Enthalpy flux vector

The enthalpy flux vector N per unit total cross section in the... 

Then in terms of h and the enthalpy flux vector the enthalpy... 

In unsteady states the situation is less satisfactory, since stoichiometric constraints need no longer be satisfied by the flux vectors. Consequently differential equations representing material balances can be constructed only for binary mixtures, where the flux relations can be solved explicitly for the flux vectors. This severely limits the scope of work on the dynamical equations and their principal field of applicacion--Che theory of stability of steady states. The formulation of unsteady material and enthalpy balances is discussed in Chapter 12, which also includes a brief digression on stability problems. 

In this form of equation (24), the effect of diffusion on the enthalpy flux is included implicitly in the first term, and the only term from the heat-flux vector that remains explicitly is that of heat conduction. The above equations serve to eliminate completely the diffusion velocities from the governing equations, replacing them by the flux fractions. The fact that equations (31) and (33) appear to be less complicated than equations (22) (with dYJdt = 0) and (24) often justifies this transformation. 

The absolute specific enthalpy of the mixture is then= u- -p/p. The total heat-flux vector is defined as... 

Furthermore, it is noted that the first three terms in the brackets on the RHS of (2.452) are similar to the terms in the Gibbs-Duhem relation (2.451). However, two of these three terms do not contribute to the sum. The pressure term vanishes because js = 0. The two enthalpy terms obviously cancel because they are identical with opposite signs. Moreover, the last term in the brackets on the RHS of (2.452), involving the sum of external forces, is zero = 0- Oue of the two remaining terms, i.e., the one containing the enthalpy, we combine with the q term. Hence, the modified entropy flux vector (1.171) and production terms (1.172) become ... 

In the energy equation, the heat flux vector q accounts for the heat conduction via —fsTgrad T, and, because of the different species, the enthalpy diffusion via... 

Equation (7.26) shows that the reactive part of energy flux density is just the enthalpy flux density. The vector Vi4>ki in (7.27) is called the molecular field by de Gennes [5] and usually denoted by h. 

The calculation of the thermal conductivity of gas hydrate using EMD and the Green-Kubo linear response theory was repeated recently. In that work, convergences of the relevant quantities were monitored carefully as a function of the model size. Subtleties in the numerical procedures were also carefully considered. The thermal conductivity of methane hydrate was found to converge within numerical accuracy for 3 x 3 x 3 and 4x4x4 supercells. In the calculation of the heat flux vector there is an interactive term that is a pairwise summation over the forces exerted by atomic sites on one another. The species (i.e., water and methane) enthalpy correction term requires that the total enthalpy of the system is decomposed into contributions from each species. Because of the partial transformation from pairwise, real-space treatment to a reciprocal space form in Ewald electrostatics, it is necessary to recast the diffusive and interactive terms in this expression in a form amenable for use with the Ewald method using the formulation of Petravic. ... 

For each balance law, the values of -0, J and 4> defines the transported quantity, the diffusion flux and the source term, respectively, v denotes the velocity vector, T the total stress tensor, gc the net external body force per unit of mass, e the internal energy per unit of mass, q the heat flux, s the entropy per unit mass, h the enthalpy per unit mass, u>s the mass fraction of species s, and T the temperature. 

This formulation assumes that the process is performed under a constant ambient pressure. Strictly considered Equ. 4-43 should therefore be called an enthalpy balance. But in daily routine the established terminology is heat balance. The vector stands for the heat flux density. In setting up a heat balance many more sources and sinks have to be accounted for than in the case of the mass balance. This is indicated by the box for additional sources and sinks enclosed by the dotted line which is enumerated in addition to the main heat fluxes, such as the heat flow exchanged through the heat transfer area. An example for such other heat sources may be the power input of the agitator in a highly viscous system. 

Gibbs free energy change of reaction (J moP ) enthalpy change of reaction (J moP ) thermodynamic flux (mol s ) equilibrium coefficient (depends) k column vector of kinetic coefficients (first order) (s )... 

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