This study numerically investigates the heat and mass transfer characteristics of water—silver nanofluid flowing in a spiral heat exchanger (HX) using the two-phase mixture model. The hot side of the HX is pure water at the temperature of 343 K and Re = 500, while the cold side is nanofluid with volume fraction up to 5% at 305 K and Re number ranging from 500 to 2000. The cold and hot tubes are concentrically twisted 3.5, 5.5 and 7.5 turns in order to explore the heat transfer effectiveness of the heat exchanger as a function of the spiral turns. The results indicate that increasing the volume fraction of nanoparticles, Re number and the number of turns increases the overall heat transfer coefficient, heat rate absorbed by the cold fluid and pumping power of the HX noticeably. The above-mentioned factors also improve the temperature stability of the input fluid along with the heat exchanger. The effectiveness of the HX decreases by increasing the Re number, the volume fraction of nanoparticles and turning rounds due to the greater pressure drop of the coolant fluid. At a constant Re number, increasing the volume fraction and number of turns enhances the NTU parameter to a great extent.