EFFECTS OF STREAM WISE CONVERGENCE IN RADIUS ON THE LAMINAR FORCED CONVECTION IN AXISYMMETRIC DUCTS

Abstract

A systematic study has been carried out on the effects of streamwise convergence in radius on the laminar forced convection in an axisymmetric duct. This transport circumstance is relevant to many practical processes such as injection molding, glass molding, fiber drawing, and extrusion, where large variations in the radius may occur downstream and where the flow rates are generally small enough to yield a laminar flow. A fairly uncommon transformation technique was used to transform the pseudo-transient conservation equations for the stream function, vorticity, and energy, and several new numerical techniques were developed. These include a nonuniform grid scheme, a second-order-accurate vorticity condition for an arbitrary surface, and a nominally second-order-accurate approximation for the derivatives on a nonuniform grid. The three geometries studied were those of the straight, periodic, and converging ducts, where the results for the first two were obtained mainly for validation purposes. However, new results were also obtained for the periodic duct, showing the attainment of a sinusoidal steady state with the local Nusselt number varying from 1.0 to 6.0. For the converging duct, the local Nusselt number was found, for the first lime, to increase with increasing convergence of the duct wall.