Discriminated dimensional analysis of the energy equation: Application to laminar forced convection along a flat plate

Abstract

In contrast to “classical” dimensional analysis, whose application is widely described in heat transfer textbooks despite its poor results, the less well-known discriminated dimensional analysis approach provides a deeper insight into the physical problems involved and much better results in all cases where it is applied. The basis of this technique is firstly used to test the dimensional homogeneity of the energy equation for incompressible fluids. It is then applied to the laminar forced convection on flat plates to determine the characteristic lengths of the problem, drag forces and heat transfer coefficient. Neither the classical Reynolds and Nusselt numbers nor the drag coefficient are relevant dimensionless parameters for the discriminated dimensional analysis and they do not play a separate (independent) role in the solution of this kind of problem. Furthermore, the dimensionless groups that really play a separate role are obtained with this technique. The apparent equivalence between dimensional analysis and scale analysis is discussed.