HW/Tutorial Week #11 WWWR Chapter 28

1. Tutorial #11 WWWR # 28.3, 28.13 & 28.25 To be discussed on April 4, 2014. By either volunteer or class list. HW/Tutorial Week #11WWWR Chapter 28

2. Convective Mass Transfer • 2 types of mass transfer between moving fluids: • With a boundary surface • Between 2 moving contacting phases • Analogy with heat transfer

3. Boundary Surfaces • Convective mass transfer coefficient • Hydrodynamic boundary layer • Laminar flow – molecular transfer • Turbulent flow – eddy diffusion

4. Example 1

5. Dimensional Analysis • Defining dimensionless ratios • Schmidt number • Lewis number

6. Sherwood number from to ratio of molecular mass-transfer resistance to convective mass-transfer resistance

7. Example 2

9. Transfer to stream flowing under forced convection • Using Buckingham- theory, 3  groups: (i)

10. (ii) (iii) • The correlation relation is in the form: Sh = NuAB = f (Re, Sc)

11. Transfer to natural convection phase • 3  groups: (i) (ii)

12. (iii) defining an analogous GrAB • The correlation relation is in the form: Sh = f (GrAB, Sc)

13. Mass, Heat and Momentum Analogies • Similarities between the transport phenomenon • 5 conditions: • No reaction to generate heat/mass • No radiation • No viscous dissipation • Low mass-transfer rate • Constant physical properties

14. Reynolds analogy • Between momentum and energy, if Pr = 1 • Between momentum and mass, if Sc = 1 • From the profiles, we get

15. Combined with coefficient of skin friction to get which is analogous to

16. For turbulent flow, we use Prandtl’s mixing length hypothesis from velocity fluctuation and shear stress we find

17. from concentration fluctuation and instantaneous transfer we get with the analogous heat transfer equation

18. Prandtl and von Karman analogies • Effect of turbulent core and laminar sublayer • In the sublayer, for momentum and mass we get

19. In the core, using Reynolds analogy, • Combining both turbulent and laminar equations and simplify to

20. At the laminar sublayer, substitute to get the Prandtl analogy • Multiply by vL/DAB and rearrange, we get

21. With a buffer layer between the laminar sublayer and turbulent core, we use the von Karman analogy for heat transfer for mass transfer

23. Chilton-Colburn analogy • Modification to Reynolds’ analogy, for all Pr and Sc • j factor for mass transfer • For fluids within 0.6 < Sc < 2500, we know

24. Divide by RexSc1/3, • Substitute in Blasius solution, • So the analogy is

25. Example 3

27. Example 4

29. Example 5