Volume 16, Issue 4, June 2016, Pages 742–757
Abderrahim Wakif1, Zoubair Boulahia2, and Rachid Sehaqui3
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
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 a more realistic model which incorporates the effects of Brownian motion and thermophoresis for studying the effect of boundary conditions and some control parameters on the onset of convective instability in presence of a uniform heat source in a confined medium filled of a Newtonian nanofluid layer and heated from below, this layer is assumed to have a low concentration of nanoparticles. The linear study which was achieved in this investigation shows that the thermal stability of Newtonian nanofluids depends of the state of the horizontal boundaries (rigid or free), the heat source strength ,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 with polynomials of high degree to obtain a fifth-order-accurate solution.
Author Keywords: Linear stability, Newtonian Nanofluid, Heat Source, Brownian motion, Thermophoresis, Power series.
Abderrahim Wakif1, Zoubair Boulahia2, and Rachid Sehaqui3
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
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 a more realistic model which incorporates the effects of Brownian motion and thermophoresis for studying the effect of boundary conditions and some control parameters on the onset of convective instability in presence of a uniform heat source in a confined medium filled of a Newtonian nanofluid layer and heated from below, this layer is assumed to have a low concentration of nanoparticles. The linear study which was achieved in this investigation shows that the thermal stability of Newtonian nanofluids depends of the state of the horizontal boundaries (rigid or free), the heat source strength ,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 with polynomials of high degree to obtain a fifth-order-accurate solution.
Author Keywords: Linear stability, Newtonian Nanofluid, Heat Source, Brownian motion, Thermophoresis, Power series.
How to Cite this Article
Abderrahim Wakif, Zoubair Boulahia, and Rachid Sehaqui, “The Effect of the Boundary Conditions on the Onset of Convection in a Newtonian Nanofluid Layer in Presence of an Internal Heat Source: A Revised Model,” International Journal of Innovation and Applied Studies, vol. 16, no. 4, pp. 742–757, June 2016.
