流体传质方程【Mass Transfer Equation】

流体传质方程

Equation of Continuity for Species α α in terms of jjα j j α

控制方程表达通式:

ρDwαDt=jjα+rα ρ D w α D t = − ∇ ⋅ j j α + r α


1.直角坐标系( x,y,z x , y , z )

直角坐标系Cartesian coordinates (  x,y,z   x,y,z  ): NO.
ρ(wαt+vxwαx+vywαy+vzwαz)=[jαxx+jαyy+jαzz]+rα ρ ( ∂ w α ∂ t + v x ∂ w α ∂ x + v y ∂ w α ∂ y + v z ∂ w α ∂ z ) = − [ ∂ j α x ∂ x + ∂ j α y ∂ y + ∂ j α z ∂ z ] + r α 1-1

2.圆柱坐标系( r,θ,z r , θ , z )

圆柱坐标系Cylindrical coordinates coordinates ( r, θ, z  r,  θ , z  ): NO.
ρ(wαt+vrwαr+vθrwαθ+vzwαz)=[1rr(rjαr)+1rjαθθ+jαzz]+rα ρ ( ∂ w α ∂ t + v r ∂ w α ∂ r + v θ r ∂ w α ∂ θ + v z ∂ w α ∂ z ) = − [ 1 r ∂ ∂ r ( r j α r ) + 1 r ∂ j α θ ∂ θ + ∂ j α z ∂ z ] + r α 2-1

3.球坐标系( r,θ,ϕ r , θ , ϕ )

球坐标系Spherical coordinates( r, θϕ  r,  θ ,  ϕ   ): NO.
ρ(wαt+vrwαr+vθrwαθ+vϕrsinθwαϕ)=[1r2r(r2jαr)+1rsinθθ(jαθsinθ)+1rsinθjαϕϕ]+rα ρ ( ∂ w α ∂ t + v r ∂ w α ∂ r + v θ r ∂ w α ∂ θ + v ϕ r s i n θ ∂ w α ∂ ϕ ) = [ 1 r 2 ∂ ∂ r ( r 2 j α r ) + 1 r s i n θ ∂ ∂ θ ( j α θ s i n θ ) + 1 r s i n θ ∂ j α ϕ ∂ ϕ ] + r α 3-1

注:如果密度被浓度代替。都要做相应的替换

质量浓度 ρ ρ wα w α jjα j j α vv v v rα r α
摩尔浓度 c c xα x α JJα J J α ∗ vv v v ∗ Rαxαβ=1NRβ R α − x α ∑ β = 1 N R β

参考文献

  1. R. Byron Bird, Warren E. stewart, Edwin N. Lightfoot.* Transport phenomena:Revised second edition* John Wiely &Sons, Inc.

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