Heat transfer in a round tube with sinusoidal wall heat flux distribution

Sufficiently accurate values of first twenty eigenvalues, eigenfunctions R n (1), and the coefficients for series expansion, as well as asymptotic expressions for these quantities, have been obtained for heat (or mass) transfer to fully developed laminar flow inside a round tube with uniform wall heat (or mass) flux. The first ten eigenfunctions are shown graphically for the radius range 0 ≤ r / r o ≤ 1. These quantities are used to calculate the Nusselt numbers for sinusoidal wall heat flux distribution and are compared with the corresponding slug flow Nusselt numbers.