Mixed convection in a lid-driven cavity filled with an alumina-water nanofluid in the presence of a bottom heat-conducting solid backward step has been studied numerically. Mathematical model includes partial differential equations formulated on the basis of conservation laws for mass, momentum and energy using dimensionless variables such as stream function, vorticity and temperature, and corresponding boundary conditions. The boundary-value problem has been solved by finite difference method of the second order accuracy. The effects of Richardson number (Ri = 0.01-10.0), wall step height ratio (0.3 <= h(2)/L <= 0.7), distance ratio between left wall and wall step (0.3 <= l/L <= 0.7), thermal conductivity ratio (1.0 <= K <= 10.0), and nanoparticles volume fraction (0 <= phi <= 0.05) on streamlines and isotherms as well as average Nusselt number at moving hot wall and fluid flow rate have been analyzed for Reynolds number (Re = 100), Prandtl number (Pr = 6.82) and solid wall thickness ratio (h(1)/L = 0.1). It has been found that sizes and thermal conductivity of a backward step can essentially modify the flow and heat transfer patterns with the process intensity. (C) 2017 Elsevier Ltd. All rights reserved.