Steady-state natural convection heat transfer in a square porous enclosure having solid walls of finite thickness and conductivity filled by a nanofluid using the mathematical nanofluid model proposed by Buongiorno is presented. The nanofluid model takes into account the Brownian diffusion and thermophoresis effects. The study is formulated in terms of the vorticity-stream function procedure. The governing equations were solved by finite difference method and solution of algebraic equations was made on the basis of successive under relaxation method. Effort has been focused on the effects of seven types of influential factors such as the Rayleigh and Lewis numbers, the buoyancy-ratio parameter, the Brownian motion parameter, the thermophoresis parameter, the thermal conductivity ratio, and solid walls thickness on the fluid flow and heat transfer. Streamlines, isotherms, isoconcentrations, local Nusselt and Sherwood numbers are presented. It has been found that the local Nusselt number at the solid-porous interface (x = D) is an increasing function of Ra, Nr and a decreasing function of Nt, Le and D. An effect of K-r on Nu and Sh is non-monotonic. Ranges of key parameters for which.a non-homogeneous model is more appropriate for the description of the system have been determined. (C) 2014 Elsevier Ltd. All rights reserved.