Heat transfer small thermal diffusion coefficient

In accordance with the usual process conditions, the initial temperature of the reactive mixture To and the upper cap temperature Tw are constant during filling, and the temperature of the insert Ti equals the ambient temperature (20°C). The model takes into account that during filling the temperature of the insert increases due to heat transfer from the reactive mix. It is assumed that the thermal properties and density of both the reactive mass and the insert are constant. It is reasonable to neglect molecular diffusion, because the coefficient of diffusion is very small 264 therefore, the diffusion term is negligible in comparison with the other terms in the mass balance equation. 

While the above criteria are useful for diagnosing the effects of transport limitations on reaction rates of heterogeneous catalytic reactions, they require knowledge of many physical characteristics of the reacting system. Experimental properties like effective diffusivity in catalyst pores, heat and mass transfer coefficients at the fluid-particle interface, and the thermal conductivity of the catalyst are needed to utilize Equations (6.5.1) through (6.5.5). However, it is difficult to obtain accurate values of those critical parameters. For example, the diffusional characteristics of a catalyst may vary throughout a pellet because of the compression procedures used to form the final catalyst pellets. The accuracy of the heat transfer coefficient obtained from known correlations is also questionable because of the low flow rates and small particle sizes typically used in laboratory packed bed reactors. 

It might be possible to neglect the external gas phase resistance to mass transfer relative to intrapellet diffusional resistance through a tortuous pathway. An increase in the gas stream flow rate reduces the external mass transfer resistance further. Remember that diffusion coefficients and mass transfer coefficients increase as one progresses from solids to liquids to gases. Hence, gas-phase mass transfer resistances are small, but the intrapellet gas-phase diffusional resistances should be significant, particularly when the intrapellet Damkohler number is quite large. In contrast, thermal conductivities and heat transfer coefficients increase... 

First, we shall use a quasi-stationary approach already mentioned earlier, based on the assumption that characteristic times of heat and mass transfer in the gaseous phase are much shorter than in the liquid phase, since the coefficients of diffusion and thermal conductivity are much greater in the gas than in the liquid. Therefore the distribution of parameters in the gas may be considered as stationary, while they are non-stationary in the liquid. On the other hand, small volume of the drop allows us to assume that the temperature and concentration distributions are constant within the drop, while in the gas they depend on coordinates. Another assumption is that the drop s center does not move relative to the gas. Actually, this assumption is too strong, because in real processes, for example, when a liquid is sprayed in a combustion chamber, drops move relative to the gas due to inertia and the gravity force. However, if the size of drops is small (less than 1 pm) and the processes of heat and mass exchange are fast enough, then this assumption is permissible. As usual, we assume the existence of local thermodynamic equilibrium at the drop s surface, as well as equal pressures in both phases. The last condition was formulated at the end of Section 6.7. 

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