Integral Transform Method for Laminar Heat Transfer Convection of Herschel-Bulkley Fluids Within Concentric Annular Ducts

Abstract

Related momentum and energy equations describing the heat and fluid flow of Herschel-Bulkley fluids within concentric annular ducts are analytically solved using the classical integral transform technique, which permits accurate determination of parameters of practical interest in engineering such as friction factors and Nusselt numbers for the duct length. In analyzing the problem, thermally developing flow is assumed and the duct walls are subjected to boundary conditions of first kind. Results are computed for the velocity and temperature fields as well as for the parameters cited above with different power-law indices, yield numbers and aspect ratios. Comparisons are also made with previous work available in the literature, providing direct validation of the results and showing that they are consistent

Effects of slip and rheological parameters on the flow and heat transfer of a Herschel-Bulkley fluid

“…Since the dimensionless yield radius increases with the increase of the Herschel-Bulkley number (see Figure 2), the size of horizontal region of these two parameters increases as the Herschel-Bulkley number is increased. For the power-law fluid, there is no this horizontal region, which is consistent with the results of Shojaeian and Kos ar (2014) and Viana et al (2001). Additionally, as shown in Figure 6, both these dimensionless parameters with lower slip number are higher within a small radius but become lower near the wall.…”

“…Nouar et al (Nouar et al, 1995;Nouar et al, 1994) and Soares et al (1999) studied the heat transfer of non-Newtonian fluid using Herschel-Bulkley equation to represent the rheological model of the fluid. Furthermore, it is worth mentioning that the heat and fluid flow of Herschel-Bulkley fluid within concentric annular ducts were presented by Viana et al (2001). Some dimensionless parameter groups were defined in their work.…”

Entrance Region Flow in Concentric Annuli with Rotating Inner Wall for Herschel–Bulkley Fluids

“…Here Y h is the Hershel-Bulkley number, Re Reynolds number, T a Taylors number, μ r is know as reference viscosity and N is known as aspect ratio of the annulus. Equations (2)-(5) and (7) in the dimensionless form are given by…”

“…Manglik and Fang [6] numerically investigated the flow of non-Newtonian fluids through annuli. The problem of laminar heat transfer convection for Herschel-Bulkley within concentric annular ducts has been studied by Vaina et al [7] with the help of integral transform method considering the plug flow region. Round and Yu [8] analyzed the developing flows of Herschel-Bulkley fluids through concentric annuli.…”

Laminar flow of soursop juice through concentric annuli: Friction factors and rheology

“…In the last 10 years, purely numerical procedures have been used to solve the complete problem of fluid flow and heat transfer of non-Newtonian fluids in concentric and eccentric annular geometries with and without centre-body rotation Escudier, Oliveira, Pinho, & Smith, 2002;Fang, Manglik, & Jog, 1999;Kaneda, Yu, Ozoe, & Churchill, 2003;Manglik & Fang, 2002;Nouar, Benaouda-Zouaoui, & Desaubry, 2000;Soares, Naccache, & Mendes, 2003;Viana, Nascimento, Quaresma, & Macêdo, 2001), which is very interesting from a theoretical point of view, but not easily applicable. On the other hand, few studies report experimental pressure loss and friction factors-Reynolds number data (Escudier, Gouldson, & Jones, 1995;Ilicali & Engez, 1996;Tuoc & Mcgiven, 1994;Vaughn, 1963;Vaughn & Bergman, 1966).…”