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 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 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 shear‐thinning phenomena. Shear thinning reduces the wall shear stress.