A review of the concepts of thermal efficiency and thermal and hydraulic irreversibilities is presented, applying the second law of thermodynamics and thermodynamic Bejan number. An example problem, typical of thermal heat exchange between two fluids, is given, with a dimensionless solution for parallel and counterflow flows. The quantities of interest presented through the example are thermal efficiency, thermal effectiveness, thermal irreversibility, the relationship between outlet and inlet temperatures versus the number of thermal units, and outlet temperature for hot fluid. The theory presented in this review has been applied to numerous problems related to heat exchangers over the last three years, as per references.