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

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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(∂wα∂t+vx∂wα∂x+vy∂wα∂y+vz∂wα∂z)=−[∂jαx∂x+∂jαy∂y+∂jαz∂z]+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

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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(∂wα∂t+vr∂wα∂r+vθr∂wα∂θ+vz∂wα∂z)=−[1r∂∂r(rjαr)+1r∂jαθ∂θ+∂jαz∂z]+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

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3.球坐标系（ r,θ,ϕ r , θ , ϕ )

球坐标系Spherical coordinates（ r, θ, ϕ  r,  θ ,  ϕ   ):	NO.
ρ(∂wα∂t+vr∂wα∂r+vθr∂wα∂θ+vϕrsinθ∂wα∂ϕ)=[1r2∂∂r(r2jαr)+1rsinθ∂∂θ(jαθsinθ)+1rsinθ∂jαϕ∂ϕ]+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	JJ∗α J J α ∗	vv∗ v v ∗	Rα−xα∑β=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.