The entropy generation (irreversibility) concept founded on the second law of thermodynamics may be applied in heat exchanger analysis. In this paper the quantity termed enthalpy exchange irreversibility norm (EEIN) is the measure of the internal heat exchanger irreversibilities. The behavior of EEIN as a function of the heat exchanger thermal size is discussed for an arbitrary flow arrangement and more precisely for two characteristic limiting cases: cocurrent and countercurrent heat exchangers.