Numerical Study of the Effect of Reynolds Number and Aspect Ratio in Heat Transfer from Elliptical Tubes to Viscoplastic Fluids Employing Constructal Design

Abstract

The present work aims to obtain geometries that ease the heat transfer from elliptical section tubes to cross flow of viscoplastic fluids. The Construtal Design method is applied to obtain aspect ratios between the axes of the elliptic sections that maximize the Nusselt number. The tubes elliptical section area is fixed, but the aspect ratio between their axes is free to change in order to optimize this geometry for different Reynolds numbers (Re). The viscoplastic fluid behavior is modeled using the Herschel-Bulkley constitutive equation for the viscosity function. The governing differential equations are solved numerically by the finite volume method. The values of the dimensionless numbers, Prandtl (Pr), modified Bingham (Bn*) and flow index (n), were kept constant and equal to 1, 1 and 0.4, respectively. The Reynolds number was varied from 1 to 40. The results obtained show that increasing the number of Reynolds results in a greater heat transfer. In addition, the optimal aspect ratio is smaller the greater the Reynolds number is. It was found that, as the aspect ratio grows, heat transfer increases due to flow acceleration, but also decreases due to the low strain rate zone downstream the tube, which possesses recirculation and unyielded material. The balance between these effects gives the optimum point.