The present work uses a perturbation procedure to deduce the small perturbation differential equations for velocity, temperature, and the diffusion equation for nanoparticle volume concentration. Thermophysical variables are obtained from conventional means (e.g., mixture and field theory estimates) for nanofluids consisting of alumina nanoparticles dispersed in water (alumina-water nanofluid) and gold nanoparticles dispersed in water (gold-water nanofluid), and, in the case of gold-water nanofluid, molecular dynamics results are used to estimate such properties, including the transport coefficients. The very thin diffusion layer, at large Schmidt numbers, is found to have a great impact on the velocity and temperature profiles, owing to the transport property dependency and has a profound influence on surface conduction heat transfer rate enhancement and skin friction suppression for the case of nanofluid concentration withdrawal at the wall. In this case, the diffusional heat transfer rate is negligible, again, owing to the large Schmidt numbers encountered. Possible experiments directed at this interesting phenomenon are discussed.