Main Article Content



In this contribution, the magnetohydrodynamic non-Newtonian nanofluid flow through a porous medium in eccentric annuli with peristalsis is investigated. This has been done under the combined effect of viscous dissipation and radiation. The inner annulus is rigid and at rest, while the outer annulus has a sinusoidal wave traveling down its wall. The fundamental equations are modulated under the long wave length assumptions, and a closed form of solution is obtained for the axial velocity. While, homotopy perturbation solution is obtained, which satisfies the energy and nanoparticles equations. Numerical results for the axial velocity, temperature and nanoparticles phenomena distributions as well as the reduced Nusselt number and Sherwood number are obtained and tabulated for various parametric conditions.

Article Details

How to Cite
ABOU-ZEID, Mohamed. HOMOTOPY PERTURBATION METHOD TO MHD NON-NEWTONIAN NANOFLUID FLOW THROUGH A POROUS MEDIUM IN ECCENTRIC ANNULI WITH PERISTALSIS. Thermal Science, [S.l.], mar. 2017. ISSN 2334-7163. Available at: <http://thermal-science.tech/journal/index.php/thsci/article/view/2117>. Date accessed: 24 june 2017. doi: https://doi.org/10.2298/TSCI150215079A.
Received 2017-03-02
Accepted 2017-03-13
Published 2017-03-13


[1] Wang, X.Q., Mujumdar, A. S., Heat Transfer Characteristics of Nanofluids: A Review, Int. J. Thermal Sci. 46 (2007), pp. 1-19
[2] Nadeem, S., Haq, R. U., MHD Boundary Layer Flow Of A Nanofluid Passed Through A Porous Shrinking Sheet With Thermal Radiation, J. Aerosp. Eng. 28 (2015), 04014061.
[3] Mustafa, M., Hayat, T., Pop, I., Asghar, S., Obaidat, S., Stagnation-Point Flow of A Nanofluid Towards A Stretching Sheet, Int. J. Heat Mass Transfer, 54 (2011), pp. 5588– 5594
[4] Ho, C. J., Chen, M. W., Li, Z. W., Numerical Simulation of Natural Convection of Nanofluid in a Square Enclosure: Effect Due To Uncertainties of viscosity And Thermal Conductivity, Int. J. Heat Mass Transfer, 51 (2008), pp. 4506–4516
[5] Santra, A. K., Sen, S., Chakraborty, N., Study of Heat Transfer Augmentation In A Differentially Heated Square Cavity Using Copper–Water Nanofluid, Int. J. Therm. Sci. 47 (2008), pp. 1113–1122
[6] Mahmoudi, A. H., Shahi, M., Talebi, F., Effect of Inlet And Outlet Location On The Mixed Convective Cooling Inside The Ventilated Cavity Subjected To An External Nanofluid, Int. Commun. Heat Mass Transfer, 37 (2010), pp. 1158–1173
[7] Mahmoudi, A. H., Shahi, M., Shahedin, A.M., Hemati, N., Numerical Modeling of Natural Convection In An Open Cavity With Two Vertical Thin Heat Sources Subjected To A Nanofluid, Int. Commun. Heat Mass Transfer, 38 (2011), pp. 110–118
[8] Abu-Nada, E., Effects of Variable Viscosity And Thermal Conductivity of Al2O3–Water Nanofluid On Heat Transfer Enhancement In Natural Convection, Int. J. Heat Fluid Flow 30 (2009), pp. 679–690
[9] Khaled, A. R. A., Vafai, K., Heat Transfer Enhancement Through Control of Thermal Dispersion Effects, Int. J. Heat Mass Transfer, 48 (2005), pp. 2172–2185
[10] Kuznetsov, A. V., Nield, D. A., Natural Convective Boundary-Layer Flow of A Nanofluid Past A Vertical Plate, Int. J. Thermal Sci. 49 (2010), pp. 243–247
[11] Choi, S. U. S., Enhancing Thermal Conductivity of Fluids With Nanoparticles, ASME Fluids Eng. Div. 231 (1995), pp. 99–105
[12] Chen, R. X., Liu, F. J., J. He, H., Fan, J., Silk Cocoon: "Emperor's New Clothes" for Pupa: Fractal Nano-Hydrodynamical Approach, J. Nano Res. 22 (2013), pp. 65-70
[13] Eldabe, N. T., Abou-zeid, M. Y., Magnetohydrodynamic Peristaltic Flow With Heat And Mass Transfer of Micropolar Biviscosity Fluid Through A Porous Medium Between Two Co-Axial Tubes, Arab J. Sci. Eng. 39 (2014), pp. 5045–5062
[14] Mustafa, M., Hina, S., Hayat, T., Alsaedi, A., Influence of Wall Properties On The Peristaltic flow of A Nanofluid: Analytic And Numerical Solutions, Int. J. Heat Mass Transfer 55 (2012), pp. 4871–4877
[15] Akbar, N. S., Nadeem, S., Endoscopic Effects On Peristaltic Flow of A Nanofluid, Commun. Theor. Phys. 56 (2011), pp. 761–768
[16] Akbar, N. S., Nadeem, S., Hayat, T., Hendi, A. A., PeristalticFlow of A Nanofluid With Slip Effects, Meccanica, 47 (2012), pp. 1283-1294
[17] Eldabe, N. T., Abou-zeid, M. Y., The Wall Properties Effect On Peristaltic Transport of Micropolar Non-Newtonian Fluid With Heat And Mass Transfer. Math. Prob. Eng. (2010), Article ID 898062, 40 pages.
[18] Akbar, N. S., Nadeem, S., Hayat, T., Hendi, A. A., Peristaltic Flow of A Nanofluid In A Non-Uniform Tube, Heat Mass Transfer/Waerme-und Stoffuebertragung 48 (2012), pp. 451–459
[19] Akbar, N. S., Nadeem, S., Peristaltic Flow of A Phan–Thien–Tanner Nanofluid In A Diverging Tube, Heat Transfer, 41 (2012), pp. 10–22
[20] Ebaid, A., Aly, E. H., Exact Analytical Solution of The Peristaltic Nanofluids Flow In An Asymmetric Channel With Flexible Walls And Slip Condition: Application To The Cancer Treatment, Comput. Math. Meth. Med. (2013), Article ID 825376, 8 pages.
[21] Ebaid, A., Remarks On The Homotopy Perturbation Method For The Peristaltic Flow of Jeffrey Fluid With Nano-Particles In An Asymmetric Channel, Comput. Math. Appl. 68 (2014), pp. 77–85
[22] Nelson, E. B., Well Cementing, Elseivier, Amsterdam, New York, USA, 1990
[23] Walton, I. C., Bittleston, S. H., The Flow of A Bingham Plastic Fluid In A Narrow Eccentric Annulus, J. Fluid Mech. 222 (1991), pp. 39-60
[24] Ahmed, M. E. S., Attia, H. A., Magnetohydrodynamic Flow And Heat Transfer of A Non-Newtonian Fluid In An Eccentric Annulus, Can. J. Phys. 76 (1998), pp. 391-401
[25] El-Sayed, M. F., Eldabe, N. T., Ghaly, A. Y., Sayed, H. M., Magnetothermodynamic Peristaltic Flow of Bingham Non-Newtonian Fluid in Eccentric Annuli With Slip Velocity and Temperature Jump Conditions, J. Mechanics, 29 (2013), pp. 493–506
[26] Rohsenow, W. M., Hartnett, J. P., Cho, Y. I., Handbook of Heat Transfer, McGraw-Hill, New York, USA, 1998
[27] Davood, D. G., Zaman, Z. G., Hosain, D. G., Determination of temperature distribution for annular fins with temperature dependent thermal conductivity by HPM, Thermal Sci. 15 (2011), pp. S111–S115
[28] He, J. H., Homotopy Perturbation Technique, Comput. Methods Appl. Mech. Eng. 178 (1999), pp. 257-262
[29] Rajeev, Homotopy perturbation method for a Stefan problem with variable latent heat, Thermal Sci. 18 (2014), pp. 391–398