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

Abstract

Purpose The purpose of this paper is to investigate the combined effects of slip and rheological parameters on the flow and heat transfer of the Herschel-Bulkley fluid. Design/methodology/approach The combinative dimensionless parameter method is introduced into the equations of the slip flow and heat transfer to make the discussion more comprehensive. More specifically, the slip and rheological parameters are transformed into the dimensionless slip number as well as Herschel-Bulkley number. We solve the dimensionless equations and then focus on the effects of these parameters on the slip flow and heat transfer. Findings The results show that, for a given value of Herschel-Bulkley number, there is a finite critical value of slip number at which the pressure gradient reaches the lowest value and both the dimensionless yield radius and slip velocity become 1. Meanwhile, the Nusselt number tends to be infinite at this critical value of slip number. For the case of slip, the Nusselt number also approaches infinity at a finite critical value of Herschel-Bulkley number. Furthermore, the dimensionless velocity as well as temperature of the yield pseudoplastic fluid with higher slip number is lower within a small radius but becomes higher near the wall. Meanwhile, from the velocity and temperature profiles, the effect of Herschel-Bulkley number on these two parameters of the Bingham fluid at the smaller radius is opposite. Originality/value These associated expressions can be generalized to the flow and heat transfer of a Herschel-Bulkley fluid under slip boundary condition. It can provide a reference for the engineering application relating to the heat transfer and flow of a Herschel-Bulkley fluid. Meanwhile, it also suggests some revelations for dealing with this similar problem.

Wall slip effects in Rayleigh–Bénard convection of viscoplastic materials

“…The slip yield stress τ s can be less than, greater than or equal to bulk yield stress τ y . The effects of wall slip on the flow of viscoplastic fluids have been investigated by some authors (Lawal et al, 1993;Lawal and Kalyon, 1998;Aktas et al, 2014;Damianou et al, 2015;Jing et al, 2017;Raza et al, 2019;Gireesha and Roja, 2020).…”

“…Previous studies have shown that yield–stress fluids exhibit wall slip, leading to dispersion phenomena adjacent to the walls (Barnes, 1995; Nikitin, 2007; Ballesta et al. , 2012; Damianou and Georgiou, 2014; Jing et al. , 2017; Raza et al.…”

Variations and model of the rheological parameters of low damage BCG − CO2 fracturing fluid

“…Luo et al [ 18 ] found that the rheological behaviour of thickened CO 2 can be described using the power law model. Jing et al [ 19 ] adopted the H‐B model for the liquid CO 2 ‐based foam fracturing fluid and investigated the combined effects of slip and rheological parameters on the flow and heat transfer. Some studies have found that that the frictional resistance formula for Newtonian fluids can be used to describe the laminar flow of a foam fluid.…”