Volume 12, Issue 1, July 2015, Pages 1–32
Nabil T. M. El-dabe1, Galal M. Moatimid2, Mohamed A. Hassan3, and Doaa R. Mostapha4
1 Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
2 Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
3 Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
4 Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
Original language: English
Copyright © 2015 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper investigates the effect of peristaltic flow of a Jeffrey nanofluid in endoscope. The flow is streaming through a tapered artery having a mild stenosis. The influences of heat and nanoparticle concentration on blood flow are also taken into account. Both velocity and thermal slip conditions are considered. The governing equations of motion, energy and nanoparticles are based on a perturbation technique. This technique depends on two parameters. Firstly, the amplitude ratio. Secondly, the small wave number. The distributions of the axial velocity, temperature and nanoparticle volume fraction are analytically derived. The pressure rise and friction force are numerically calculated. The numerical calculations are adopted to obtain the effects of several physical parameters, such as the slip parameter, Brownian motion parameter, thermophoresis parameter, the Reynolds number, the taper angle, nanoparticles Rayleigh number, thermal Rayleigh number and the maximum height of stenosis. It is found that the axial velocity increases with the decrease of the slip parameter. Meanwhile, it increases with the increase of both the nanoparticles Rayleigh number and the thermal Rayleigh number in the region of stenosis. The stream lines are also depicted. It is observed that the trapped bolus decreases in size with the increase of both the Brownian motion parameter and the thermophoresis parameter. In addition, the trapped bolus increases in size with the increase of both the maximum height of stenosis and the taper angle.
Author Keywords: Peristaltic flow, Jeffrey model, Tapered artery, Stenosis flow, Nanoparticles, Slip condition, Heat transfer, Trapping phenomena.
Nabil T. M. El-dabe1, Galal M. Moatimid2, Mohamed A. Hassan3, and Doaa R. Mostapha4
1 Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
2 Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
3 Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
4 Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
Original language: English
Copyright © 2015 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
This paper investigates the effect of peristaltic flow of a Jeffrey nanofluid in endoscope. The flow is streaming through a tapered artery having a mild stenosis. The influences of heat and nanoparticle concentration on blood flow are also taken into account. Both velocity and thermal slip conditions are considered. The governing equations of motion, energy and nanoparticles are based on a perturbation technique. This technique depends on two parameters. Firstly, the amplitude ratio. Secondly, the small wave number. The distributions of the axial velocity, temperature and nanoparticle volume fraction are analytically derived. The pressure rise and friction force are numerically calculated. The numerical calculations are adopted to obtain the effects of several physical parameters, such as the slip parameter, Brownian motion parameter, thermophoresis parameter, the Reynolds number, the taper angle, nanoparticles Rayleigh number, thermal Rayleigh number and the maximum height of stenosis. It is found that the axial velocity increases with the decrease of the slip parameter. Meanwhile, it increases with the increase of both the nanoparticles Rayleigh number and the thermal Rayleigh number in the region of stenosis. The stream lines are also depicted. It is observed that the trapped bolus decreases in size with the increase of both the Brownian motion parameter and the thermophoresis parameter. In addition, the trapped bolus increases in size with the increase of both the maximum height of stenosis and the taper angle.
Author Keywords: Peristaltic flow, Jeffrey model, Tapered artery, Stenosis flow, Nanoparticles, Slip condition, Heat transfer, Trapping phenomena.
How to Cite this Article
Nabil T. M. El-dabe, Galal M. Moatimid, Mohamed A. Hassan, and Doaa R. Mostapha, “Analytical solution of the peristaltic flow of a Jeffrey nanofluid in a tapered artery with mild stenosis and slip condition,” International Journal of Innovation and Applied Studies, vol. 12, no. 1, pp. 1–32, July 2015.
