Effect of slip on Herschel–Bulkley fluid flow through narrow tubes

Abstract

A two-fluid model of Herschel-Bulkley fluid flow through tubes of small diameters and slip at the wall is studied. It is assumed that the core region consists of Herschel-Bulkley fluid and Newtonian fluid in the peripheral region. Following the analysis of Chaturani and Upadhya, the equations of motion have been linearized and analytical solution for velocity, flow flux, effective viscosity, core hematocrit and mean hematocrit has been obtained. The expressions for all these flow relevant quantities have been numerically computed by using Mathematica software and the effects of various relevant parameters on these flow variables have been studied. It is found that effective viscosity, core hematocrit and mean hematocrit of Newtonian fluid are less than those for Bingham fluid, power-law fluid and Herschel-Bulkley fluid. Effective viscosity increases with the yield stress, power-law index, slip and tube hematocrit but decreases with Darcy number. It is observed that the effective viscosity and mean hematocrit increase with tube radius but the core hematocrit decreases with tube radius. Further, it is noticed that the flow exhibits the anomalous Fahraeus-Lindqvist effect. ª 2015 Production and hosting by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).

Flow of two immiscible non-Newtonian fluids in an elastic tube

“…The axisymmetric flow of two immiscible, Newtonian fluids driven by a constant pressure gradient in a periodically constricted tube was studied by Fraggedakis et al (2015). Santhosh et al (2015) studied two-fluid model of Herschel-Bulkley fluid in the core region and Newtonian fluid in the peripheral region through small diameters of tubes with slip effect. It was observed that the flow shows abnormal Fahraeus-Lindqvist effect.…”

“…Santhosh et al (2015) studied two-fluid model of Herschel–Bulkley fluid in the core region and Newtonian fluid in the peripheral region through small diameters of tubes with slip effect. It was observed that the flow shows abnormal Fahraeus–Lindqvist effect.…”

Role of slip and heat transfer on peristaltic transport of Herschel-Bulkley fluid through an elastic tube

“…Besides, the Herschel-Bulkley model can be reduced to different models, for example, Newtonian, Bingham-plastic and Power law for a related estimation of yield stress and fluid behavior index. The examinations on the peristaltic mechanism of Herschel-Bulkley fluid for various geometries, physiological circumstances, and assumptions have been introduced in the investigations of Chunhui et al (2010), Manjunatha et al (2013Manjunatha et al ( , 2014, Santhosh et al (2015).…”