Introduction to Convection: Flow and Thermal Considerations

1. Introduction to Convection:Flow and Thermal Considerations Chapter Six and Appendix D Sections 6.1 through 6.8 and D.1 through D.3 Lecture 11a

2. Basic Definitions • Convection Heat Transfer Local convection coefficient h (W/m2K) Average convection coefficient (W/m2K)

3. Basic Definitions

4. Basic Definitions 2. Convection Mass Transfer Local convection mass transfer coefficient hm (m/s) Average convection mass transfer coefficient (m/s)

5. Basic Definitions

6. Convection Boundary Layers • Velocity Boundary Layer Boundary layer thickness δ(x) is at u=0.99u

7. Convection Boundary Layers Local friction coefficient Cf Shear stress τs

8. Convection Boundary Layers 2. Thermal Boundary Layer Boundary layer thickness δt(x) is at (Ts-T)/(Ts-T)=0.99

9. Convection Boundary Layers Local convection coefficient h

10. Convection Boundary Layers 3. Concentration Boundary Layer Boundary layer thickness δc(x) is at (CA,s-CA)/(CA,s-CA,)=0.99

11. Convection Boundary Layers Fick’s Law

12. Summary of Boundary Layers Velocity boundary layer: velocity gradients and shear stress, Cf Thermal boundary layer: T gradients and heat transfer, h Concentration boundary layer: C gradients and mass transfer, hm

13. Laminar and Turbulent Flow Reynold’s Number:

14. Boundary Layer Similarity

15. Boundary Layer Approximation Consider concurrent velocity, thermal and concentration boundary layer development for steady, two-dimensional, incompressible flow with constant fluid properties and negligible body forces. Apply conservation of mass, Newton’s 2nd Law of Motion and conservation of energy to a differential control volume and invoke the boundary layer approximations. Velocity Boundary Layer: Thermal Boundary Layer: Thermal Boundary Layer: u>>v

16. Boundary Layers Equations Momentum: Energy: Species:

17. Convection Boundary Layers Normalizing the boundary layer equations

18. Convection Boundary Layers Normalized boundary layer equations Velocity: Thermal: Concentration:

19. Convection Boundary Layers Solutions Velocity: Thermal: Concentration:

20. Convection Boundary Layers Dimensionless Group Parameters Prandtl Number: Schmidt Number: Reynolds Number:

21. Convection Boundary Layers Friction Coefficient For prescribed geometry:

22. Convection Boundary Layers Convection Heat Transfer Coefficient Nusselt Number:

23. Convection Boundary Layers Convection Mass Transfer Coefficient Sherwood Number:

24. Boundary Layer Analogies To establish relationship between Cf, Nu and Sh Lecture 11a