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Numerical analysis is carried out on an unsteady MHD natural convective   boundary layer flow of a nanofluid past an isothermal vertical plate in the   presence of thermal radiation. The governing partial differential equations   are solved numerically by an efficient, iterative, tri-diagonal,   semi-implicit finite-difference method. In particular, we investigate the   effects of radiation, magnetic field and nanoparticle volume fraction on the   flow and heat transfer characteristics. The nanofluids containing   nanoparticles of aluminium oxide, copper, titanium oxide and silver with   nanoparticle volume fraction range less than or equal to 0.04 are considered.   The numerical results indicate that in the presence of radiation and magnetic   field, an increase in the nanoparticle volume fraction will decrease the   velocity boundary layer thickness while increasing the thickness of the   thermal boundary layer. Meanwhile, an increase in the magnetic field or   nanoparticle volume fraction decreases the average skin-friction at the   plate. Excellent validation of the present results has been achieved with the   published results in the literature in the absence of the nanoparticle volume   fraction

Radiation effects on an unsteady MHD natural convective flow of a nanofluid past a vertical plate