A rigorous mathematical approach is presented to understand the transparent impacts of Buongiorno nanofluid model on the rate of heat and mass transfer in different fluid flow geometries. Unlike the numerical simulations available in the recent open literature, the currently derived formulas enable us to analytically explain why heat and mass transfer should be enhanced or reduced by the frequently used Buongiorno nanofluid model accounting for the Brownian motion and thermophoresis effects. Two distinct boundary constraints are taken into account usually employed in this model by the active researchers working in this field. Hence, both the constant wall mass as well as the zero net particle mass flux on the wall are studied analytically. Initially, the obtained results are tested on the well-documented Crane's linearly stretching sheet solution with perfect agreement and accuracy. Then, the solutions are validated on some published results. From the asymptotic formulas not only the special quantitative values but also the general trends of heat and mass transfer can be estimated accurately.