A numerical investigation for examining the effect of a uniform partial magnetic field on fluid flow and heat transfer of Multi Walled Carbon Nano Tube (MWCNT)-water nanofluid is done in a vented square cavity considering aiding and opposing flows without changing temperature boundary conditions. Modified Maron-Pierce equation for dynamic viscosity and Xue equation for thermal conductivity of nanofluid are achieved. The radial basis function (Rbf) based pseudo spectral method with cubic polyharmonic spline Rbf and nonuniform Gauss-Chebyshev-Lobatto (GCL) nodes are performed to solve the problem governed by stream function-vorticity formulation. The considered parameters are Richardson number (0.1 <= Ri <= 100), the center of the partial magnetic field (0.25 <= lbc <= 0.75), Hartmann number (0 <= Ha <= 100), Reynolds number (100 <= Re <= 400) and concentration of nanoparticles (0 <= phi <= 0.05). The results show that the partial magnetic field centered in the middle of the left wall has more reducing effect on convective heat transfer than the bottom and top centered one in both cases of flows. Convective heat transfer increases with the rise in solid volume fraction up to 0.02, but then a decrease is remarkably noticed.