 Article highlights AGM is the more accurate method than fem and rendicuda by less than 7% error. The maximum difference between the three methods happened near the wall of the vessel. Fem is more accurate than rendicuda by less than 9% error. AL-203 is the best nanoparticle for decreasing the maximum temperature of the blood. This article was authored by Payam Jalalai, Amad Sadegi Gahare, Baram Jalalai, and others. The following article was authored by Payam Jalalai, Amad Sadegi Gahare, Baram Jalalai, and others.