Interfacial transfer heat transport

Similar constitutive equations are used to approximate the integrals representing the interfacial heat transfer rates by convection and conduction through the stagnant films in the vicinity of a catalytic solid surface. Hence, the film model can be used to approximate the interfacial heat transport (3.167) by ... 

Stemling and Scriven wrote the interfacial boundary conditions on nonsteady flows with free boundary and they analyzed the conditions for hydrodynamic instability when some surface-active solute transfer occurs across the interface. In particular, they predicted that oscillatory instability demands suitable conditions cmcially dependent on the ratio of viscous and other (heat or mass) transport coefficients at adjacent phases. This was the starting point of numerous theoretical and experimental studies on interfacial hydrodynamics (see Reference 4, and references therein). Instability of the interfacial motion is decided by the value of the Marangoni number, Ma, defined as the ratio of the interfacial convective mass flux and the total mass flux from the bulk phases evaluated at the interface. When diffusion is the limiting step to the solute interfacial transfer, it is given by... 

Heat and Mass Transfer Using the film theory, both phenomena mainly depend on the film and gas stream thickness and the type of reaction. Other parameters are the interfacial area, the residence time and the axial dispersion. Good mass and heat transport presume a good fiow equipartition in the channels. In mesh reactors the mesh open area determines the interfacial area. Mass transfer coefficients ki a from 3 to 8 L s and higher values in catalytic systems can be achieved [25]. 

For the catalyst layers, the foremost objective is to obtain the highest reactivity or transfer current density with respect to the desired electrochemical reactions with a minimum amount of the catalyst (DOE target for 2010 0.29 g Pt per kW). This requires a huge electrocatalytically active surface area, small kinetic barriers to bulk transport and interfacial transfer of protons, electrons and reactant gases, and proper handling of product water and waste heat. 

Recall the mathematical classification of boundary conditions summarized in Table 3.5. For example, in energy transport, the first type corresponds to the specified temperature at the boundary the second type corresponds to the specified heat flux at the boundary and the third type corresponds to the interfacial heat transport governed by a heat transfer coefficient. 

When two or more phases are present, it is rarely possible to design a reactor on a strictly first-principles basis. Rather than starting with the mass, energy, and momentum transport equations, as was done for the laminar flow systems in Chapter 8, we tend to use simplified flow models with empirical correlations for mass transfer coefficients and interfacial areas. The approach is conceptually similar to that used for friction factors and heat transfer coefficients in turbulent flow systems. It usually provides an adequate basis for design and scaleup, although extra care must be taken that the correlations are appropriate. 

The effect of ultrasound is ascribed to promotion of cavitation, which is the rapid generation and collapse of microbubbles within the medium this cavitational collapse results in dramatic pressure and thermal differentials on a microscopic scale, which accelerate mass transport and enhance energy transfer [16]. The enhanced mass transport has also been used to increase the sensitivity of voltammetric analysis [17]. Besides the enhanced mass transport, heating and interfacial cleaning due to the asymmetric collapse of the bubbles at the solid/liquid interface may influence electrolysis. 

Kocamustafaogullari G, Ishii M (1995) Foundation of the interfacial area transport equation and its closure relations. Int J Heat Mass Transfer 38(3) 481-493... 

Though most simulators provide a library of standard models for process units, there is only limited support for very specific units such as those typically occurring in polymerization processes. Ecpiation-oriented ]895, 916] and object-oriented [54, 1002[ process modeling environments are suitable for the development of customized models for non-standard units such as for the leacher in the PA6 process. Complex transport problems involving fluid dynamics as well as other kinetic phenomena (i. e. chemical reaction, nucleation and growth of particles, interfacial heat and mass transfer etc.) can be treated... 

At high enough qualities and mass fluxes, however, it would be expected that the nucleate boiling would be suppressed and the heat transfer would be by forced convection, analogous to that for the evaporation for pure fluids. Shock [282] considered heat and mass transfer in annular flow evaporation of ethanol water mixtures in a vertical tube. He obtained numerical solutions of the turbulent transport equations and carried out calculations with mass transfer resistance calculated in both phases and with mass transfer resistance omitted in one or both phases. The results for interfacial concentration as a function of distance are illustrated in Fig. 15.112. These results show that the liquid phase mass transfer resistance is likely to be small and that the main resistance is in the vapor phase. A similar conclusion was reached in recent work by Zhang et al. [283] these latter authors show that mass transfer effects would not have a large effect on forced convective evaporation, particularly if account is taken of the enhancement of the gas mass transfer coefficient as a result of interfacial waves. 

In the rate-based models, the mass and energy balances around each equilibrium stage are each replaced by separate balances for each phase around a stage, which can be a tray, a collection of trays, or a segment of a packed section. Rate-based models use the same m-value and enthalpy correlations as the equilibrium-based models. However, the m-values apply only at the equilibrium interphase between the vapor and liquid phases. The accuracy of enthalpies and, particularly, m-values is crucial to equilibrium-based models. For rate-based models, accurate predictions of heat-transfer rates and, particularly, mass-transfer rates are also required. These rates depend upon transport coefficients, interfacial area, and driving forces. It... 

In slurry systems, similar to fluidized beds, the overall rate of chemical transformation is governed by a series of reaction and mass-transfer steps that proceed simultaneously. Thus, we have mass transfer from the bubble phase to the gas-liquid interface, transport of the reactant into the bulk liquid and then to the catalyst, possible diffusion within the catalyst pore structure, adsorption and finally reaction. Then all of this goes the other way for product. Similar steps are to be considered for heat transfer, but because of small particle sizes and the heat capacity of the liquid phase, significant temperature gradients are not often encountered in slurry reactors. The most important factors in analysis and design are fluid holdups, interfacial area, bubble and catalyst particle sizes and size distribution, and the state of mixing of the liquid phase. ... 

Bohnet, M. Influence of the Transport Properties of the Crystal/Heat Transfer Surface Interfacial on Fouling Behavior, Chemical Engineering and Technology, Band 26, Heft 10 (2003), p. 1055/1060... 

Wu Q, Kim S, Ishii M, Beus SG. (1998) One-group interfacial area transport in vertical bubbly flow. Int. J. Heat Mass Transfer, 41 1103-1112. 

Heat and Mass Transfer The flow pattern, that is to say the fluid particle shape and dimensions, and the film thickness play a dominant role concerning these transport phenomena due to their importance for the determination of the size of the interfadal area. In bubbly and foam flow it can be characterized by the interfacial... 

Pitchumani, R., Ranganathan, S., Don, R., Gillespie, J. W. and Lamontia, M. A., Analysis of transport phenomena governing interfacial bonding and void dynamics during thermoplastic tow-placement , Intematiorud Journal of Heat and Mass Transfer, 1996,39(9), 1883. 

Heat transfer at the interfacial surfaces is complex and involves radiation, convection, and at the covered bed/covered wall interface, conduction as well. Although a heat transfer coefficient can be allocated to each transport path shown in Figure 8.8 (Gorog et al., 1983) this should not obscure the difficulty associated with realistic determination of values for these coefficients. As mentioned earlier, the one-dimensional model is required only to produce a framework from which to operate... 

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