Arterioles with a curve shape are normally associated with a slow, blood flow, which led to a consequent emergence of thrombosis. In spite of the practical importance, there are not enough computational models that studied blood flow in very tiny diameters into one efficient framework. This study has addressed the dynamics of blood effects during porous medium and blood recirculation zones. Simulations of blood flow as a porous medium through an elbow artery have been investigated. The arteries have been treated as a porous medium. The blood is supplied with various geometries of arteries, which have different diameters. The outputs from numerical simulations have presented the details of blood flow patterns and the local distribution of blood flow along the artery. The effects of permeability, with respect to the variations in the Reynolds number (Re = 0.1,1 and 5) as well for changing porosity levels has been discussed. The effects due to different vessel diameters on the resultant distribution of velocity inside the vessel have been studied. Results are presented in the form of variations of velocity distributions and local variations of flow rates through the vessel dimensions. Simulations are compared with the available data and a good agreement is found. The study shows to be potentially useful to evaluate the role of porosity and flow conditions when the body is subjected to diseases.