A dimensionless group is a combination of dimensional or dimensionless quantities having zero overall dimension. In a system of coherent units, it can therefore be represented by a pure number.
The value of dimensionless groups for generalizing experiemental data has been long recognized. Over a hundred years ago, G. G. Stokes demonstrated the importance of the group now known as Reynolds Number as a criterion for similarity of fluid behavior under different conditions [Stokes, (1966)]. It was Helmholtz who showed the significance of the groups now known as Froude Number and Mach Number. Initially, the dimensionless groups did not have specific names, and the first to attach names was M. G. Weber in 1919, when he allocated the titles Froude, Reynolds and Cauchy to groups.
The naming of numbers is an informal process, and there are several cases where the same dimensionless group has been given more than one name, e.g., Froude and Boussinesq, Bond and Eötvös. On the other hand, some savants have been honored by a multiplicity of numbers; Lagrange for instance has three, and Damköhler, no less than five. There does however seem to be one law which, though unwritten, is broken only rarely; that is, that dimensionless titles are awarded posthumously.
The following table lists the dimensionless groups most relevant to heat and mass transfer.
Catchpole, J. P. and Fulford, D., Dimensionless Groups, Ind. Eng. Chem. 58(3):46, 1966 and 60(3):71 (1968).
Stokes, G. G. (1966) Mathematical and Physical Papers 2nd ed, vol. 3.