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\begin{minipage}{0.99\textwidth} 
\begin{Large}

Chapman-Enskog Development:\\
$$ f = \rho({\bf x}) \exp \left( -\frac{|{\bf v} -
\bar{\bf v} ({\bf x})|^2}{2T({\bf x})} \right) (1 + \phi^{(2)}) 
+ ... $$
\vspace{0.3cm}

Quasi-Maxwell Model Solution: $\;\;\;\phi^{(2)}_{heat} \;\;+\;\; \phi^{(2)}_{shear}$\\
$$ \phi^{(2)}_{shear} = \frac{-\mu}{\rho T({\bf x})^2}
({\bf v}-\bar{\bf v})^T {\bf D}({\bf x}) ({\bf v}-\bar{\bf v}), $$

$$ D_{\alpha\beta}({\bf x}) = \frac{1}{2} \left(\frac{\partial \bar{v}_\alpha}
{\partial x_\beta} + \frac{\partial \bar{v}_\beta}{\partial x_\alpha} \right),\;\;\;\;
\mu = -\frac{(2T)^{1/2}}{2\sigma\lambda_{02}}. $$
\vspace{0.3cm}

We then approximate $$1 + \phi^{(2)} \;\approx\; \exp(\phi^{(2)}) $$

\end{Large}
\end{minipage}}

\newpage
\begin{Large}

Couette flow:
$$\left(v_x-\bar{v}_x(z), \;\;v_y, \;\;v_z \right) \;\;\;\;\cdot\;\;\;\;
\left(\begin{array}{ccc}1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1\end{array} \right)
\rightarrow
\left(\begin{array}{ccc}1 & 0 & \tau_{xz}/\rho T\\ 
0 & 1 & 0\\ \tau_{xz}/\rho T & 0 & 1 \end{array} \right) 
 \;\;\;\;\cdot\;\;\;\;
\left(\begin{array}{c}v_x-\bar{v}_x(z)\\ v_y \\v_z \end{array} \right)
$$
\end{Large}
\vspace{0.1cm}

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