STUDY OF THE LAMINAR NATURAL CONVECTION PROBLEM ALONG AN ISOTHERMAL VERTICAL PLATE BASED ON DISCRIMINATED DIMENSIONAL ANALYSIS
Abstract
The results derived from the application of “classical” dimensional analysis to the natural convection heat transfer problem are poor, particularly in the case of two- or three-dimensional problems. “Discriminated” dimensional analysis provides more precise solutions, which frequently lead to only one dimensionless monomial. The main feature of the discrimination, on one hand, is that the dimensional basis is extended, taking into account that each of the spatial coordinates of a problem is dimensionally independent. On the other hand, discrimination provides different dimensional equations (derived from the basic laws) for quantities of vectorial character according to its inherent spatial direction. As a result, the quantities that take part in the solution are related each other in a more restricted way than in the case of classical dimensional analysis, leading, in general, to a minor number of dimensionless groups. Many of the known dimensionless numbers, such as the Rayleigh, Grashof, Boussinesq, and Nusselt numbers, have dimensions in a discriminated basis and, per se, do not play an independent role in the solution of the problem. Discriminated dimensional analysis groups these numbers, both among themselves and with other quantities, forming new (discriminated) dimensionless monomials with a precise physical significance. Here, we study natural convection on an isothermal vertical plate using this technique and compare the results with those obtained by classical dimensional analysis.