Analytical determination of the temperature distribution and Nusselt numbers in rectangular ducts with constant axial heat flux

A rigorous solution is obtained for the temperature field and the Nusselt numbers in the fully developed thermal region of rectangular ducts, wherein a laminar fully developed velocity profile occurs. The H1 thermal boundary condition, constant axial wall heat flux with a constant peripheral wall temperature, has been examined. The two dimensional (2D) temperature distribution and the Nusselt numbers are calculated as functions of the aspect ratio. The results, in terms of 2D-temperature profiles and Nusselt numbers, are presented and discussed in tables and graphs, considering all the possible combinations of heated and adiabatic walls of the rectangular cross section. A comparison with the numerically evaluated H1 Nusselt numbers found in literature is presented. The present analytical results are a powerful tool to test the commercial or self-produced thermal fluid-dynamic codes which permit the investigation of the internal forced convection of incompressible flows.