Analysis for Mass Transfer by Natural Convection in Finite Space

Dimensional Analysis for Mass Transfer by Natural Convection in Finite Space 

We introduce this problem with two particular examples. The first is the etching of a metal placket immersed in a large specifically formulated liquid, with no gas production. The second is the drying of a recently built wall. In both cases, we have a non-observable flow and a particularization of the dimensional analysis is required. 

These two examples do not appear to have any similarities. Nevertheless, after a deep analysis, we can conclude that both cases consist of a natural convection process produced by a concentration gradient. 

This is presented schematically in Fig. 6.3, which also shows that the kinetics of these processes is described by the transport rate of A from the wall to the adjacent media. Using Fig. 6.3, we can establish that two elementary processes are presented in this system. The first is the flow induced by the concentration gradient and the second is the mass transfer sustained by the processes on the surface (a chemical reaction in the case of the metal placket immersed in a specifically formulated liquid and the transport through the porosity in the case of the drying wall). The case presented here corresponds to the situation when, in respect of the bulk density, the fluid density begins to decrease near the wall. This generates the displacement of the media and the specific ascension force, which is equivalent to the density difference. This phenomenon depends on the concentration difference in fluid A Aca=(cap - c ). From Fig. 6.3 we can write a list of process variables  

3 concentration of A, 4 fluid velocity, 5 and 6 fluid global displacement. System properties Geometric properties H height of placket. Fluid properties  

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