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Type: Artigo
Title: Integral transform solution of the Navier–Stokes equations in full cylindrical regions with streamfunction formulation
Author(s)/Inventor(s): Silva, Carlos Alexandre Moreira da
Macêdo, Emanuel Negrão
Quaresma, João Nazareno Nonato
Pereira, Luiz Mariano
Cotta, Renato Machado
Abstract: Indisponível.
Abstract: 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.
Keywords: Navier–Stokes equations
Hydrodynamically developing flow
Circular tubes
Integral transforms
Hybrid methods
Friction factor
Production unit: Núcleo Interdisciplinar de Dinâmica dos Fluidos
Publisher: Wiley
In: International Journal for Numerical Methods in Biomedical Engineering
Volume: 26
Issue: 11
Issue Date: 28-Oct-2010
DOI: 10.1002/cnm.1222
Publisher country: Brasil
Language: eng
Right access: Acesso Aberto
ISSN: 2040-7939
Appears in Collections:Engenharias

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