The Binary Powell-Eyring Nanofluid of Peristaltic Flow with Heat Transfer in a Ciliated Tube

Bothaina Mohamed Agoor,Mohamed Eissa Sayed-Ahmed,Heba Alam

doi:10.11648/j.ijfmts.20210701.11

Bothaina Mohamed Agoor, Mohamed Eissa Sayed-Ahmed + Show 1 more

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https://doi.org/10.11648/j.ijfmts.20210701.11

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Abstract

These articles show the mathematical investigation of the binary Powell- Eyring Nanofluid of peristaltic flow with heat transfer in a ciliated tube. The approximation of long wavelength and low Reynolds number is taken into consideration. We obtain a system of partial differential equations which solved by using the perturbation method. The velocity and the temperature are computed for various values of the physical parameters. The results are illustrated graphically through a set of Figures. We found that the increase of Grashof number causes an increase in the velocity, then the velocity decrease near the wall of the tube. When the volume fraction of the Nanoparticles increase the velocity increase and decrease near the wall of the tube. The increase in the cilia length leads to an increase in the velocity, then a decrease near the wall of the tube. The increase of the first Eyring-Powell parameter gives an increase in the velocity and decrease near the wall of the tube. The increase of the second Eyring-Powell parameter cause decrease in the velocity. The temperature parameter increase then decreases with the increase of the Sink parameter. The increase of the volume fraction of the Nanoparticles leads to decreases then increase in the temperature parameter. The increase of the cilia length parameter causes an Increase in the temperature.

Highlights

IntroductionPeristaltic is a well-known mechanism to pump the fluid which generated contraction and relaxation due to change in pressure along the wall of the tube
Peristaltic is a well-known mechanism to pump the fluid which generated contraction and relaxation due to change in pressure along the wall of the tube. Such mechanism occurs widely in many biological and biomedical systems. It play an important role in the human body such as the passage of urine from the kidneys to bladder through the ureter, swallowing food through the esophagus, the movement of spermatozoa in the ducts afferents of the male reproductive tract, transport of chime in the gastro-intestinal tract, the passage of ovum in the female fallopian tube, the transport of feces in the large intestine, Venules and tube capillaries involve peristaltic motion, peristaltic phenomenon plays an important role of biomedical instruments like heart-lung machines, artificial heart and ortho machines, dialysis machines and transport of toxic material waste inside the sanitary ducts, peristaltic is used in nuclear industry
We investigate the effect of various physical parameters as Grashof number ( Gr ), volume fraction of the Nanoparticle (φ ), heat source or Sink parameter ( Q ), Cilia length ( ε ) and the first and second parameters of Eyring-Powell ( K1 and K 2 ) on the velocity w(r, z) and the temperature θ (r, z)

Summary

Introduction

Peristaltic is a well-known mechanism to pump the fluid which generated contraction and relaxation due to change in pressure along the wall of the tube. Such mechanism occurs widely in many biological and biomedical systems. The Eyring-Powell peristaltic fluid flow with heat and mass transfer in cylindrical coordinates for fixed and moving frame have been investigated [6]. The influence of heat and mass transfer on peristaltic flow through a porous space in the presence of the magnetic field with compliant walls is investigated [8].

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