Heat and Mass Transfer Coefficient Concepts

Fairly rigorous expressions for the interfacial heat and mass transfer terms are defined in sect 3.3 for the different averaging methods commonly applied in chemical reactor analysis. However, since the modeling concepts are analogous for the different averages, we choose to examine these constitutive equations in the framework of the volume averaging method descibed in sect 3.4.1. This modeling approach is used extensively in reactor analysis because the basic model derivation is intuitive and quite easy to understand. 

The definitions of the heat and mass transfer fluxes are thus merely based on empirical arguments, so in the literature there are given more than one way to interpret the transfer coefficients [15, 139]. Basically, the transfer coefficients are either treated as an alternative model to the fundamental diffusion models (i.e., the Fourier s and Pick s laws) or the transfer coefficients are taking both diffusive and convective mechanisms into account through empirical parameterizations. However, in reaction engineering practice the distingtion between these approaches is rather blurred so it is not always clear which of the fundamental transport processes that are actually implemented. 

The advantage of working in terms of the traditional joint diffusive and convective flux concept is that the contribution of convection is automatically taken into account and we do not need separate models for the interfacial transfers due to phase change. The disadvantage is that the transfer coefficients show a more complicated dependence upon concentration and mass transfer rates. 

In a scientific view the loss in physical rigor might outweigh the possible gain in computational ease [139]. Nevertheless, in most chemical reactor analysis the transfer coefficients are defined in terms of the combined fluxes including both diffusive and convective contributions [27]. 

In the following sections a survey of the elementary diffusion theories that are determining the basis for the mass transfer coefficient concepts is given. No heat and mass transfer models dealing with simultaneous chemical reactions are considered to maintain attention to the fundamental principles. 

1 Mass Ti ansfer in Regions Close to a Stagnant Interface 

The description of the interfacial transport processes in terms of mass transfer coefficients is an approximate engineering concept that normally results in simpler mathematical problems than the alternative description in terms of the more fundamental Pick s law. The definition of the mass transfer coefficient is thus based on an oversimplified picture of the actual physics. The mass transfer coefficient concept relies on the hypothesis that the changes in concentrations are limited to two hypothetical stagnant films, one on each side of the stagnant interface. The transfer flux is thus transfering mass between the interface and the well mixed bulk solution. The amount of matter transferred is expected to be proportional to the concentration difference and the interfacial area. The proportionality coefficient, kc, is called 

Correspondingly, the mean interfacial mass flux is assumed to be proportional to the difference between the interfacial average and the intrinsic volume average of the quantity determing the driving force of the fluxes [91, 92]. 

The species transfer can thus be expressed as a mass flux ( i,yt)A/ (kg/s m ) in line with (3.185), simply by multiplying the conventional mole flux by the molecular weight Mo,-  

---