This paper aims to determine the exact solutions of non-Newtonian fluid namely
micropolar fluid with MHD in a porous medium by traveling wave method. The
governing equations of incompressible micropolar fluid with MHD in a porous medium
are non-linear PDEs reduced to ODEs through wave parameter ξ = mx + ny + Ut. The
set of new exact solutions are determined for five different cases. In special cases, the
solution for micropolar fluid with and without MHD and porous effects can also be
obtained from general solutions. Furthermore, these solution reduces to a Newtonian
solution if we put vortex viscosity κ → 0. Finally, the influence of the material and
other parameters of interest on the fluid motion, as well as a comparison among
micropolar and Newtonian fluids is also analyzed by 2D and 3D graphical illustrations.