In the present study, laminar forced convective nanofluid flow over a backward-facing step was numerically investigated. The bottom wall downstream of the step was flexible, and finite element method was used to solve the governing equations. The numerical simulation was performed for a range of Reynolds number (between 25 and 250), elastic modulus of the flexible wall (between 10^{4} and 10^{6}), and solid particle volume fraction (between 0 and 0.035). It was observed that the flexibility of the bottom wall results in the variation of the fluid flow and heat transfer characteristics for the backward-facing step problem. As the value of Reynolds number and solid particle volume fraction enhances, local and average heat transfer rates increase. At the highest value of Reynolds number, heat transfer rate is higher for the case with the wall having lowest value of elastic modulus whereas the situation is reversed for other value of Reynolds number. Average Nusselt number reduces by about 9.21% and increases by about 6.1% for the flexible wall with the lowest elastic modulus as compared to a rigid bottom wall for Reynolds number of 25 and 250. Adding nano-additives to the base fluid results in higher heat transfer enhancements. Average heat transfer rates enhance by about 35.72% and 35.32% at the highest solid particle volume fraction as compared to nanofluid with solid volume fraction of 0.01 for the case with wall at the lowest and highest elastic modulus. A polynomial type correlation for the average Nusselt number along the flexible hot wall was proposed, which is dependent on the elastic modulus and solid particle volume fraction. The results of this study are useful for many thermal engineering problems where flow separation and reattachment coupled with heat transfer occur. Control of convective heat transfer for such configurations with wall flexibility and nanoparticle inclusion to the base fluid was aimed in this study to find the effects of various pertinent parameters for heat transfer enhancement.