The main objective of this study is to explore the existence of thermodynamic irreversibility Extrema for laminar fluid flow with heat transfer under fully developed conditions through different cross-sectional, free-flow area ducts. The evaluation of thermodynamic trade-offs caused by simultaneous heal transfer at a finite temperature difference and fluid friction will be emphasized in terms of the dimensionless entropy generation as a performance criterion. A set of duct geometries under investigation included circular, rectangular, square, triangular, sine and a set of longitudinal finned circular tubes. One of the pragmatical goals of the analysis is to establish the mutual relationship between the hydrodynamic and thermal aspects using, from one side, the conventional area goodness factor, and from the other side, the thermodynamic performance evaluation criterion. The quantitative results for the set of parameters under investigation show that the improvement and/or the deterioration of the performance of one geometry with respect to another depend on the duct geometry, the Reynolds number and the inlet-wall temperature ratio for a given fluid and a certain duct length.