The paper presents a computational study of steady, laminar, two-dimensional (2D) mixed convection heat transfer from a continuously moving isothermal vertical plate to alumina–water nanofluid as in hot extrusion. The simulation is based on a heterogeneous flow model which takes into account Brownian diffusion and thermophoresis of nanoparticles. The finite difference method is used to discretize the governing equations. The SIMPLE algorithm has been applied to obtain flow, thermal, and nanoparticle concentration fields. The numerical results have been validated satisfactorily with the published results for pure fluids. A detailed parametric study reveals that in the mixed convection regime, the enhancement factor (EF) (defined as the ratio of average heat transfer coefficient in nanofluid to that in base fluid) increases with nanoparticle concentration. The enhancement is more at lower Richardson number (Gr/Re^{2}), that is, closer to forced convection regime. In the regime close to free convection, the EF is found to be very small. Larger plate velocity (that is, higher Reynolds number) has a positive effect on heat transfer enhancement but higher plate-fluid temperature difference results in lower EF. An enhancement in heat transfer coefficient as high as 22% is realized at the plate velocity of 0.4 m/s. The effectiveness (defined as the ratio of average heat transfer coefficient in nanofluid to the power required to pull the plate), in general, falls with higher volume fraction of nanoparticles and plate velocity and escalates with a rise in Richardson number and plate-fluid temperature difference.