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The mixed convection flow in a differentially heated grooved channel filled with water based nanofluid under the influence of external magnetic field has been analyzed numerically in this study. Nanofluid's thermal conductivity model has been modified to develop a new physical problem and finite element method has been implemented to solve the dimensionless governing equations. Numerical simulations have been performed for different values of pertinent parameters. Fluid flow and temperature distributions have been exhibited in terms of streamlines and isotherms due to the variation of Richardson number, Hartmann number and concentration of nanoparticles in base fluid water. The results show that flow field and temperature distributions within the channel affected significantly with the effects of Richardson number, Hartmann number and concentration of nanoparticles. In addition, it is found that heat transfer rate increases and decreases respectively with the increase in strength of magnetic field which depends strongly on Richardson number. Moreover, heat transfer rate accelerates effectively for increasing volume fraction, Reynolds number and Richardson number. The present simulation has been validated by comparing the present results with other published works on the basis of special cases.