Peristaltic Flow of Giesekus Fluids through Curved Channels: an Approximate Solution

Abstract

Peristaltic flow of a viscoelastic fluid is numerically studied in a plane channel. The fluid is assumed to obey the Giesekus model as its constitutive equation, and the flow is assumed to be occurring under incompressible, laminar, and two-dimensional conditions. To simplify the equations of motion, use is made of the long-wavelength assumption together with the creeping-flow assumption. It is shown that for this particular fluid model, the governing equations are reduced to a system of coupled nonlinear ODEs, which are solved numerically using finite difference method. Numerical results show that the elastic behavior of a fluid can significantly decrease the pressure rise of peristaltic pumps. On the other hand, a radially-imposed magnetic field is shown to increase the pressure rise of the pump when the flow rate is less than a certain value. The results are interpreted in terms of the extensional-flow behavior of the fluid as represented by the fluid's mobility (or, extensional) factor.

Numerical simulation of peristaltic flow of a biorheological fluid with shear-dependent viscosity in a curved channel

“…Ali et al 4 The above definition of stream function enables us to write Equations (17 -19) after using the long wavelength and low Reynolds number approximations (Kumar and Naidu 1995;Yi et al 2002;Takagi and Balmforth 2011;Hina et al 2013;Kalantari et al 2013;Narla et al 2013; …”

“…They further noted that reflux close to the outer wall exhibits greater strength than near the inner wall and that the trapped bolus of fluid has two asymmetrical components, with the outer one growing and the inner one depleting as the channel curvature rises. The analysis by Sato et al (2000) has been extended by several researchers (Ali, Sajid, and Hayat 2010;Ali et al 2010aAli et al , 2010bHina et al 2013;Kalantari et al 2013;Narla et al 2013;) to a variety of nonlinear material and other effects including non-Newtonian behavior, unsteadiness, wall compliance etc. However, thus far no studies have appeared in the literature where peristaltic flow analysis in a curved channel is considered under long wavelength approximation for a fluid capable of predicting shear thinning, shear thickening, and relaxation effects.…”

Simulations of peristaltic slip-flow of hydromagnetic bio-fluid in a curved channel

“…The study performed by Sato et al 28 is pioneering in this direction. The results presented by Sato et al 28 were generalized by Ali et al, [29][30][31] Hayat et al, 32,33 Hina et al, [34][35][36] Ramanamurthy et al 37 and Narla et al 38 In this connection also the paper of Kalantari et al 39 is worth mentioning. It is related to those situation where the curvature of the channel, applied magnetic field and non-Newtonian effects are equally important.…”

“…The non-Newtonian model chosen in Ref. 39 is Phan-Thien-Tanner (PTT) model. In the present paper we investigate the effects of fluid slippage at the channel walls, applied magnetic field and non-Newtonian rheology on peristaltic flow in a curved channel.…”

Convective heat and mass transfer analysis on peristaltic flow of Williamson fluid with Hall effects and Joule heating

“…(26)-(30) into Eqs. (21)- (24) and then comparing the coefficients of like powers of We up to the first order and neglecting powers of order two and higher we have the following. …”