When the governing equations of a problem are known, the non-dimensionalization of these equations (applied in their classical form) is a useful and widely used method that can be used to identify the dimensionless groups that rule the solution. However, neither this technique nor dimensional analysis necessarily provides the most precise solution in terms of the sought numbers. The use of discrimination, a qualitative rather than quantitative extension of the non-dimensionalization method, has demonstrated notable advantages over the classical method because it invariably provides a more precise set of dimensionless groups. The basis for the correct application of discrimination depends on a deep understanding of the phenomena involved in the problem, particularly in complex (coupled) problems. In this paper, discriminated non-dimensionalization is applied to investigate a mixed convection problem in porous media, the Yusa problem. The derived discriminate groups are compared with those already known in the literature and deduced by classical methods. A number of scenarios are numerically solved to check the reliability of the discriminated groups in contrast with classical groups. Copyright (C) 2016 John Wiley & Sons, Ltd.