Nusselt number is hL/k where k is thermal conductivity which is supposed to increase in nanofluids. How this Nusselt number is enhancing if thermal conductivity is improved?
I assume the heat transfer coefficient factor of this matter because the heat transfer coefficient (h) is increasing at a higher rate than the thermal conductivity (k).
When k is increased by nano material effect, thermal conductivity of fluid increases which results in higher heat transfer from the surface and consequent higher convection coefficient and Nu number.
Nusselt number is also a funcion of h, which is a convective heat transfer coefficient . It is not a material property and depends on flow parameters, but it can be defined as h=k/δt where δt represents the local thickness of the thermal boundary layer and k is the local effective thermal conductivity of nanofluids. Therefore, k and δt, strongly influence the convective heat transfer coefficient such that either a decrease in δt and an increase in k, or both, lead to enhance the convective heat transfer coefficient at a defined location.