MHD flow and heat transfer of a third order fluid in a porous channel with stretching wall: Application to hemodynamics

Of concern in the paper are the magnetohydrodynamic (MHD) boundary layer flow and heat transfer of a third order fluid flowing in a channel. The walls of the channel are considered to be porous and stretchable, where the surface velocity is proportional to the longitudinal distance from a fixed point. The governing equation is a non-linear partial differential of the third order. Using the similarity transformations and boundary layer approximations, the nonlinear partial differential equations are reduced to a system of ordinary differential equations. But these equations are also non-linear. In order to solve this system of non-linear equations, a suitable numerical method has been developed. The study reveals that a back flow occurs near the central line of the channel due to the stretching walls and further that the flow reversal can be stopped by applying a sufficiently strong external magnetic field. The results presented bear the promise of important applications in the study of the hemodynamic flow of blood in the cardiovascular system when subjected to an external magnetic field.