The present paper investigates numerically the free convection of a non-Newtonian carbopol-TiO2 nanofluid confined in a square cavity with vertical walls subject to uniform and constant heat flux and insulated horizontal walls. The rheological behavior is taken into account by combining the regularized Herschel-BulkleyPapanastasiou model with the model of He et al. [1]. The partial differential equations governing fluid flow and heat transfer are discretized using the Finite Volume Method. The numerical experiments are carried out for a range of parameter values, namely, Rayleigh number 10(3)-10(6), Herschel-Bulldey number 0-20, Prandtl number 10-1000, power law index 0.4-1.0 and nanoparticle solid volume fraction 0.0-0.09. The numerical results are presented in terms of streamlines, isotherms, unyielded plugs, velocity profiles and average Nusselt number. It is found that, all the problem parameters, except for the Prandtl number, have a significant effect on both the hydrodynamic and the thermal fields. (C) 2017 Elsevier B.V. All rights reserved.