This article consists of an analytical solution for obtaining the outlet temperatures of the hot and cold fluids in a shell and tube heat exchanger. The system analyzed through the concepts of efficiency, effectiveness (ε-NTU), and irreversibility consisted of a shell and tube heat exchanger, with cold nanofluid flowing in the shell and hot water flowing in the tube. The nanofluid consists of 50% of ethylene glycol and water as the base fluid and copper oxide (CuO) nanoparticles in suspension. The volume fractions of the nanoparticles range from 0.1 to 0.5. The flow rate in the nanofluid ranges from 0.0331 to 0.0568 Kg/s, while two mass flow rates, from 0.0568 and 0.5 Kg/s, for the hot fluid, are used as parameters for analysis. Results for the efficiency, effectiveness, irreversibility, heat transfer rate, and outlet temperatures for cold and hot fluids were obtained graphically. The flow laminarization effect was observed through the results obtained and had significant relevance in the results.