Effect of Fluid Viscoplasticity on the Constructal Design of Elliptic Tubes Subjected to Forced Convection

Abstract

The main purpose of this work is to study the effects of flow on the Herschel–Bulkley number (HB), a parameter that should account for fluid viscoplasticity, in the optimal designs of elliptical section tubes subjected to forced convection of viscoplastic fluids. The constructal design was associated with exhaustive search to obtain the ellipse aspect ratios that maximize the Nusselt number and minimize dimensionless pressure drop, for fixed ellipse area and distance between tubes.We employed a modified Herschel–Bulkleymodel to predict viscoplastic behavior, and a fixed flow index equal to 0.4. To solve the system of differential equations for flow and heat transfer, we used a finite volume method code. We investigated the HB ranging from 1 to 100. The maximum dimensionless heat transfer increased with the increase of the HB. Still, the HB did not affect the ellipse aspect ratio that maximized dimensionless heat transfer. For all values of HB, the optimal aspect ratio was equal to 0.96. The Herschel–Bulkley number strongly affected dimensionless pressure drop. The minimum pressure drop increased with the increase of HB, and the optimal geometry was slender as HB increased.