Analysis of MHD flow characteristics of an UCM viscoelastic flow in a permeable channel under slip conditions

In the present study, the problem of two-dimensional magneto-hydrodynamic (MHD) flow of an upper-convected Maxwell (UCM) fluid has been investigated in a permeable channel with slip at the boundaries. Employing the similarity variables, the basic partial differential equations are reduced to ordinary differential equations with Dirichlet and Neumann boundary conditions which are solved analytically and numerically using the Homotopy Analysis Method and fourth-order Runge–Kutta–Fehlberg method, respectively. The influences of the some physical parameters such as Reynolds number, slip condition, Hartman number and Deborah number on non-dimensional velocity profiles are considered. As an important outcome, comparison between HAM and numerical method shows that HAM is an exact and high-efficient method for solving these kinds of problems. Moreover, it can be found that the velocity profiles are a decreasing function of Hartmann number and Deborah number.