Derivation of the Discriminated Dimensionless Numbers that Rule the Forced Mass Convection

Abstract

Discriminated dimensional analysis (DDA, hereinafter), a fundamental extension of classical dimensional analysis (CDA, hereinafter), assumes as independent quantities or physical characteristics of vector character such as length, surface, velocity, viscosity, diffusivity… As a consequence, the dimensional equations of these quantities depend on the spatial direction they are influencing on the physical phenomenon. This causes that the resulting re-grouping of variables to form the dimensionless independent groups are different according to the use of DDA or CDA. The mass transfer problem between a horizontal plate and a forced surrounding fluid is studied assuming two type of boundary conditions, isoconcentration (Diritchlet) and prescribed mass flow at the plate (Neumann). The application of the (-theorem to the set of relevant variables provides an only dimensionless group, the Schmidt number (Sc, hereinafter). To determine the unknowns (thickness of the velocity and concentration boundary layers, as well as the mass transfer coefficient) it is enough to separately introduce these variables in the relevant list of quantities. The two dimensionless groups that emerge for the three unknowns reduce to only one for the limit cases Sc >1, providing for these scenarios the order of magnitude of the unknowns, a result not given by CDA.