Enthalpy conservation

Cyclic enthalpy conservation relationships such as (3.100) are summarized by... 

The enthalpy conservation equation of the multiphase medium, obtained from the sum of the appropriate balance equations of the constituents includes the heat effects due to phase changes and hydration (dehydration) process, as well as the convectional and latent heat transfer,... 

The region over which this balance is invoked is the heterogeneous porous catalyst pellet which, for the sake of simplicity, is described as a pscudohomoge-ncous substitute system with regular pore structure. This virtual replacement of the heterogeneous catalyst pellet by a fictitious continuous phase allows a convenient representation of the mass and enthalpy conservation laws in the form of differential equations. Moreover, the three-dimensional shape of the catalyst pellet is replaced by assuming a one-dimensional model... 

In reality however, situations also exist where a more complex form of the rate expression has to be applied. Among the numerous possible types of kinetic expressions two important cases will be discussed here in more detail, namely rate laws for reversible reactions and rate laws of the Langmuir-Hinshelwood type. Basically, the purpose of this is to point out additional effects concerning the dependence of the effectiveness factor upon the operating conditions which result from a more complex form of the rate expression. Moreover, without going too much into the details, it is intended at least to demonstrate to what extent the mathematical effort required for an analytical solution of the governing mass and enthalpy conservation equations is increased, and how much a clear presentation of the results is hindered whenever complex kinetic expressions are necessary. 

The main advantage of using a Lagrangian framework for dispersed phase particles is that particle-level phenomena can be modeled rigorously. Species and enthalpy conservation equations for individual particles can be written ... 

Other conservation equations (enthalpy and species) for multiphase flows can be written following a similar general format. For example, the enthalpy conservation equation is written ... 

These considerations have been accomplished in an example to model the SPS behavior of graphitic elements that are inserted between the two stainless steel rams used in the model 515S system (Sumitomo), which is schematically shown in Fig. 6.30 [42]. The geometry of the graphitic elements has been designed in such a way that it not necessary to consider the effect of vertical interfaces between them. As a result, the horizontal contact resistances can be excluded in the mathematical models. A 2D model in cylindrical coordinates based on the usual enthalpy conservation equation that takes into account the Joule heat generation is developed, which is coupled to density current balances expressed in terms of the RMS portion of the electric potential and the mechanic equilibrium equations due to elastic behavior and thermal expansion of the materials. Thermophysical properties of... 

Calculation of enthalpy conservation efficiencies for aerobic growth processes. 

The same methods used above in Section 3.5.2. for calculating free energy conservation efficiencies can be used to calculate enthalpy conservation efficiencies. Using appropriate data from Table 3, the enthalpy change Af-l f accompanying the process represented by equation (25) is calculated to be -463.89 kJ ICCmol. For the growth of 5. cerevisiae aerobically on glucose as represented in Table 2 ... 

Values for the fi ee energy and enthalpy conservation efficiency during anaerobic growth can also be calculated using the same methods as for aerobic growth. To calculate free energy conservation efficiencies... 

Calculating enthalpy conservation efficiencies for anaerobic growth processes. 

The sum of the efficiency values above represents the total enthalpy conservation efficiency. The fraction of the enthalpy that is lost during metabolism must then be (1 - 0.964). From this... 

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