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{\large
\begin{eqnarray*}
\rho (\frac{d \textbf{v}}{dt}+\textbf{v} \cdot \nabla \textbf{v})=- \nabla p + \mu \nabla ^2 \textbf{v} + \textbf{f}
\end{eqnarray*}
}

One thing to notice in the Navier-Stokes equation is that the viscosity coefficient of

{\large\begin{equation*}\mu\end{equation*}}

is not a constant but rather a function of shear rate. Blood gets less viscous as the shear rate increases (shear thinning). Here, we model the blood viscosity using the Carreau fluids model. The mathematical formulation of the Carreau model is as follows:

{\large
\begin{eqnarray*}
\mu_{eff}(\dot{\gamma})=\mu_{inf}+(\mu_0-\mu_{inf})(1+(\lambda \dot{\gamma})^2)^\frac{n-1}{2}
\end{eqnarray*}
}

In the equations above,

{\large\begin{equation*}\mu_{eff}\end{equation*}}

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