Volume 4, Issue 1, March 2018, Page: 11-17
Influence of Heat Transfer on MHD Oscillatory Flow for Williamson Fluid with Variable Viscosity Through a Porous Medium
Wissam Sadiq Khudair, Faculty of Computer Science and Information Technology, University of Al-Qadisiyah, Diwaneyah, Iraq
Dheia Gaze Salih Al-Khafajy, Faculty of Computer Science and Information Technology, University of Al-Qadisiyah, Diwaneyah, Iraq
Received: Feb. 21, 2018;       Accepted: Mar. 9, 2018;       Published: Apr. 3, 2018
DOI: 10.11648/j.ijfmts.20180401.12      View  1092      Downloads  80
The main theme of the present examined the influence of heat transfer on magnetohydrodynamics (MHD) for the oscillatory flow of Williamson fluid with variable viscosity model for two kinds of geometries "Poiseuille flow and Couette flow" through a porous medium channel. The momentum equation for the problem, is a non-linear differential equations, has been found by using "perturbation technique" and intend to calculate the solution for the small number of Weissenberg (We <<1) to get clear forms for the velocity field by assisting the (MATHEMATICA) program to obtain the numerical results and illustrations. The physical features of Darcy number, Reynolds number, Peclet number, magnetic parameter, Grashof number and radiation parameter are discussed simultaneously through presenting graphical discussion. Investigated through graphs the variation of a velocity profile for various pertinent parameters. While the velocity behaves strangely under the influence of the Brownian motion parameter and local nanoparticle Grashof number effect. On the basis of this study, it is found that the velocity directly with Grashof number, Darcy number, radiation parameter, Reynolds number and Peclet number, and reverse variation with magnetic parameter and frequency of the oscillation and discussed the solving problems through graphs.
Williamson Fluid, Variable Viscosity, Heat Transfer, (MHD), Porous Medium
To cite this article
Wissam Sadiq Khudair, Dheia Gaze Salih Al-Khafajy, Influence of Heat Transfer on MHD Oscillatory Flow for Williamson Fluid with Variable Viscosity Through a Porous Medium, International Journal of Fluid Mechanics & Thermal Sciences. Vol. 4, No. 1, 2018, pp. 11-17. doi: 10.11648/j.ijfmts.20180401.12
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
T. Hayat, R. Ellahi, F. M. Mahomed, and S. Africa, “Acta Mechanica Exact solutions for Couette and Poiseuille flows for fourth grade fluids,” vol. 78, pp. 69–70, 2007.
K. M. Joseph, S. Daniel, and G. M. Joseph, “Unsteady MHD Couette Flow between Two Infinite Parallel Porous Plates in an Inclined Magnetic Field with Heat Transfer,” Int. J. Math. Stat. Invent., vol. 2, no. 3, pp. 103–110, 2014.
B. S. D. Nigamf and S. N. Singhj, “Heat Transfer By Laminar Flow Between Parallel Plates Under the Action of transverse magnetic field,” Quart. Journ. Mech Applied. Math, vol. XIII, no. 5, 1960.
M. Y. Malik, I. Zehra, and S. Nadeem, “Flows of Carreau fluid with pressure dependent viscosity in a variable porous medium : Application of polymer melt,” Alexandria Eng. J., 2014.
I. Zehra, M. M. Yousaf, and S. Nadeem, “Numerical solutions of Williamson fluid with pressure dependent viscosity,” Results Phys., vol. 5, pp. 20–25, 2015.
S. Nadeem and M. Awais, “Thin film flow of an unsteady shrinking sheet through porous medium with variable viscosity,” Phys. Lett. A, vol. 372, pp. 4965–4972, 2008.
D. G. S. Al-khafajy, “Influence of MHD and Wall Properties on the Peristaltic Transport of a Williamson Fluid with Variable Viscosity Through Porous Medium,” Iraqi J. Sci., vol. 58, no. 2, pp. 1076–1089, 2017.
W. S. Khudair and D. G. S. Al-khafajy, Influence of heat transfer on Magneto hydrodynamics oscillatory flow for Williamson fluid through a porous medium, Iraqi J. Sci., vol. 59, no. 1B, pp. 389–397, 2018.
A. A. Khan, R. Ellahi, and K. Vafai, “Peristaltic Transport of a Jeffrey Fluid with Variable Viscosity through a Porous Medium in an Asymmetric Channel,” vol. 2012.
T. Hayat, S. Nawaz, A. Alsaedi, and M. Rafiq, “Results in Physics Influence of radial magnetic field on the peristaltic flow of Williamson fluid in a curved complaint walls channel,” Results Phys., vol. 7, pp. 982–990, 2017.
S. E. G. A. C. Cogley. W. G. Vincenti, “Differential approximation for radiative transfer in a Nongrey gas near equilbrium,” Am. Inst. Aeronaut. Astronaut., vol. 6, no. 3, pp. 551–553, 1968.
J. D. Kevorkian, Jirair, Cole, Perturbation Methods in Applied Mathematics. Springer-Verlag New York, 1981.
Browse journals by subject