Peristaltic Transport of Maxwell Viscoelastic Fluids With a Slip Condition: Homotopy Analysis of Gastric Transport

Viscoelastic fluids arise frequently in numerous biophysical transport processes including gastric flow, embryology, haemo-dynamics and synovial lubrication. In the present article, we examine the effect of slip condition on peristaltic transport of viscoelastic fluids with the fractional Maxwell model through a two-dimensional deformable channel under the long wavelength and low Reynolds number assumptions, as a simulation of gastric flow. The channel is subjected to sinusoidal waves traveling along the walls. A versatile semi-analytical technique, the homotopy analysis method (HAM) is used to obtain approximate analytical solutions for the non-dimensionalized flow problem. The convergence of the HAM which depends on ℏ-curves is illustrated for relevant parameters. The effects of fractional parameters, relaxation time and slip parameter on the pressure difference and frictional force across one wavelength against time and averaged flow rate are illustrated graphically. It is found that effect of both fractional parameters on pressure is opposite to each other. The relaxation time and slip parameter are found to assist the peristaltic transportation. The behavior of frictional force is found to be similar to pressure in a magnitude sense whereas it is opposite in direction.