[物理学与PDEs]第2章第2节 粘性流体力学方程组 2.4 粘性热传导流体动力学方程组

粘性热传导流体动力学方程组: $$\beex \bea \cfrac{\p \rho}{\p t}+\Div(\rho{\bf u})&=0,\\ \rho \cfrac{\rd {\bf u}}{\rd t} +\n p -\n\sez{ \sex{\mu'-\cfrac{2}{3}\mu}\Div{\bf u} } -2\Div(\mu {\bf S})&=\rho {\bf F},\\ \rho\cfrac{\rd e}{\rd t} +p\Div{\bf u} -\mu\sum_{i,j=1}^3 \sex{\cfrac{\p u_i}{\p x_j}+\cfrac{\p u_j}{\p x_i}}\cfrac{\p u_j}{\p x_i} -\sex{\mu'-\cfrac{2}{3}\mu}(\Div{\bf u})^2 &=\Div(\kappa\n T). \eea \eeex$$