Analytical solutions of magnetohydrodynamic newtonian and second grade fluids in a porous medium - Ali, Farhad (2011)
This study is concentrate on developing the exact solutions of Newtonian and non-Newtonian fluid (second grade) problems. The fluid is considered electrically conducting (MH D) and passing through the porous medium. The modified Darcy's law is also incorporated in the mathematical formulation of the second grade problem. In addition to no-slip conditions, the influence of slip condition is also taken into account. Since, in many polymeric liquids when the weight of the molecule is high, the molecules near to the boundary show slip. Then the no-slip boundary condition is not appropriate. Therefore, this study incorporates the slip effects to handle this problem. The linear partial differential equations are reduced to the ordinary differential equations by using Laplace transform method. Then the final solutions for velocity and shear stress fields are obtained by taking the Laplace inverse, even though, to get the inverse Laplace is not always a trivial matter. Graphical results for the velocity profile and shear stress are presented and discussed. Comparison with earlier results for a limiting cases show a very good agreement. These solutions facilitate the verification of numerical solvers and also aid in the stability analysis of the solutions.