Exact solution of Nusselt problem for laminar fluid flow in a round tube

Nusselt heat exchange problem for steady state laminar fluid flow in a round tube was solved exactly as a row of eigenfunctions with decomposition coefficients being depended of initial temperature profile on tube inlet. These eigenfunctions in turn was found to be exponential row of radius coordinate with coefficients to be a function of eigenvalues. Analytical expression for eigenvalues was also found out. All analytical results including exact Nusselt criterion was checked up numerically using finite difference method