*Article* **Thermal Calculations of Four-Row Plate-Fin and Tube Heat Exchanger Taking into Account Different Air-Side Correlations on Individual Rows of Tubes for Low Reynold Numbers**

**Mateusz Marcinkowski \*, Dawid Taler, Jan Taler and Katarzyna W˛eglarz**

Faculty of Environmental Engineering and Energy, Cracow University of Technology, 31-155 Cracow, Poland; dawid.taler@pk.edu.pl (D.T.); jan.taler@pk.edu.pl (J.T.); katarzyna.weglarz@doktorant.pk.edu.pl (K.W.) **\*** Correspondence: mateusz.marcinkowski@doktorant.pk.edu.pl

**Abstract:** Currently, when designing plate-fin and tube heat exchangers, only the average value of the heat transfer coefficient (HTC) is considered. However, each row of the heat exchanger (HEX) has different hydraulic–thermal characteristics. When the air velocity upstream of the HEX is lower than approximately 3 m/s, the exchanged heat flow rates at the first rows of tubes are higher than the average value for the entire HEX. The heat flow rate transferred in the first rows of tubes can reach up to 65% of the heat output of the entire exchanger. This article presents the method of determination of the individual correlations for the air-side Nusselt numbers on each row of tubes for a four-row finned HEX with continuous flat fins and round tubes in a staggered tube layout. The method was built based on CFD modelling using the numerical model of the designed HEX. Mass average temperatures for each row were simulated for over a dozen different airflow velocities from 0.3 m/s to 2.5 m/s. The correlations for the air-side Nusselt number on individual rows of tubes were determined using the least-squares method with a 95% confidence interval. The obtained correlations for the air-side Nusselt number on individual rows of tubes will enable the selection of the optimum number of tube rows for a given heat output of the HEX. The investment costs of the HEX can be reduced by decreasing the tube row number. Moreover, the operating costs of the HEX can also be lowered, as the air pressure losses on the HEX will be lower, which in turn enables the reduction in the air fan power.

**Keywords:** plate-fin and tube heat exchanger; air-side Nusselt number; different heat transfer coefficient in particular tube row; mathematical simulation; numerical simulation; CFD simulation
