In this paper, an incompressible couple stress fluid flow with magnetic field in a porous
channel with expanding or contracting walls and slip boundary condition is considered. Lie group
analysis and group invariant solutions are obtained, the governing equations are reduced to nonlinear
ordinary differential equations. The resulting equations are solved analytically, also this equations are
solved by using Adomian method. The graphs for the axial and the normal velocity components and
the pressure distribution for different values of the physical and geometric parameters are plotted
and discussed. Finally, the comparison between the analytic and Adomian methods is discussed. It is
found that for no-slip case φ = 0 the fluid adheres to the walls and axial velocity is maximum at the
center of the channel, also by increasing the slip parameter the velocity at the channel walls increases.
However, it decreases at center of the channel by increasing slip parameter.