Nusselt number is variable or constant for laminar fully developed pipe flow?

[Maulik Chaudhary]

It is the case that the Nusselt number along the fully developed (hydrodynamically and thermally) laminar flow through the constant cross section is 4.36 for constant heat flux and 3.66 for constant wall temperature. But the formula of the nusselt number is Nu = h Lc/K so for pipe it becomes Nu = h D/K where all of the terms are constant so my question is why does it have 2 different values for the different cases shown above when the formula clearly indicates that it should be constant irrespective of other conditions?

 

[Arjan82]

Why do you think it is constant? Do you know what the h stands for?