This paper conflates two heat exchanger design approaches - the epsilon-N-tn, (effectiveness-number of transfer units) and the EGM (entropy generation minimization) - focusing on heat exchangers with uniform wall temperature, i.e. condensers and evaporators. An algebraic formulation which expresses the dimensionless rate of entropy generation as a function of the heat exchanger geometry (number of transfer units), the thermal-hydraulic characteristics (friction factor and Colburn j-factor), and the operating conditions (heat transfer duty, core velocity, surface temperature, and fluid properties) is derived. It is shown that there does exist a particular number of transfer units which minimizes the dimensionless rate of entropy generation. An algebraic expression for the optimum heat exchanger effectiveness, based on the working conditions, heat exchanger geometry and fluid properties, is also presented. The theoretical analysis led to the conclusion that a high effectiveness heat exchanger design does not necessarily provide the best thermal-hydraulic performance. (C) 2012 Elsevier Ltd. All rights reserved.