Double-diffusive mixed convection in a backward-facing step (BFS) channel for different shapes of nanoparticles is analyzed using velocity–vorticity equations. The effect of four shapes of alumina nanoparticles at volume fractions of 1–5% on heat and mass transfer are studied for buoyancy ratios, N from −3 to 3 at Re = 200, Ri = 0.1, and Pr = 6.2. As χ increases, the Nuav decreases for all shapes at N = −3; however, it increases with an increase in N from 1 to 3. At N = 3, the Nu increases by 29% for blades shape, whereas a 28% decrease was noticed for platelets shape. An increase in χ of nanoparticles results in a decrease of Shav for N = 1–3, with a maximum decrease of 57% being observed at N = −3 for cylinders shape. The τav at the bottom wall continues to increase up to a maximum of 400% for platelets shape for N = 3.