The present article focuses on the second law attributes of a counter-flow spiral heat exchanger working with an Al2O3-H2O nanofluid with employing the two-phase mixture model. To improve the cogency of the simulations, the turbulence modeling is performed using four-equation transition Shear Stress Transport (SST) model. The simulations are conducted for different nanoparticle volume fractions and nanofluid flow rates. It is shown that by dispersing further nanoparticles in the common fluid, the total entropy generation of the hot nanofluid significantly diminishes, whereas the cold water and the heat exchanger body exhibit higher thermal entropy generation. The overall exergy destruction in the heat exchanger significantly decreases by the increase of the volume fraction, while it tends to increase by the flow rate increment. For instance, an about 9.2% reduction in the overall exergy destruction is observed as the volume fraction increases from 0.01 to 0.04. All the conditions exhibit great second law efficiency so that the minimum second law efficiency is larger than 0.84, and increases with the raise of either the volume fraction or flow rate. (c) 2021 The Society of Powder Technology Japan. Published by Elsevier B.V. and The Society of Powder Technology Japan. All rights reserved.