[物理学与PDEs]第4章第2节 反应流体力学方程组 2.2 反应流体力学方程组形式的化约

1.  粘性热传导反应流体力学方程组 $$\beex \bea \cfrac{\rd \rho}{\rd t}&+\rho \Div{\bf u}=0,\\ \cfrac{\rd Z}{\rd t}&=-\bar k(\rho,p,Z)Z,\\ \cfrac{\rd {\bf u}}{\rd t}&+\cfrac{1}{\rho}\n p =\cfrac{1}{\rho}\Div(2\mu{\bf S}) +\cfrac{1}{\rho}\n \sez{\sex{\mu'-\cfrac{2}{3}\mu}\Div{\bf u}} +{\bf F},\\ \cfrac{\rd E}{\rd t} +p\cfrac{\rd \tau}{\rd t}& -\cfrac{2\mu}{\rho}\tr({\bf S}\cdot\n{\bf u}) -\cfrac{1}{\rho}\sex{\mu'-\cfrac{2}{3}\mu}|\Div{\bf u}|^2 =\cfrac{1}{\rho}\Div(\kappa\n T), \eea \eeex$$ 或 $$\bex T\cfrac{\rd S}{\rd t} -\cfrac{2\mu}{\rho}\tr({\bf S}\cdot\n{\bf u}) -\cfrac{1}{\rho}\sex{\mu'-\cfrac{2}{3}\mu} |\Div{\bf u}|^2 =\cfrac{1}{\rho}\Div(\kappa\n T) -\cfrac{\p S}{\p Z}\bar k(\rho,p,Z)TZ. \eex$$

 

 

2.  理想反应流体力学方程组 $$\beex \bea \cfrac{\rd \rho}{\rd t}&+\rho\Div{\bf u}=0,\\ \cfrac{\rd Z}{\rd t}&=-\bar k(\rho,p,Z)Z,\\ \cfrac{\rd {\bf u}}{\rd t}&+\cfrac{1}{\rho}\n p={\bf F},\\ \cfrac{\rd S}{\rd t}&=-\cfrac{\p S}{\p Z}\bar k(\rho,p,Z)Z. \eea \eeex$$