This paper examines thermohydraulic performance of a spiral heat exchanger operated with the water–alumina nanofluid under turbulent flow regime. The hot water flows in one side while the cold nanofluid flows inside the other side of the heat exchanger. The effects of Reynolds number, mass flow rate, nanoparticle concentration and gap between the plates on the convective heat transfer coefficient, pumping power, overall heat transfer coefficient as well as effectiveness of the heat exchanger are evaluated. The average heat flux enhances with the increase of concentration and Reynolds number, while reduces by increasing the gap magnitude. Moreover, convective heat transfer coefficient and overall heat transfer coefficient enhance with increasing Reynolds number and concentration. Thereby, the convective heat transfer coefficient increases about 134.4% with increase of Reynolds number from 4000 to 11,000 at concentration of 2%, while it enhances almost 26.3% with increment of the concentration from 0 to 5% at Reynolds number of 10,000. The pumping power intensifies by increasing either concentration or Reynolds number, and at higher Reynolds numbers, the effect of concentration on the pumping power becomes more noticeable. Moreover, the pumping power intensifies by decreasing the gap, and this augmentation is more significant at higher concentration. Based on constant mass flow rate, however, an optimum concentration is obtained in which maximum heat transfer occurs. Meanwhile, the pumping power decreases by increasing the concentration at a constant mass flow rate. Furthermore, the effectiveness enhances by increasing the Reynolds number and reducing the gap.