We construct a stress tensor in a blood vessel which is governing by Oldroyd-B constitutive differential equations and a momentum equation, first, we derive, the orientation stress tensor based on Brownian configuration fields, using Hookean dumbbells. Then, we formulate a new three-dimensional Oldroyd-B model, coupled with the momentum equation by patching the orientation stress tensor. The total stress tensor consists of the isotropic pressure stress tensor, the shear stress tensor, and the orientation stress tensor. We discuss in detail and show that the qualitative behavior of the flow is influenced by the rheological properties of the fluid, namely, its viscoelastic and inertial effects, as well as the shear-thinning viscosity. Finally, we present our numerical analysis of the model and give the effect of the orientation stress tensor in a blood vessel.