[物理学与PDEs]第4章第3节 一维反应流体力学方程组 3.2 一维反应流体力学方程组的 Lagrange 形式

1.  一维粘性热传导反应流体力学方程组的 Lagrange 形式 $$\beex \bea \cfrac{\p \tau}{\p t'}-\cfrac{\p u}{\p m}&=0,\\ \cfrac{\p u}{\p t'}+\cfrac{\p p}{\p m}-\cfrac{\p}{\p m} \sez{\sex{\cfrac{4}{3}\mu+\mu'}\rho \cfrac{\p u}{\p m}}&=F,\\ T\cfrac{\p S}{\p t'}-\sex{\cfrac{4}{3}\mu+\mu'}\rho\sex{\cfrac{\p u}{\p m}}^2 &=\cfrac{\p}{\p m}\sex{\kappa\rho \cfrac{\p T}{\p m}} -\cfrac{\p S}{\p Z}\bar k(\rho,p,Z)TZ,\\ \cfrac{\p Z}{\p t'}&=-\bar k(\rho,p,Z)Z. \eea \eeex$$

2.  一维理想反应流体力学方程组的 Lagrange 形式 $$\beex \bea \cfrac{\p \tau}{\p t'}-\cfrac{\p u}{\p m}&=0,\\ \cfrac{\p u}{\p t'}+\cfrac{\p p}{\p m}&=F,\\ \cfrac{\p S}{\p t'} &=-\cfrac{\p S}{\p Z}\bar k(\rho,p,Z)Z,\\ \cfrac{\p Z}{\p t'}&=-\bar k(\rho,p,Z)Z. \eea \eeex$$