Homotopy semi-numerical simulation of peristaltic flow of generalised Oldroyd-B fluids with slip effects

Abstract

This investigation deals with the peristaltic flow of generalised Oldroyd-B fluids (with the fractional model) through a cylindrical tube under the influence of wall slip conditions. The analysis is carried out under the assumptions of long wavelength and low Reynolds number. Analytical approximate solutions are obtained by using the highly versatile and rigorous semi-numerical procedure known as the homotopy analysis method. It is assumed that the cross section of the tube varies sinusoidally along the length of the tube. The effects of the dominant hydromechanical parameters, i.e. fractional parameters, material constants, slip parameter, time and amplitude on the pressure difference across one wavelength, are studied. Graphical plots reveal that the influence of both fractional parameters on pressure is opposite to each other. Interesting responses to a variation in the constants are obtained. Pressure is shown to be reduced by increasing the slip parameter. Furthermore, the pressure in the case of fractional models (fractional Oldroyd-B model and fractional Maxwell model) of viscoelastic fluids is considerably more substantial than that in the corresponding classical viscoelastic models (Oldroyd-B and Maxwell models). Applications of the study arise in biophysical food processing, embryology and gastro-fluid dynamics.

Keywords::

• peristaltic flow
• generalised Oldroyd-B fluids
• slip condition
• homotopy analysis method
• amplitude
• biophysics

Acknowledgements

The authors are grateful to both reviewers for their comments which improved the article.

Notes

^1. http://www.verder.com (DOI: Peristaltic hose pump delivers a maximum continuous flow rate of 3180 l/hr), Novel materials and engineered structures (Oil & Gas Engineer – Exploration Drilling) (2011).

^2. http://www.bulk-online.com/Co/203279.htm (Larox Flowsys Lappeenranta, Finland, Larox Flowsys Oy, supplier of cutting-edge flow control technology including pinch valves and peristaltic pumps). (2011).