Combined forced and free flow in a vertical rectangular duct with prescribed wall heat flux

In this paper, combined forced and free convection is studied in a vertical rectangular duct with a prescribed uniform wall heat flux (H2 boundary condition). A different heat flux value for each plane wall is considered; the condition of a uniform wall heat flux throughout the duct results as a special case. The local momentum and energy balance equations are written in a dimensionless form and solved numerically, by means of a Galerkin finite element method. The numerical solution gives the dimensionless velocity and temperature distributions, together with the values of the Fanning friction factor, of the Nusselt number, of the momentum flux correction factor and of the kinetic energy correction factor. These dimensionless parameters are reported as functions of the aspect ratio and of the ratio between the Grashof number, Gr, and the Reynolds number, Re. The threshold values of Gr/Re for the onset of flow reversal are evaluated.