Laminar forced convection in converging or diverging planar symmetric ducts

Approximate velocity profiles are developed as well as a new transformation that will reduce the heat transfer problem for laminar forced convection inside a planar symmetric duct of varying cross section to the standard thermal entrance region problem for forced convection between two parallel plates. It is assumed that the variation of the duct cross section with the distance along the direction of flow is sufficiently smooth and gradual so that the axial component of the velocity retains a parabolic profile, but its magnitude changes to satisfy the requirement of continuity.