Peclet number axial, definition

Equations (8) are based on the assumption of plug flow in each phase but one may take account of any axial mixing in each liquid phase by replacing the molecular thermal conductivities fc, and ku with the effective thermal conductivities /c, eff and kn eff in the definition of the Peclet numbers. The evaluation of these conductivity terms is discussed in Section II,B,1. The wall heat-transfer terms may be defined as... 

Values of the radial dispersion coefficient, or the corresponding radial Peclet number, udp/Dr), in packed beds have been determined for both liquids and gases by a number of researchers they are definitely not the same as those in the axial direction. These results are shown in Figure 5.10a and b for liquids and gases, respectively. The corresponding empirical equations fitting these data are... 

Convergence is obtained when the appropriate guess for d p./di at the reactor inlet predicts the correct Danckwerts condition in the exit stream, within acceptable tolerance. To determine the range of mass transfer Peclet numbers where residence-time distribution effects via interpellet axial dispersion are important, it is necessary to compare plug-flow tubular reactor simulations with and without axial dispersion. The solution to the non-ideal problem, described by equation (22-61) and the definition of Axial Grad, at the reactor outlet is I/a( = 1, RTD). The performance of the ideal plug-flow tubular reactor without interpellet axial dispersion is described by... 

The axial heat Peclet number (with a definition similar... 

Here v and d represent dimensionless convection velocity and dimensionless thermal dif-fusivity, resp. (axial mass dispersion is neglected) B is dimensionless reaction enthalpy. Da is the Damkohler number and Le is the Lewis number. We have avoided the conventional introduction of the Peclet number since we would like to examine the effects of convection and thermal diffusion separately. Otherwise, the scaling of the variables and definitions of the dimensionless quantities are conventional, see e.g. (Nekhamkina et al. (2000)). 

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