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 gastrofluid dynamics.
