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Abstract In the present study, the combination of both the secondary flow and the nanofluids as a passive approach as a method to maximize the effectiveness of heat exchangers, and reducing the size was examined. The thermo-fluid behavior of annular curved tubes was investigated numerically ANSYS-FLUENT 14.5 CFD package. The effects of key design parameters, such as different annular tube designs (helical, spiral, and conical), different annular cross-sectional shapes (circular, elliptical, square, rectangular, and triangular), and different annular cross-sectional areas, were studied to evaluate the best design for annular curved heat exchanger. Furthermore, the effects of Al2O3–water nanofluids were presented to evaluate their superiority over the water. To achieve thermal and fluid characteristics, the coils are the same length and cross-sectional area. The numerical simulations were performed at Reynolds numbers, Re, of 850–6400 for various nanofluid concentrations, φ, of 1%, 3%, and 5%. The numerical findings showed that the annular helical tube design exhibited better performance than both the spiral and conical tube designs by 5.1% and 10.4%, respectively, while the pressure drop, ΔP, growth was almost negligible. A circular cross section achieved better heat transfer enhancement among the elliptical, square, rectangular, and triangular shapes by 13%, 30%, 40.5%, and 52.9%, respectively, for the same cross section area. At an Al2O3/water nanofluid concentration of 5%, the heat transfer augmentation was 31.7% greater than that of water, while the pressure drop was 2.37 times greater than that of water. The maximum thermo-hydraulic performance index, η, reaches 1.1% for Al2O3–water at a nanofluid concentration of 5%. Graphical abstract