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.

Fluid flow in concentric or eccentric annular ducts have been studied for decades due to large application in medical sciences and engineering areas. This paper aims to study fully developed fluid flow in straight ducts of concentric annular geometries (circular with circular core, elliptical with circular core, elliptical with elliptical core, and circular with elliptical core) using the Galerkin-based Integral method (GBI method). The choice of method was due to the fact that in the literature it is not applied in ducts of cross-sections of the annular shape with variations between circular and elliptical. Results of different hydrodynamics parameters such as velocity distribution, Hagenbach factor, Poiseuille number, and hydrodynamic entrance length, are presented and analyzed. In different cases, the predicted hydrodynamic parameters are compared with results reported in the literature and a good concordance was obtained.

Fluid flow in pipes plays an important role in different areas of academia and industry. Due to the importance of this kind of flow, several studies have involved circular cylindrical pipes. This paper aims to study fully developed internal laminar flow through a corrugated cylindrical duct, using the Galerkin-based integral method. As an application, we present a study using heavy oil with a relative density of 0.9648 (14.6 °API) and temperature-dependent viscosities ranging from 1715 to 13000 cP. Results for different fluid dynamics parameters, such as the Fanning friction factor, Reynolds number, shear stress, and pressure gradient, are presented and analyzed based on the corrugation number established for each section and aspect ratio of the pipe.

In a two-dimensional domain, bounded cross-sections are interpretable from the generalized concept of “aperture” and embrace uncountable applications. Shapefactors for apertures confined by irregular boundaries are much less known than regular ones. Besides, they are poorly estimated due to restrictions in experimental measurements of underlying properties and do not have immediate determination. An example is the estimation of the Kozeny constant in models derived from the classical Kozeny-Carman equation. This paper presents a numerical Galerkinbasedintegral (GBI) model that computes shape factors for apertures confined by arbitrary boundaries, thus filling a knowledge gap regarding shape factor determination. The technique relies on two underlying pillars: accurate boundary reconstruction by high-order piecewise polynomials and shape factor recovery using the Poiseuille number. The GBI technique treats the fluid flow as fully developed under the laminar regime, thus allowing a reasonable comprehension of the cross-sectional dynamics. Our study stands on realistic apertures modeled from rock core samples and is additive to understanding transport mechanisms in fractured media. The outcomes are specifically helpful for people who deal with fluid injection of any kind and need to compute shape factors for ducts, fissures, or cracks, either for biotechnology, engineering, or medical applications.