Recent research on nanofluids under forced convection experiment shows that there is little relationship between convective heat transfer and thermal conductivity increase of nanofluids. This kind of new findings are totally different from the traditional theory of nanofluids, which says that the higher thermal conductivity is a prerequisite for convective heat transfer enhancement. To elucidate this controversial issue in a very comprehensible manner, simple natural convection experiment has been carried out for the water- and oil-based nanofluids. ($water-Al_2O_3$, transformer $oil-Al_2O_3$) Present research shows that there exists strong dependence between natural convection performance and thermal conductivity increase of nanofluids.