Volume 14, Issue 4, February 2016, Pages 1048–1065
Abderrahim Wakif1, Zoubair Boulahia2, Mostafa Zaydan3, Naoufal Yadil4, and Rachid Sehaqui5
1 University of Hassan II, Faculty of Sciences Aïn Chock, Laboratory of Mechanics, B.P.5366 Mâarif, Casablanca, Morocco
2 University of Hassan II, Faculty of Sciences Aïn Chock, Laboratory of Mechanics, B.P.5366 Mâarif, Casablanca, Morocco
3 University of Hassan II, Faculty of Sciences Aïn Chock, Laboratory of Mechanics, B.P. 5366 Mâarif, Casablanca, Morocco
4 University of Hassan II, Faculty of Sciences Aïn Chock, Laboratory of Mechanics, B.P. 5366 Mâarif, Casablanca, Morocco
5 University of Hassan II, Faculty of Sciences Aïn Chock, Laboratory of Mechanics, B.P.5366 Mâarif, Casablanca, Morocco
Original language: English
Copyright © 2016 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.
The aim of this paper, is to use the Buongiorno's mathematical model for studying the effect of boundary conditions and some control parameters on the onset of convective instability in presence of a uniform vertical magnetic field in a confined Darcy-Brinkman porous medium filled of an electrically conducting nanofluid which will be considered as Newtonian and heated uniformly from below. The linear study which was achieved in this investigation shows that the thermal stability of nanofluids depends of the state of the horizontal boundaries (rigid or free), the magnetic Chandrasekhar number, the buoyancy forces, the Brownian motion, the thermophoresis and other thermo-physical properties of nanoparticles. The governing differential equations are transformed into a set of ordinary differential equations by using similarity transformations, these equations will be solved analytically by converting our boundary value problem to an initial value problem, after this step we will approach the searched solutions numerically by polynomials of high degree to obtain a fourth-order-accurate solution.
Author Keywords: Linear stability, Nanofluid, Magnetic field, Brownian motion, Thermophoresis, Power series.
Abderrahim Wakif1, Zoubair Boulahia2, Mostafa Zaydan3, Naoufal Yadil4, and Rachid Sehaqui5
1 University of Hassan II, Faculty of Sciences Aïn Chock, Laboratory of Mechanics, B.P.5366 Mâarif, Casablanca, Morocco
2 University of Hassan II, Faculty of Sciences Aïn Chock, Laboratory of Mechanics, B.P.5366 Mâarif, Casablanca, Morocco
3 University of Hassan II, Faculty of Sciences Aïn Chock, Laboratory of Mechanics, B.P. 5366 Mâarif, Casablanca, Morocco
4 University of Hassan II, Faculty of Sciences Aïn Chock, Laboratory of Mechanics, B.P. 5366 Mâarif, Casablanca, Morocco
5 University of Hassan II, Faculty of Sciences Aïn Chock, Laboratory of Mechanics, B.P.5366 Mâarif, Casablanca, Morocco
Original language: English
Copyright © 2016 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
The aim of this paper, is to use the Buongiorno's mathematical model for studying the effect of boundary conditions and some control parameters on the onset of convective instability in presence of a uniform vertical magnetic field in a confined Darcy-Brinkman porous medium filled of an electrically conducting nanofluid which will be considered as Newtonian and heated uniformly from below. The linear study which was achieved in this investigation shows that the thermal stability of nanofluids depends of the state of the horizontal boundaries (rigid or free), the magnetic Chandrasekhar number, the buoyancy forces, the Brownian motion, the thermophoresis and other thermo-physical properties of nanoparticles. The governing differential equations are transformed into a set of ordinary differential equations by using similarity transformations, these equations will be solved analytically by converting our boundary value problem to an initial value problem, after this step we will approach the searched solutions numerically by polynomials of high degree to obtain a fourth-order-accurate solution.
Author Keywords: Linear stability, Nanofluid, Magnetic field, Brownian motion, Thermophoresis, Power series.
How to Cite this Article
Abderrahim Wakif, Zoubair Boulahia, Mostafa Zaydan, Naoufal Yadil, and Rachid Sehaqui, “The Power Series Method to Solve a Magneto-Convection Problem in a Darcy-Brinkman Porous Medium Saturated by an Electrically Conducting Nanofluid Layer,” International Journal of Innovation and Applied Studies, vol. 14, no. 4, pp. 1048–1065, February 2016.
