Dat analysis types element types input listing test 2

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Unformatted text preview: y conditions: VX = 0 at r = R and dVX = 0 at r = 0 dr we readily obtain: VX = R2 ∆P r2 1− 2 4µ L R or r2 VX = 2 ( VX)average 1 − R2 where ( VX)average = 1R ∫ Vx r dr R2 0 For this problem, species transport equation can be simplified as follows: ∂ 2 Yi ∂r 2 + VX ∂Yi ∂ 2 Yi 1 ∂Yi , i = A,B = − r ∂r DAB ∂x ∂x2 ANSYS Verification Manual . ANSYS Release 9.0 . 002114 . © SAS IP, Inc. 1–475 VM209 Let us introduce the following dimensionless variables: θi = ( Yi )w − Yi ( Yi )w − ( Yi )in r+ = r , R VX ( VX)average VX+ = , x+ = x /R Re Sc where, Reynold's number is ρ ( VX)average D Re = µ and, Schmidt number is µ ρDAB Sc = Substituting the non-dimensional variables into the species transport equation, we get: ∂ 2θi VX+ ∂θi 1 − = + 2 ∂x + (Re Sc )2 ∂x +2 ∂r +2 r + ∂r + ∂ 2θi 1 ∂θi For large values of the product (ReSc) second term on the right-hand side of the equation can be neglected. For our problem: VX = (0.0025)2 1.28 (1 − 1.6 × 105 r 2 ) −...
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