Peristaltic transport of fractional Maxwell fluids in uniform tubes: Applications in endoscopy

This paper presents the effect of endoscope on peristaltic transport of fractional Maxwell fluids through the gap between two concentric uniform tubes under the assumptions of large wavelength and low Reynolds number. The inner tube is an endoscope and the outer tube has a sinusoidal wave traveling down its wall, i.e. the inner tube is rigid and outer tube is flexible. Solutions for the problem are obtained by two numerical methods named as homotopy perturbation method and variational iteration method. The impacts of endoscope, relaxation time and fractional parameters on pressure per wavelength and friction force (on inner and outer tubes) per wavelength are discussed with the help of computational results which are presented in graphical form. On the basis of the present study, it is revealed that pressure diminishes with increase in the magnitude of first fractional parameter, ratio of tube radii and relaxation time whereas it enhances with increasing the magnitude of second fractional parameter and amplitude ratio. The study further reveals the important fact that the effects of all pertinent parameters (except ratio of tube radii) on friction force at inner tube are similar in magnitude but opposite in direction to that of pressure and the effects of same parameters on friction force at outer tube are similar in magnitude but opposite in direction to that of pressure. (C) 2011 Elsevier Ltd. All rights reserved.