The majority of publications in the field of convective transport enhancement in conduits with wavy walls have provided the distribution of the mean Sherwood or Nusselt number per wavelength. The mechanisms, however, driving the increase in heat and mass transfer have not been clearly understood so far. This paper presents the results of a detailed numerical investigation of local heat and mass transfer enhancement in a pipe with sinusoidally varying diameter, covering a wide range of Reynolds numbers from laminar to turbulent how. The discussion is focused on the predicted how field and the turbulence structure, allowing a better understanding of the calculated Sherwood and Nusselt numbers. Part II of this paper deals with the experimental validation of the numerically achieved results.