In the present study, effect of different geometries of inner and outer tube surfaces on heat transfer of a double pipe heat exchanger is studied. Water-CuO nanofluid, that is assumed to be a single phase, flows in the outer tube. Two-equation standard κ-εturbulence model is used to model the turbulent flow. Simulations are done for different cases include convex, concave and smooth surfaces for inner and outer tubes at different Reynolds numbers. Results show that the maximum heat transfer corresponds to the convex-concave case in comparison with the smooth-smooth one. Heat transfer rate increases with the Reynolds number, but the slope of the increase for nanofluid is lesser than that for the pure fluid. It is demonstrated that the friction factor decreases with the Reynolds number, so the pressure drop decreases as the Reynolds number increases. Also, the simulations are done for two other nanofluids, water-ZnO oxide and water-SiO2 dioxide with a volume fraction of 3%. It is found that water-CuO nanofluidflow leads to more heat transfer rate in a double pipe heat exchanger in comparison with the other nanofluids.