper we give a general thermodynamic theory including complete energy conservation equation, entropy equation, evolution equations of the heat conduction and the mass diffusion, especially the complete governing equations of these couple systems. The theory given here revises previous theories, clearly shows which factors should be considered and is valuable for the engineering of chemical reaction and other transport and rate processes.
In this paper we give an appropriate energy equation considering the diffusion and the energy production contributions of species for a complex coupled system with chemical reaction. It is shown that ...the contribution of the mass diffusion on the internal energy is the same whether it is introduced by the mass flow through the outer boundary or by the inner chemical reaction. In addition, the diffusion is a purely irreversible process and does not produce reversible entropy or entropy flow. Based on this theory a new entropy production rate equation is derived for the coupled thermal diffusive chemical heterogeneous system. The evolution equations of the heat conduction and the mass diffusion derived from this theory are fully consistent with the Fourier and Fick’s laws.
This paper discusses some extensions of energy principles in classical and continuum thermodynamics. The modified energy principles will extend the first and second laws in classical continuum ...thermodynamics to the case where the temperature is varied with time. it is shown that the modified energy principles are consistent with the statistical mechanics. The inertial heat and inertial entropy concepts play the kernel roles in the modified energy principles. The temperature wave equation with finite phase velocity is a natural result of the inertial entropy theory. The effect of the temperature inertia in multi-field coupling case is discussed shortly.
The purpose of this paper is to discuss some extensions of classical and continuum thermodynamics. At first the first law in continuum thermodynamics is approximately or exactly extended to the case ...where the temperature is varied with time. Secondly an inertial entropy concept is introduced to the second law of the thermodynamics. The temperature wave equation with finite phase velocity is derived by the inertial entropy theory (IET) in a very simple fashion. Comparison of the inertial entropy theory and the Cattaneo–Vernotte’s equation is given. Some other problems to illustrate the rationality of IET are also discussed shortly.
Many transport and rate processes in chemical, physical, mineral, material and biological fields are controlled by the coupled chemo-electro-thermo-mechanical (CETM) process. Though many literatures ...discussed these coupled problems, but a unified rigorous theory and a unified method based on the chemical thermodynamics are lacked. In this paper on the basis of electrochemistry, the non-equilibrium thermodynamics and modern continuum mechanics we modify some previous theories and give a general theory including mass conservation equation, the electric charge conservation equation, complete energy conservation equation, entropy equation, evolution equations and the complete governing equations of these couple CETM systems. An extension of Nernst–Planck equation is derived for the CETM system. This theory gives a theoretical foundation and a universal method to improve and develop engineering theories, especially for the gradual failure components and cells. In appendix we also discuss the interdiffusion problems in solids with vacancies shortly as a complement of the continuum diffusion.
The universal thermodynamic variational principle proposed in the previous papers for nonlinear dielectrics and thermopiezoelectricity is extended to the thermodiffusion theory in pyroelectricity, ...and it is used as a fundamental physical principle to derive the simple complete governing equations of the generalized thermo-electro-diffuso-elastic theory in this paper. In the generalized thermo-electro-diffuso-elastic theory it is assumed that the variation of temperature needs the extra heat which introduces the inertial entropy, and the variation of chemical potential also needs the extra heat which introduces the inertial concentration, etc. The electro-chemical Gibbs function variational principle, the electric Gibbs function variational principle and the internal energy variational principle are derived in this paper.
The physical variational principle (PVP) in a static magneto-elastic field without source current is discussed first, and then, the PVP in a general electromagnetic field is derived. It is especially ...useful in the plate vibration problem. Using the PVP and the pseudo total stress principle, the electro-magneto-elastic thin plate bending theory in first order and a Mindlin-type plate bending theory for a moderate thickness plate are easily obtained. This method significantly simplifies the derivation of the governing equations of the thin and moderate plates with nonlinear electromagnetic behavior. The Maxwell stress is naturally included in the governing equation. Using the governing equation of a thin plate, the analyses of the stability and vibration of a plate in an external homogeneous magnetic field are discussed.
The physical variational principle (PVP) is a physical principle which is implied in the thermodynamic laws. For a conservative system, the PVP is implied in the first thermodynamic law and gives the ...motion equation. But for a dissipative system, PVP is implied in the extended Gibbs equation, which is the result of the first and second thermodynamic laws. The precision of the PVP in a dissipative system is in the same order of the Gibbs equation. The dissipative work and its converted internal irreversible heat are simultaneously included in the PVP to get the governing equation and the boundary condition of the dissipated variables. The “generalized motion equations” including governing equations of the mechanical momentum and thermoelastic, thermal viscoelastic, thermal elastoplastic, linear thermoelastic diffusive and linear electromagnetic thermoelastic materials etc. can be derived by the PVP of dissipative media in this paper. The conservative system is the special case of the dissipative system. Other than the mathematical variational principle, which is obtained by a known governing equation, the PVP is used to deduce the governing equation. The PVPs including the hyperbolic temperature wave equation with a finite phase speed are also discussed shortly.
The first thermodynamic law contains a universal thermodynamic variational principle. The complete internal energy variational principle in the electroelastic analysis is not discussed in previous ...papers. In this paper this principle will be discussed. From this principle the simple complete governing equations can be deduced, and the Maxwell stress can be naturally derived from this variational principle. It is shown that the Maxwell stress has slightly different forms determined by using internal energy or electric Gibbs free energy variational principle, but substantially they are the same. In the second-order precision the Maxwell stress is uniquely determined, and its expression has the same form for all deformable and rigid dielectrics. The electroelastic analyses in the dielectric should be studied together with its environment, because the electric field exists in all materials except the ideal conductor. The complete governing equations under finite deformation in the initial configuration are also discussed.
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