Comparison of a constructal heat exchanger (CHE) and normal heat exchanger (NHE) is analyzed by using second law analysis. Analysis is carried out by considering the three irreversibilities due to heat transfer, pressure drop, and production of the materials and the construction of the heat exchanger. The entropy generation minimization method is used to formulate the entropy generation number expressions of all three irreversibilities for both CHE and NHE to study the differences. Also to realize the advantages of the CHE over the NHE, ratios of each of the entropy generation numbers are considered. Additionally, the thermo‐economic aspect of the heat exchanger is considered to further analyze the economic differences between the CHE and NHE. Graphical results are presented to investigate the influence of different parameters such as the number of pairing levels and initial length‐to‐diameter ratio on the behavior of the three entropy generation numbers along with effectiveness and NTU. From the overall results, we can find that there is an increase in the performance and a cost reduction in the CHE when compared to the NHE. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(1): 39–60, 2014; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21062