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Microsoft PowerPoint - Intoduction to Diffusion Mass Transfer1

Microsoft PowerPoint - Intoduction to Diffusion Mass Transfer1

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INTRODUCTION TO DIFFUSION MASS TRANSFER prepared by: S.M. rafigh 2011
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Convective Mass Transfer 2 types of mass transfer between moving fluids: With a boundary surface Between 2 moving contacting phases Analogy with heat transfer
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Boundary Surfaces Convective mass transfer coefficient Hydrodynamic boundary layer ( 29 A As c A c c k N - = Laminar flow –molecular transfer Turbulent flow –eddy diffusion
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Example 1
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Dimensional Analysis Defining dimensionless ratios Schmidt number μ υ momentum Lewis number AB AB D D ρ = = Sc mass AB P D c k ρ = Le mass thermal
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Sherwood number from to 0 = - = y A AB A dy dc D N ( 29 ( 29 L c c dy c c d D L k y As A c / / Sh 0 = - - - = ratio of molecular mass-transfer resistance to convective mass-transfer resistance A s A AB , ,
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Example 2
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Transfer to stream flowing under forced convection Using Buckingham- π theory, 3 π groups: (i) c c b a AB k D D ρ π = 1 ( 29 = L L M L c b a 2 1 t L t 3 AB c D L k = 1 π
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(ii) (iii) v D D f e d AB ρ π = 2 AB D Dv = 2 π μ ρ π i h g AB D D = 3 μ The correlation relation is in the form: Sh = Nu AB = f (Re, Sc) AB D ρ π = 3
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Transfer to natural convection phase 3 π groups: (i) c c b a AB k L D μ π = 1 AB c D L k = 1 π (ii) ρ μ π f e d AB L D = 2 μ ρ π AB D = 2
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(iii) defining an analogous Gr AB A i h g AB g L D ρ μ π = 3 AB A D g L μ ρ π = 3 3 The correlation relation is in the form: Sh = f (Gr AB , Sc) AB A A AB A AB v g L g L D g L D Gr 2 3 2 3 3 3 2 = = = = ρ ρ μ ρ ρ μ ρ μ ρ π π
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Exact Analysis Blasius solution for hydrodynamic boundary layer for laminar flow parallel to flat surface Analogous situation in mass transfer if no reaction, constant D , steady state, if no reaction, constant D AB , steady state, incompressible 2 2 y c D y c v x c v A AB A y A x = +
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Boundary conditions: at y = 0 - c c at y = 0 , , , = - s A A s A A c c 1 , , , = - - s A A s A A c c c c
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Defining then Solving in a similar manner to momentum, we s A A s A A c c c c C , , , - - = 2 2 y C D y C v x C v AB y x = + define s A A s A A c c c c f , , , 2 ' - - = x x y xv x y Re 2 2 = = ν η
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