A general method for calculating momentum and heat transfer in laminar and turbulent duct flows

A method for solving boundary-layer equations with boundary conditions corresponding to two-dimensional plane and axisymmetric, laminar and turbulent internal flows is described and results are presented. This method represents an extension of a procedure previously used with considerable success for an extensive range of two- and three-dimensional external flows, and is shown here to be equally successful when applied to internal flows. The efficient and accurate numerical scheme, which considers the pressure gradient as a nonlinear eigenvalue, is coupled with eddy-viscosity and eddy-conductivity assumptions for turbulent flow and is shown to represent the mean flow and heat transfer properties of flows including those with transition, provided the location of the onset of transition is known. An alternative method of considering the pressure gradient, the Mechul function approach, which offers the advantage of allowing solutions in the regions of flow separation, is also described.