Effect of Non-Zero Second Grade Parameter on Magnetohydrodynamic Blood Flow Through A Porous Artery

In this paper, Mathematical model and simulation of a non-Newtonian magnetohydrodynamic blood flow through a porous artery was constructed, and due to non-linearity of the constructed model a Hybrid Algorithm based on classical Homotopy Perturbation Method (HPM) for solving non-linear model equations was also proposed. The analytic solution for the velocity profile of the constructed model was obtained applying Laplace transform and the Hybrid Algorithm, where the present solution of the velocity profile (non-zero second grade parameter) was validated using the exiting work in the literature (zero second grade parameter). And for the complexity of the present model the analytic solution was obtained with aid of Mathematica software and present the result in graphical form showing the effect of non-zero second-grade parameter, third grade parameter, Hartman number, Porosity, Prandtl number, body acceleration, pressure gradient and Frequency ratio on velocity profile is presented and analyzed. The presented result for the velocity of blood modeled by non-zero second-grade parameter are significantly different from those corresponding to the velocity modelled by zero second-grade parameter. This may be advantageous for some biomedical practical problems. The values of the momentum boundary layer increases as time progresses; thereby decreasing the velocity distributions as time decreases and as third grade parameter also increases. The consequence of increasing Hartman number is that it decreases the velocity profile of the blood.