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The purpose of this study is to analyze the two-dimensional blood flow in the artery slant from the axis at an angle with mild stenosis under the joint effects of the electro-osmotic, magnetic field, chemical reaction and porosity using a new analytical method. In addition, the mathematical model presented by the researchers Tripathi and Sharma (2018c) was successfully developed by adding the effect of electro-osmosis and studying the impact of the new addition in the developed model on blood flow.

A new analytical method was used to find the analytical approximate solutions of two-dimensional blood flow in artery slant from the axis at an angle with mild stenosis. This technique is based on integrating the Akbari-Ganji and the homotopy perturbation methods.

The results of axial velocity, concentration, temperature and the wall shear stress for blood flow were analyzed in the cases of the absence and presence of electro-osmosis. Furthermore, in these two states of electro-osmosis, a contour plot was created to show the difference in the profile of velocity to the flow of blood when the magnetic field was increased and the altitude of stenosis was increased. The results showed that the new technique is effective and has high accuracy to determine the analytical approximate solutions of two-dimensional blood flow in artery slant from the axis at an angle with mild stenosis. The validity, utility and necessity of the new method were illustrated from the graphs of the new solutions; in addition, there is an excellent agreement with the results of previous studies.

This paper focuses on developing the mathematical model which was presented by the researchers Tripathi and Sharma (2018c), by adding the effect of the electro-osmosis to it, which has been successfully developed. According to the authors’ modest information, the new system has not been studied before. This current problem is solved by using an innovative approach known as the Akbari-Ganji homotopy perturbation method (AGHPM) which has not been used before in two cases: the presence and absence of the effect of electro-osmosis. This new technique afford new with effective and has high accuracy results. Furthermore, the new study (i.e. adding effect of electro-osmosis) with the applications of (variable viscosity, magnetic field, chemical reaction and porosity) illustrated the importance of applying electro-osmosis and how doctors can benefit from it during surgeries through proper use.