Heat Transfer and Fluid Flow in Concentric Annular Ducts Using the Galerkin-Based Integral Method: A Numerical Study

Abstract

In this paper, we cope with the problem of presents a numerical analysis for heat transfer in a duct with geometry circular annular elliptical using the Galerkin-based integral method. The analysis is performed for different geometries of the duct (circular annular circular and circular annular elliptical), and the method is validated for circular cylindrical geometry. Parameters such as mean temperature and mean and location Nusselt numbers for two boundary conditions: constant wall temperature and axial constant heat flux in the wall with constant wall temperature are presented and analyzed.

Irregularly-bounded cross sections’ shape factors from high-order piecewise-polynomials

“…Although this fact allow us to infer that the curvature may be responsible for pushing the Poiseuille number down and, consequently the aperture's shape factor F val , we deemed that the assumption is weakly confirmed, since no clear pattern emerges from the other curvature expressions. While the curvature effect remains an open issue, one verifies that the rugosity of regular shapes, which induces an increase of curvature over the boundary, and consequently, of the friction, is a reducing factor for the Poiseuille number [44].…”

“…Detailed information on this procedure can be found in earlier papers by the authors [15,34,35,37] and in a broad literature timeframe [38][39][40][41]. This time, we put special emphasis on the construction of the basis functions Bi , which have a direct dependence on the local approximants.…”

“…This paper aims to present a model to compute shape factors for apertures with arbitrary boundaries, besides enabling hydrodynamic characterization and flow profiling for generic cross-sections. Our method is based on the GBI formulation proposed in [15,34,35], which relies on two underlying pillars: accurate shape reconstruction by high-order piecewise polynomials, and factor recovery by Poiseuille number. The GBI technique treats the fluid flow as fully developed under the laminar regime, thus allowing a reasonable comprehension of cross-sectional motion.…”