Boundary layer, laminar, combined

Quite new ideas for the reactor design of aqueous multiphase fluid/fluid reactions have been reported by researchers from Oxeno. In packed tubular reactors and under unconventional reaction conditions they observed very high space-time yields which increased the rate compared with conventional operation by a factor of 10 due to a combination of mass transfer area and kinetics [29]. Thus the old question of aqueous-biphase hydroformylation "Where does the reaction takes place " - i.e., at the interphase or the bulk of the liquid phase [23,56h] - is again questionable, at least under the conditions (packed tubular reactors, other hydrodynamic conditions, in mini plants, and in the unusual,and costly presence of ethylene glycol) and not in harsh industrial operation. The considerable reduction of the laminar boundary layer in highly loaded packed tubular reactors increases the mass transfer coefficients, thus Oxeno claim the successful hydroformylation of 1-octene [25a,26,29c,49a,49e,58d,58f], The search for a new reactor design may also include operation in microreactors [59]. 

Before turning to a discussion of other methods of solving the laminar boundary layer equations for combined convection, a series-type solution aimed at determining the effects of small forced velocities on a free convective flow will be considered. In the analysis given above to determine the effect of weak buoyancy forces on a forced flow, the similarity variables for forced convection were applied to the equations for combined convection. Here, the similarity variables that were previously used in obtaining a solution for free convection will be applied to these equations for combined convection. Therefore, the following similarity variable is introduced ... 

Tbe numerical procedure for solving the laminar boundary layer equations for forced convection that was described in Chapter 3 is easily extended to deal with combined convection. The details of the procedure are basically the same as those for forced convection and the details will not be repeated here [16]. A computer program, LAMBMIX, based on the procedure is available in the way discussed in the Preface. This program can actually allow the wall temperature or wall heat dux to vary with X but as available, the program is set for the case of a uniform wall temperature or a uniform wall heat flux. 

This phenomenon is the same for ail types of geometric shapes of catalysts, monoliths, pellets or nets, In a monolith the mass transfer, between gas bulk and the outer surface of catalyst, is not particular good since the flow, at least in the boundary layers, tends to become laminar, but the pressure drop is low. In a packed bed with pellets the mass transfer is very good in general, but the pressure drop is high. A stack of nets, however, combine good mass transfer and low pressure drop, it is in between a monolith and a packed bed. 

Gas flow through the small channels of a honeycomb matrix is nearly always laminar, and analytical solutions are available for heat and mass transfer for fully developed laminar flow in smooth tubes. In the inlet region, where the boundary layers are developing, the coefficients are higher, and numerical solutions were combined with the analytical solution for fully developed flow and fitted to a semitheoretical equation [14] ... 

Inamura and Tomoda [28], and Inamura et al. [2] investigated the behavior of liquid sheet generated by impingement of a liquid jet onto a solid wall. They [2] combined Dombrowski s model of sheet breakup with the sheet thickness model developed based laminar boundary-layer analysis to predict the droplet size. However, they did not provide any correlation for droplet size. Fard et al. [10] studied numerically the effect of liquid properties and nozzle geometry on the droplet size distribution produced by splash plate nozzle. Again, no correlation to relate the droplet size with the studied parameters was provided. 

Entry Lengths and Boundary Layers It is the case that most flow investigations at the microscale happen in the laminar flow regime with developing boundary layer (combined entry lengths). As for macroscale cases, the velocity entry length Le is often simply calculated by... 

Mass transfer coefficients are the basis for models where the dissolved species are transported by a combination of diffusive and advective processes. The diffusive mass transfer coefficient ko, m/sec) is based on boundary layer theory. The basic premise of boundary layer theory is that, for laminar ffow, the ffuid velocity adjacent to a solid surface is zero (the no slip condition ) and the velocity increases as a parabolic function of distance away from the surface until it matches the velocity of the bulk fluid (Figure 7.5). This means that there is a thin layer of fluid with a thickness of 5d (m) adjacent to the surface that is effectively static. The rate of mass transport through this layer is limited by the diffusion rate of the dissolved species. The diffusional boundary layer is much thinner than the velocity boundary layer. For laminar flow past a flat surface, the thickness of the diffusional boundary layer is related to the thickness of the velocity boundary layer (Sy) by the Schmidt number, which compares the fluid viscosity to the diffusivity (Probstein, 1989). 

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