An analysis is made for the effect of throughflow on the onset of convection in a rectangular box under the assumption that total flux (sum of diffusive, thermophoretic, and convective) is zero on the boundaries. A linear stability analysis and Galerkin weighted residual method are used to obtain the Rayleigh number and stability curves for the onset of convection. Three dominating combination of parameters are extracted from the non-dimensional analysis. All rescaled parameters promote the convection. Aspect ratios, throughflow, and nanoparticles play an important role in the formulation of cell distribution and development of convection. Oscillatory convection is possible for permissible range of nanofluid parameters. It is also found that the size of a cellular mode is altered by throughflow and nanoparticles.