Equation of Continuity for Species A with Constant ρDAB ρ D A B in terms of wA w A
控制方程表达通式：
ρDwADt=ρDAB∇2wA+rA ρ D w A D t = ρ D A B ∇ 2 w A + r A
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(∂wA∂t+vx∂wA∂x+vy∂wA∂y+vz∂wA∂z)=ρDAB[∂2wA∂x2+∂2wA∂y2+∂2wA∂z2]+rA ρ ( ∂ w A ∂ t + v x ∂ w A ∂ x + v y ∂ w A ∂ y + v z ∂ w A ∂ z ) = ρ D A B [ ∂ 2 w A ∂ x 2 + ∂ 2 w A ∂ y 2 + ∂ 2 w A ∂ z 2 ] + r A
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.
ρC^p(∂wA∂t+vr∂wA∂r+vθr∂wA∂θ+vz∂wA∂z)=ρDAB[1r∂∂r(r∂wA∂r)+1r2∂2wA∂θ2+∂2wA∂z2]+rA ρ C ^ p ( ∂ w A ∂ t + v r ∂ w A ∂ r + v θ r ∂ w A ∂ θ + v z ∂ w A ∂ z ) = ρ D A B [ 1 r ∂ ∂ r ( r ∂ w A ∂ r ) + 1 r 2 ∂ 2 w A ∂ θ 2 + ∂ 2 w A ∂ z 2 ] + r A
2-1
3.球坐标系（r,θ,ϕ r , θ , ϕ )
球坐标系Spherical coordinates（r, θ, ϕ r, θ , ϕ ):
NO.
ρC^p(∂wA∂t+vr∂wA∂r+vθr∂wA∂θ+vϕrsinθ∂wA∂ϕ)=ρDAB[1r2∂∂r(r2∂wA∂r)+1r2sinθ∂∂θ(sinθ∂wA∂θ)+1r2sin2θ∂2wA∂ϕ2]+rA ρ C ^ p ( ∂ w A ∂ t + v r ∂ w A ∂ r + v θ r ∂ w A ∂ θ + v ϕ r s i n θ ∂ w A ∂ ϕ ) = ρ D A B [ 1 r 2 ∂ ∂ r ( r 2 ∂ w A ∂ r ) + 1 r 2 s i n θ ∂ ∂ θ ( s i n θ ∂ w A ∂ θ ) + 1 r 2 s i n 2 θ ∂ 2 w A ∂ ϕ 2 ] + r A
3-1
参考文献
R. Byron Bird, Warren E. stewart, Edwin N. Lightfoot.* Transport phenomena:Revised second edition* John Wiely &Sons, Inc.
