On the electroosmotic and MHD Jeffery–Hamel flow of Nano fluid influenced by wall slip conditions

Year 2016, Volume: 19 Issue: 4, 555 - 568, 01.12.2016

Jacob Nagler

Abstract

Combined MHD and electroosmotic Jeffery–Hamel flow of Nano fluid type inside a wedge (inclined walls) with non-linear viscosity and wall friction are investigated analytically. As a result of similarity relations, one nonlinear ordinary differential equation is obtained and solved analytically with the appropriate assumptions. Moreover, excellent agreement was found between the obtained analytic solution and suggested simple parabolic approximation. Although it was found that in case where more effects are gradually being considered, a slight difference is emerged, but the most dramatic change between solutions occurs when solid to fluid ratio gets significant value. In addition, suitable match in the quantitatively and qualitatively aspects was found between literature results and obtained solution. In addition, analytical solution parametric investigation was performed for specific parameters choice. It was found that the normalized velocity was found to decrease gradually with the tangential direction progress and/or with friction coefficient increase. However, the normalized velocity profile gets higher values as long as the solid to fluid ratio increases. Additionally, Reynolds, Hartmann and solid volume fraction coefficient increase (separately or all together) have raised the normalized velocity function values. Finally, unprevail distinguished cases were introduced to understand flow complexity. It was found that the electrical field magnitude effect is significantly, especially for small friction coefficient values and for high wedge semi angle. Also, the combination between small friction coefficient values including small parameter flow values (Re and Ha numbers) and high electrically field may lead to un-optimized course of normalized velocity profile. The last case that was examined is concerned with friction coefficient variation effect on the normalized velocity profile for different values of wedge semi angle with high electric field for specific parameters choice. It was found that increasing friction coefficient leads to normalized velocity profile consolidation.

Keywords

MHD, electroosmosis, Jeffery–Hamel flow, Nano fluid, slip conditions, friction, nonlinear ordinary differential equations, analytical solution, approximate solutions