Transport of proteins in liquid-filled nanometer-sized apertures with charged surfaces based on both diffusion and convective flow is investigated with the use of fluorescence correlation spectroscopy. The measured fluctuations of fluorescence allow the evaluation of the concentration of molecules directly inside the nanochannel. Here, we supply theoretical models describing the concentration profile of proteins inside nano-confinements, taking into account the steric exclusion, the presence of reversibly adsorbed molecules on surfaces and the exclusion-enrichment effect due to interaction with the electrical double layer. Therefore, this study presents a new step for a deeper understanding of the transport of molecules in nanofluidics.