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

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The Nusselt number for fully developed laminar flow in a pipe is 4.36 for constant heat flux and 3.66 for constant wall temperature, indicating it is not constant across different boundary conditions. The formula Nu = h D/K suggests a constant value, but this applies primarily to long pipes where the flow is fully developed. In shorter pipes, the Nusselt number varies along the length due to the influence of boundary conditions. The differences arise because the heat transfer coefficient (h) changes based on these conditions. Thus, the Nusselt number is not a single constant value but varies depending on the specific heat transfer scenario.
Maulik Chaudhary
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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?
 
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Why do you think it is constant? Do you know what the h stands for?
 
The values you gas are asymptotic values for very long pipes. For shorter pipes, Nu varies along the length of the pipe. Also, Nu depends on the wall boundary conditions (constant temperature vs constant heat flux).
 
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