Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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PERISTALTIC PUMPING OF AN ELLIS FLUID IN AN INCLINED ASYMMETRIC CHANNEL

  • A., SMALL (Faculty of Engineering, Caribbean Maritime University) ;
  • P., NAGARANI (Department of Mathematics, The University of the West Indies) ;
  • M., NARAHARI (Fundamental and Applied Sciences Department, Universiti Teknologi PETRONAS)
  • Received : 2021.08.04
  • Accepted : 2022.10.12
  • Published : 2023.01.30
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Abstract

The flow of an incompressible Ellis fluid in an inclined asymmetric channel, driven by peristaltic waves was studied under low Reynolds number and long wavelength assumptions. The wave on each side of the channel are assumed to be an infinite train of sinusoidal waves, both having the same constant wave speed and wavelength however, they vary in wave amplitude, channel half width and phase angle. We derived expressions for the axial and transverse velocities, volume flow rate, pressure rise per unit wavelength and streamlines. The effects of varying the wave amplitudes, the phase angle, the channel width, the angle of inclination of the channel as well as the fluid parameters on the flow were analyzed. Trapping conditions were determined and the presence of reflux highlighted using the streamlines for the necessary channel and fluid conditions. By varying the fluid parameters, changes in the fluid that deviated from the Newtonian case resulted in a reduction in the axial velocity in the neighborhood of the center of the channel and a simultaneous increase in the velocity at the periphery of the channel. A nonlinear relation was observed with the pressure rise and the volume flow rate. This nonlinear relation is more pronounced with an increase in the absolute value of the volume flow rate. For Newtonian fluids a linear relation exists between these two variables. The fluid parameters had little effects on the streamlines. However, variations of the wave amplitudes, volume flow, channel width and phase angle had greater effects on the streamlines and hence the trapped region.

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References

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