The numerical analysis of heat transfer of laminar nanofluid flow over a flat stretching sheet is presented. Two sets of boundary conditions (BCs) are analyzed, i.e., a constant (Case 1) and a linear streamwise variation of nanoparticle volume fraction and wall temperature (Case 2). The governing equations and BCs are reduced to a set of nonlinear ordinary differential equations (ODEs) and the corresponding BCs, respectively. The dependencies of solutions on Prandtl number Pr, Lewis number Le, Brownian motion number Nb, and thermophoresis number Nt are studied in detail. The results show that the reduced Nusselt number and the reduced Sherwood number increase for the BCs of Case 2 compared with Case 1. The increases of Nb, Nt, and Le numbers cause a decrease of the reduced Nusselt number, while the reduced Sherwood number increases with the
increase of Nb and Le numbers. For low Prandtl numbers, an increase of Nt number can cause to decrease in the reduced Sherwood number, while it increases for high Prandtl numbers.