New traveling wave solutions of MHD micropolar fluid in porous medium

Abstract

Abstract 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=m x+n y+U t. 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.

Keywords

• Traveling wave
• MHD
• Micropolar fluid
• Porous medium
• Exact solutions
• 2D & 3D graphs