Olubode Kolade Koriko, Tosin Oreyeni, Adeola John Omowaye, Isaac Lare Animasaun

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Department of Mathematical Sciences, Federal University of Technology, Akure, Nigeria.
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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.

Keywords: Porous Medium, Thermal Stratification, Homotopy Analysis Method, Free Convection, Micropolar

Cite this paper: Kolade Koriko, O. , Oreyeni, T. , John Omowaye, A. and Lare Animasaun, I. (2016) Homotopy Analysis of MHD Free Convective Micropolar Fluid Flow along a Vertical Surface Embedded in Non-Darcian Thermally-Stratified Medium. Open Journal of Fluid Dynamics, 6, 198-221. doi: 10.4236/ojfd.2016.63016.

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