Energy conservation solid phase

Taking into account the axial conduction of heat in the solid phase, the energy conservation equation for the gas is... 

In equation 13, C1 and Cs are the total concentrations in the liquid and solid phases, respectively. This statement of the problem assumes that the convective flux due to the moving boundary (growing surface) is small, the diffusion coefficients are mutual and independent of concentration, the area of the substrate is equal to the area of the solution, the liquid density is constant, and no transport occurs in the solid phase. Further, the conservation equations are uncoupled from the equations for the conservation of energy and momentum. Mass flows resulting from other forces (e.g., thermal diffusion and Marangoni or slider-motion-induced convective flow) are neglected. 

Heterogeneous Models. The two-phase character of a packed-bed is preserved in a heterogeneous model. Thus mass and energy conservation equations are written separately for the fluid and solid phases. These equations are linked together by mass and heat transport between the phases. 

The combustion mechanism addressed involves inert heat conduction in the solid, surface gasification by an Arrhenius process and a gas-phase deflagration having a high nondimensional activation energy. With the density, specific heat, and thermal conductivity of the solid assumed constant, the equation for energy conservation in the solid becomes... 

A model describing one-dimensional heat transfer in parous material [S] is used and modified to study drying and pyrolysis of large wood particles. The model solves the conservation equations of energy, solid phase, liquid water, bound water and the concentrations of species in the gas phase of the porous material. The phases are assumed to be in thermal equilibrium and the variables are calculated as volume averages [6]. 

Since very little RDX decomposes in the solid phase, due to its low temperature conditions, only the energy conservation equation that includes both conductive and radiative heat transfer is required to model the solid-phase processes. The equation takes the form... 

E. Vieil, Simple and direct interpretation of phase angles or derivation degrees in term of energy conservation vs. dissipation with Formal Graphs, J. Solid State Electrochem., 15, 2011, 955-969, doi 10.1007/ S10008-011-1308-9. 

It is the first one that will be emphasized, and can be broken into conservation of mass and energy, which are coupled with Einstein s mass-energy equivalence (E=mc ). As such, the accumulation terms of the conservation of mass are not affected. Also, we could neglect forced convection effects in the system. The resulting mass diffusion equation would be similar to that in Eq. (1.5.2), except that a so-called elastic strain energy could be added to the potential function to take into account crystal lattice differences between solid phases (De Fontaine, 1967). 

Following equations are the basis of the model the conservation of mass for each component, the continuity equation, the conservation of energy for the gaseous phase as well as for the solid phase and - concerning the two-dimensional case - one equation of conservation of momentum for each of the two velocity components. These differential equations are solved numerically by a commercial CFD code using the SIMPLER algorythm. The source terms in the differential equations are due to heat transfer between the two phases, heat loss to the environment and - most important - due to the occuring chemical reactions. The calculation of these source terms is one of the main features of REBOS. 

In the last century Dupre obtained another relationship between ogi, agg, and aig in terms of the work, unit area of the liquid-solid interface. Consider a unit area of a liquid-solid surface (Fig. 1.20). Now, the energy of a unit area of interface plus the work done in separating the surfaces must be equal to the final energy of the unit areas of the solid surface and the liquid surface after they have been separated and are in contact with the gaseous phase. Thus using energy conservation Dupre s equation is obtained,... 

A model has been developed to simulate the non-suspension moving-bed type of flow in pneumatic conveying systems. The flow is modelled as two layers a dilute gas-solids mixture flowing above a dense gas-solids mixture. For each layer the conservation equations for mass, momentum and energy were solved for both the gas and solids phases. In addition mass, momentum and energy transfers between the two layers were modelled. The prediction of pressure profile and the depth of the dense layer showed good agreement with experimental observations. 

Raman scattering arises from the radiating dipole moment induced by the electric field of incident electromagnetic radiation. The laws of momentum and energy conservation govern the interaction between a phonon and a photon. When we consider a solid containing numerous Bravais unit cells and each cell contains n atoms, there will be 3n modes of vibrations. Among the 3n modes, there will be three acoustic modes, LA, TAj and TA2 and 3(n — 1) optical modes. The acoustic mode represents the in-phase motion of the mass center of the unit cell or the entire solid. 

As a further, apparently trivial consequence of this asymmetry, surface atoms are freely accessible from the vacuum side. On the one hand, they are freely accessible by experimental probes, and, on the other hand, they would be the first to be exposed to atoms or molecules of an adjacent (gaseous, liquid, or solid) phase. Third, the applied energy needed to rapture the bonds must now (to a large extent) be stored in the unsaturated bonds of all surface atoms at the newly created surfaces (energy conservation). 

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