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Unformatted text preview: INTRODUCTION TO DIFFUSION MASS TRANSFER prepared by: S.M. rafigh 2011 Convective Mass Transfer • 2 types of mass transfer between moving fluids: – With a boundary surface etween oving contacting phases – Between 2 moving contacting phases • Analogy with heat transfer Boundary Surfaces • Convective mass transfer coefficient ( 29 A As c A c c k N = • Hydrodynamic boundary layer – Laminar flow – molecular transfer – Turbulent flow – eddy diffusion Example 1 Dimensional Analysis • Defining dimensionless ratios – Schmidt number omentum – Lewis number AB AB D D ρ μ υ = ≡ = Sc mass momentum AB P D c k ρ ≡ = Le mass thermal – Sherwood number from to = = y A AB A dy dc D N ( 29 dy c c d L k y As A c / Sh = = ≡ ratio of molecular masstransfer resistance to convective masstransfer resistance ( 29 L c c D A s A AB / , , ∞ Example 2 • 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 b a 2 ( 29 = t L L L M t L c 3 1 AB c D L k = ⇒ 1 π (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 – The correlation relation is in the form: Sh = Nu AB = f (Re, Sc) AB D ρ μ π = ⇒ 3 • Transfer to natural convection phase – 3 π groups: (i) c c b a AB k L D μ π = 1 B c D L k = ⇒ 1 π (ii) AB ρ μ π f e d AB L D = 2 μ ρ π AB D = ⇒ 2 (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 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 AB , steady state, incompressible 2 2 y c D y c v x c v A AB A y A x ∂ ∂ = ∂ ∂ + ∂ ∂ – Boundary conditions: at y = 0 at y = ∞ , , , = ∞ s A A s A A c c c c 1 , , , = ∞ s A A s A A c c c c –...
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This note was uploaded on 06/21/2011 for the course CHE 329 taught by Professor Prof. rafigh during the Winter '10 term at Sharif University of Technology.
 Winter '10
 prof. rafigh
 pH, Mass Transfer

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