[en] The principle aim of the present investigation is to study the boundary layer analysis of nanofluid flow over a bidirectional exponentially stretching sheet in the presence of transverse magnetic field and also in convective condition. The effects of Brownian motion and thermophoretic diffusion of nanoparticle are considered from the mathematical model. Governing partial differential equations are reduced into coupled non-linear ordinary differential equations using suitable similarity transformations, further the system of equations are solved by a new spectral relaxation method. Validation of the results is achieved by comparison with emitting case from previous studies in the literature. Also, it has been shown that the convergence rate of the spectral relaxation method is significantly improved by using the method in conjunction with the successive over relaxation method. The results reveal the existence of interesting Sparrow–Gregg-type Hills for temperature distribution pertinent to some range of parametric values. Moreover the numerical data of drag coefficient, local heat and mass transfer rates are evaluated and analyzed. Effects of local Biot number on temperature and concentration profiles are qualitatively similar. Both the temperature and concentration profiles are enhanced for higher values of local Biot number. (author)