TITLE:
Homotopy Analysis of MHD Free Convective Micropolar Fluid Flow along a Vertical Surface Embedded in Non-Darcian Thermally-Stratified Medium
AUTHORS:
Olubode Kolade Koriko, Tosin Oreyeni, Adeola John Omowaye, Isaac Lare Animasaun
KEYWORDS:
Porous Medium, Thermal Stratification, Homotopy Analysis Method, Free Convection, Micropolar
JOURNAL NAME:
Open Journal of Fluid Dynamics,
Vol.6 No.3,
September
16,
2016
ABSTRACT: The dynamics of steady, two-dimensional magnetohydrodynamics (MHD) free convective
flow of micropolar fluid along a vertical porous surface embedded in a thermally
stratified medium is investigated. The ratio of pressure drop caused by liquid-solid interactions to that of pressure drop caused by viscous resistance are equal;
hence, the non-Darcy effect is properly accounted for in the momentum equation.
The temperature at the wall and at the free stream which best accounts for thermal
stratification are adopted. Similarity transformations are used to convert the nonlinear
partial differential equation to a system of coupled non-linear ordinary differential
equation and also to parameterize the governing equations. The approximate
analytical solution of the corresponding BVP are obtained using Homotopy Analysis
Method (HAM). The effects of stratification parameter, thermal radiation and other
pertinent parameters on velocity, angular velocity and temperature profiles are
shown graphically. It is observed that increase in the stratification parameter leads to
decrease in both velocity and temperature distribution and also makes the microrotation
distribution to increase near the plate and decrease away from the plate. The
influence of both thermal stratification and exponential space dependent internal
heat source on velocity, micro-rotation and temperature profiles are presented. The
comparison of the solutions obtained using analytical techniques (HAM) and
MATLAB package (bvp4c) is shown and a good agreement is observed.