In this study, the relation between exergy losses and heat flux and their ratio are expressed as a dimensionless number for counter and parallel flow heat exchangers. The relation between the proposed dimensionless number and the number of transfer units (NTU) is formulated as a function of heat capacity and inlet temperatures. The findings based on this research are scrutinized via diagrams both as parametric case and experimental studies. The proportion of exergy losses to heat flux increases with a decreasing heat capacity rate. It has been found that the counter-flow heat exchanger has a lower exergy loss than the parallel one for the same heat exchanger. It was seen that when nanoparticles were added in the fluid used in the exchanger, the effectiveness slightly increased and therefore the necessary heat transfer area decreased. It was also observed that under condensing or boiling states the effectiveness reached its top level. Moreover, it was found that for increasing values of the temperature rates of hot and cold fluids the exergy losses also increased. The model and findings are supported both by a parametric analysis and experimental data revealed in a detailed table in the paper.