Abstract
This paper presents a theoretical study for peristaltic flow of a non-Newtonian compressible Maxwell fluid through a tube of small radius. Constitutive equation of upper convected Maxwell model is used for the non-Newtonian rheology. The governing equations are modeled for axisymmetric flow. A regular perturbation method is used for the radial and axial velocity components up to second order in dimensionless amplitude. Exact expressions for the first-order radial and axial velocity components are readily obtained while second-order mean axial velocity component is obtained numerically due to presence of complicated non-homogenous term in the corresponding equation. Based on the mean axial velocity component, the net flow rate is calculated through numerical integration. Effects of various emerging parameters on the net flow rate are discussed through graphical illustrations. It is observed that the net flow rate is positive for larger values of dimensionless relaxation time λ1. This result is contrary to that of reported by [D. Tsiklauri and I. Beresnev, “Non-Newtonian effects in the peristaltic flow of a Maxwell fluid,” Phys. Rev. E. 64 (2001) 036303].” i.e. in the extreme non-Newtonian regime, there is a possibility of reverse flow.
Highlights
Peristaltic motion of fluids has acquired a special status amongst the recent investigators
This paper presents a theoretical study for peristaltic flow of a non-Newtonian compressible Maxwell fluid through a tube of small radius
Based on the mean axial velocity component, the net flow rate is calculated through numerical integration
Summary
Peristaltic motion of fluids has acquired a special status amongst the recent investigators. Abundant information on the topic is available for viscous materials since the seminal work of Latham,[1] Shapiro et al.[2] and Fung and Yih.[3] Peristaltic transport of viscous materials in the existing studies have been especially examined through different aspects of heat and mass transfer, convective conditions, compliant boundary, various waveforms, symmetric and axisymmetric channels, uniform and non- uniform flow configurations etc. All these studies have been presented through the use of one or more assumptions of long wavelength, low Reynolds number, small wave number and small amplitude of wave. Mention may be made to few studies in this direction through the attempts[4,5,6,7,8,9,10,11,12,13] and many refs
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