An unsteady peristaltic transport phenomenon of non-Newtonian fluid – A generalised approach Md. Asif Ikbal, Santabrata Chakravarty, Prashanta Kumar Mandal * Department of Mathematics, Visva-Bharati University, Santiniketan 731 235, India Abstract Peristaltic transport of a non-Newtonian power law fluid characterised by the streaming blood through an axisymmetric tapered tubular vessel is studied under long wave length approximation. The flow is considered to be unsteady and two-dimensional so that both the axial and the radial velocity components of the fluid come into play. The generalised constitutive relations for the power law fluid are thoroughly encountered in the present analysis. The input pressure–radius relationship based on the assumption of the incompressibility and viscoelasticity of the vascular wall material in confor- mity to the experimental observations is given much attention in order to have resemblance to the in vivo situation. The nonlinear equations of motion governing the peristaltic transport phenomena are properly discretised with the use of suitable finite difference explicit scheme. The resulting difference equations are solved numerically by exploiting the appropriate initial and boundary conditions resulting from the physical and the biomechanical point of view. An extensive quantitative analysis is performed through numerical computations of the desired quantities of interest in order to estimate the effects of nonlinear inertial forces, the wall viscoelasticity, the tapering angle and the unsteadiness on the flow phenom- ena indicating their own role of importance in peristaltic transportation. Ó 2007 Elsevier Inc. All rights reserved. Keywords: Peristaltic transport; Non-Newtonian fluid; Tapered vessel; Pressure–radius relationship; Generalised power law; Finite difference scheme 1. Introduction The study of peristaltic transport in fluid mechanics has long been carried out by many researchers to look for its implications in the biological sciences in general and the bio-fluid mechanics, in particular. The peristaltic flow occurs due to the contraction and expansion of a progressive wave propagating along the length of a dis- tensible tube containing fluid. Peristaltic wave causing transportation of the fluid through muscular tubes is indeed an important biological mechanism responsible for various physiological functions of the organs of the human body. Such mechanism may be involved in urine transport from kidney to bladder through the ure- ter, swallowing foods through the oesophagus, the transport of spermatozoa in the cervical canal, the movement 0096-3003/$ - see front matter Ó 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2007.11.051 * Corresponding author. E-mail addresses: santabrata2004@yahoo.co.in (S. Chakravarty), pkmind02@yahoo.co.uk (P.K. Mandal). Available online at www.sciencedirect.com Applied Mathematics and Computation 201 (2008) 16–34 www.elsevier.com/locate/amc