The coiled flow inverter (CFI) is an enhanced heat exchanger. This device uses the principle of flow inversion to increase heat transfer and has potential for industrial applications. A mathematical model based on experimental and numerical data was developed for the case of single phase flow with water as working fluids. This model includes (ε-NTU) Effectiveness Number of Transfer Units curves, Nusselt correlations, for this specific neither parallel nor counter flow setup. A range of Reynolds numbers from 2,000 to 18,000 in the tube side, and 500 to 2,000 in the shell side was considered. The coiled flow inverter is made of coils and 90◦ bends, inserted in a closed shell. The shell side is cylindrical. The average temperatures at input and output of the heat exchanger were reported for different tube and shell side flow rates. Overall heat-transfer coefficients (Uf) were calculated as well as the Number of Transfer Units (NTU) and Effectiveness (ε) at various process conditions. A Nusselt correlation was proposed for the shell side of this configuration. The ε-NTU curves of the selected heat exchanger have a high resemblance to the parallel flow tube heat exchanger, with a maximum of 2.1 % error. The coiled flow inverter has increases of 200 %, 300 % and 500 %, respectively for effectiveness, number of transfer units and overall heat transfer coefficient compared to a regular parallel flow heat exchanger at the same conditions. Correlations for the CFI in its shell were proposed. This heat exchanger provides higher Uf, reduces cumbersomeness and length of piping.