Peristaltic Transport of a Herschel–Bulkley Fluid in an Elastic Tube

Abstract

In this paper, we investigate the peristaltic transport of a non-Newtonian viscous fluid in an elastic tube. The governing equations are solved using the assumptions of long wavelength and low Reynolds number approximations. The constitution of blood has a non-Newtonian fluid model and it demands the yield stress fluid model: The blood transport in small blood vessels is done under peristalsis. Among the available yield stress fluid models for blood flow, the non-Newtonian Herschel-Bulkley fluid is preferred (because Bingham, power-law and Newtonian models can be obtained as its special cases). The Herschel-Bulkley model has two parameters namely the yield stress and the power-law index. The expressions for velocity, plug flow velocity, wall shear stress, and the flow rate are derived. The flux is determined as a function of inlet, outlet, external pressures, yield stress, amplitude ratio, and the elastic property of the tube. Further when the power-law index n = 1 and the yield stress 0 → 0 and in the absence of peristalsis, our results agree with Rubinow and Keller [J. Theor. Biol. 35, 299 (1972)]. Furthermore, it is observed that, the yield stress, peristaltic wave, and the elastic parameters (t 1 or t 2 ) have strong effects on the flux of the non-Newtonian fluid flow. Effects of various wave forms (namely, sinusoidal, trapezoidal and square) on the flow are discussed. The results obtained for the flow characteristics reveal many interesting behaviors that warrant further study on the non-Newtonian fluid phenomena, especially the shearthinning phenomena. Shear thinning reduces the wall shear stress. C⃝ 2014 Wiley Periodicals, Inc. Heat Trans Asian Res, 44 (7): 585-598, 2015; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj).

Impact of Variable Liquid Properties on Peristaltic Mechanism of Convectively Heated Jeffrey Fluid in a Slippery Elastic Tube

“…(28) reduces to that given by Rubinow and Keller (1972) for the flow of Newtonian fluid in an elastic tube. Further, the behavior of relevant parameters on theoretical flux obtained from both the models are in good agreement with the results of Vajravelu et al (2015), Vajravelu et al (2016) and Srinivas et al (2017).…”

Peristaltic transport of a power-law fluid in an elastic tube

“…Sochi [19] proposed the expression for the volumetric flow as a function pressure in an elastic tube using two pressure-area constitutive relations. The effect of peristalsis on the Herschel-Bulkley fluid flow in an elastic tube was discussed by Vajravelu et al [20]. Chaube et al [21] analysed the peristaltic creeping flow of power-law physiological fluids through a non-uniform channel with slip effects.…”

Peristaltic Pumping of a Generalized Newtonian Fluid in an Elastic Tube

“…Sochi (2014) used lubrication approximation to understand the flow behaviour of Newtonian fluid and powerlaw fluid in elastic tubes by considering the pressurearea constitutive relation. The effect of peristalsis on Herschel -Bulkley fluid flow in an elastic tube was discussed by Vajravelu et al (2014). Sochi (2015) derived analytical expressions for the Newtonian flow characteristics by considering cylindrically shaped elastic tubes.…”