Fully Developed Flow of Fourth Grade Fluid through the Channel with Slip Condition in the Presence of a Magnetic Field

In this paper, to study the incompressible fully developed flow of a non-Newtonian fourth grade fluid in a flat channel under an externally applied magnetic field, an appropriate analysis has been performed considering the slip condition on the walls. The governing equations, Ohm’s law, continuity and momentum for this problem are reduced to a nonlinear ordinary form. The nonlinear equation with robin mixed boundary condition is solved with collocation (CM) and least square (LSM) methods. The effects of parameters such as non-Newtonian, magnetic field and slip parameters on dimensionless velocity profiles will be discussed. In the end, the results could bring us to this conclusion that collocation and least square methods can be used for solving nonlinear differential equations with robin mixed condition.

Keywords:

Collocation method , Fourth grade fluid , channel , Least Square Method