Laminar flow and heat transfer behaviors of two different metal oxide, Al2O3 (36 nm) and CuO (29 nm), nanofluids flowing through an annular coiled tube heat exchanger (ACTHE) with constant wall temperature boundary condition have been numerically studied to evaluate their superiority over the base fluid (water). Simulations covered a range of nanoparticles volume concentrations of 1.0–6.0% and mass flow rates from 0.025 to 0.125 kg/s. Numerical results indicated that a considerable heat transfer enhancement is achieved by both nanofluids. Results at the same Reynolds number for the pressure drop and heat transfer coefficient show an increase with increasing particle volumetric concentration. The maximum enhancements in heat transfer coefficient were 44.8% and 18.9% for CuO/water and Al2O3/water, respectively. On the other hand, the pressure loss was seven times in comparison to water for CuO/water and about two times for Al2O3/water nanofluid. Also, comparing to the base fluid, nanofluids at low concentrations (up to 3%) can provide the same heat transfer amount at lower pumping power. The overall performance of the enhanced heat transfer technique utilized has been evaluated using a thermohydrodynamic performance index which indicated that Al2O3/water nanofluid is a better choice than CuO/water nanofluid. Moreover, conventional correlations for helical circular tubes for predicting friction factor and average heat transfer in laminar flow regime such as the correlations of Mori and Nakayam and Manlapaz and Churcill, respectively, are also valid for water and the tested nanofluids with small nanoparticle loading in the ACTHE.