The present study numerically investigates a double pipe heat exchanger with a simple and corrugated tube assuming three different wave amplitudes. The simulation is performed using ANSYS package, considering turbulent flow and k-ω SST turbulence model. Accordingly, the heat exchanger type is considered to be water-to-water and the corresponding flow is parallel so that the hot and cold fluids pass through the inner tube and the shell, respectively. The results show that, in the similar Reynolds number, corrugating increases Nusselt number so that at the maximum state the average Nusselt number of the corrugated heat exchanger is about 1.75 times as compared to the simple heat exchanger. Furthermore, the maximum value of local Nusselt number and local skin friction coefficient occur at the bottleneck and the minimum value occur during reverse flow. Moreover, from effectiveness and efficiency of the second law of thermodynamics, the corrugation of the tube also improves the corresponding performance. Hence, compared to the simple heat exchanger, the ratio of effectiveness and second law efficiency of thermodynamics of the corrugated heat exchanger is 1.73 and 1.17, respectively.