The convective instability driven by buoyancy and heat transfer characteristics of nanofluids are investigated analytically. This paper proposes a factor which describes the effect of nanoparticle addition on the convective instability and heat transfer characteristics of a base fluid. The Bruggeman model based on the mean field approach for expressing the thermal conductivity enhancement is chosen as a lower bound of the thermal conductivity relationship. The results show that as the density and heat capacity of nanoparticles increase and the thermal conductivity and the shape factor of nanoparticles decrease, the convective motion in a nanofluid sets in easily. The heat transfer coefficient of a nanofluid is enhanced by all parameters with respect to the volume fraction of nanoparticles.