Natural Convection Where we’ ve been. Up to now, have considered forced convection that is an external driving force causes the flow. Where we’ re going: Consider the case where fluid movement is by buoyancy effects caused by temperature differential Heat Transfer Su Yongkang

Heat Exchangers. NTU-8 Method Where we’ ve been∴ Analysis of heat exchangers using log mean temperature difference (LMTD)

Natural Convection Where we’ ve been Up to now, have considered basic concepts of natural convection, the governing equations and laminar free convection on vertical surface Where were going Consider empirical correlations for natural convection Heat Transfer

用 Green函数方法求解 Schroedinger方程 定态方程

变分方法思想: 取不同的态v),计算(E)=mv),其中最小的(E)最接近Eo,可近似看成基态能E

零级能量有a重简并,但通过 Schmidt方法等可以保证互相之间正交归一

量子态满足 Schroedinger方程ih,(1)=Bv(F, 但是可以精确求解的物理问题太少,大部分实际问题不能严格求解,只能用近似方法

总波函数(=2S2) 若忽略耦合,则 y(s,2)=y()x(s,2)(总的Hilbert空间是位形空间和自旋空间的直积) 体系总波函数交换反对称性要求: a)空间对称y+(),自旋反对称x(S,S2), 或b)空间反对称y(,),自旋对称x(S12,S2)。 若忽略SS2耦合,自旋波函数:

若体系具有空间反演不变性,[,]=0,则 a)宇称守恒 b)宇称Ⅰ与H有共同本征态

对称性是一个体系最重要的性质。前面求解 Schrodinger方程时,我们看到,利用体系 的左右对称性就可以大大简化方程的求解