In the present work, the dimensionless model developed and validated by Baritto and Bracamonte (2012) for thermal behavior of flat plate solar collectors without glass cover was improved by adding the entropy balance equation in a dimensionless form. The model was solved for a wide range of aspect ratios and mass flow numbers. A parametric study was developed and thermodynamically optimal configurations were identified. A set of equations were fitted to reproduce the results and a straight forward method is proposed for the estimation of optimal aspect ratios as functions of the mass flow number and the outlet temperature, which are, in most of cases, requirements for practical applications. (C) 2013 Elsevier Ltd. All rights reserved.