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Submitted by Jairo Amaro (jairo.amaro@sibi.ufrj.br) on 2019-07-04T16:00:45Z No. of bitstreams: 1 2010_COTTA_CNME_v26_p1417-1434-min.pdf: 590631 bytes, checksum: 810055efdc402f6d2a744085fcefbe9e (MD5) Made available in DSpace on 2019-07-04T16:00:45Z (GMT). No. of bitstreams: 1 2010_COTTA_CNME_v26_p1417-1434-min.pdf: 590631 bytes, checksum: 810055efdc402f6d2a744085fcefbe9e (MD5) Previous issue date: 2010-10-28 Indisponível. A hybrid numerical–analytical solution based on the generalized integral transform technique is proposed to handle the two‐dimensional Navier–Stokes equations in cylindrical coordinates, expressed in terms of the streamfunction‐only formulation. The proposed methodology is illustrated in solving steady‐state incompressible laminar flow of Newtonian fluids in the developing region of a circular tube. The flow modeling also considers two limiting inlet conditions, namely, uniform velocity profile representing a parallel flow, and zero vorticity that characterizes irrotational inlet flow. The integral transform analysis for such a full cylindrical region brings up singularities at the channel centerline, and, as previously described in a work dealing with the boundary‐layer formulation, a way to alleviate this difficulty is to adopt a recently introduced fourth‐order eigenvalue problem as the basis for the eigenfunction expansion. A thorough convergence analysis of the proposed expansion is then undertaken, for different values of Reynolds number, and a set of reference results for the velocity distributions and friction factors are then presented in tabular and graphical forms.

The analysis of two-dimensional laminar flow in the entrance region of arbitrarily shaped ducts is undertaken by application of the Generalized Integral Transform Technique (GITT) in the solution of the steady Navier-Stokes equations for incompressible flow. The streamfunction-only formulation is adopted, and a general filtering solution that adapts to the irregular contour is proposed to enhance the convergence behavior of the eigenfunction expansion. The case of a wavy-wall channel is then considered more closely in order to report some numerical results illustrating the expansions convergence behavior. In addition to reporting results of streamfunction, the product of friction factor-Reynolds number is also calculated and compared against results from discrete methods available in the literature for different Reynolds numbers and amplitudes of the wavy channel.Copyright © 2007 by ASME