## Single Fluid Equations of Magnetofluid Mechanics

$p=\rho RT=nkT\text{.}$

$\frac{\partial \rho}{\partial t}+\nabla \xb7\left(\rho \overrightarrow{v}\right)=0.$

$\rho \left[\frac{\partial \overrightarrow{v}}{\partial t}+\left(\overrightarrow{v}\xb7\nabla \right)\overrightarrow{v}\right]=-\nabla p+\nabla \xb7\overleftrightarrow{\tau}+{\rho}_{e}\overrightarrow{E}+\overrightarrow{J}\times \overrightarrow{B}\text{,}\text{where}:{\tau}^{ij}=\mu \left(\frac{\partial {u}^{i}}{\partial {x}^{j}}+\frac{\partial {u}^{j}}{\partial {x}^{i}}\right)-\frac{2}{3}\mu \left(\nabla \xb7\overrightarrow{v}\right){\delta}_{ij}\text{.}$

$\rho \frac{D{\overline{e}}_{m}}{Dt}=-\nabla \xb7\left(p\overrightarrow{v}\right)+\nabla \xb7\left(\overrightarrow{v}\xb7\overleftrightarrow{\tau}\right)+\nabla \xb7\overrightarrow{Q}+\overrightarrow{J}\xb7\overrightarrow{E}\text{.}$

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