1. (Heat and Mass Transfer) Lecture 17: Unsteady-State Diffusion
CE 318: Transport Process 2
(Heat and Mass Transfer)
Lecture 17: Unsteady-State Diffusion
(Chapter 27)
NSC 210
4/14/2015 1

2. Midterm Grades The midterm grades only serve as guidance Total: 44 pts
4 HWs, 4pts
2 Quizzes, 10 pts
2 Midterms, 30 pts
Average: 29.6/44; STDEV: 6.7/44
The class still has 60 pts (Note: the lowest score for the quizzes will be dropped). 2

3. Third Quiz Date: 4/16 (Molecular diffusion, steady state diffusion)
Duration: 20 mins
Open book/notes
Bring your calculator
No electronics with internet access 3

4. The Third Midterm Take-home exam
Problems will be given at 9 am on 4/24
Solutions due before the class on 4/28
Open book/notes
No discussion with anyone else on the problems/solution, except the instructor. 4

5. Ruckenstein Lecture: Robert Langer
Biomaterials and biotechnology: From the discovery of the first angiogenesis inhibitors to the development of controlled drug delivery systems and the foundation of tissue engineering
Robert S. Langer has written over 1,280 articles.  He also has nearly 1,050 patents worldwide.  Dr. Langer’s patents have been licensed or sublicensed to over 250 pharmaceutical, chemical, biotechnology and medical device companies.  He is the most cited engineer in history. 5

6. Overview of Mass Transfer
Steady State Molecular Diffusion
Fick’s Law for Molecular Diffusion
DA: gas, liquid, solid, biological materials
calculation:
Counter-diffusion; Unimolecular diffusion; diffusion/reaction
Convective Mass-Transfer Coefficient
Unsteady State Diffusion
Mass Transfer Equipment 6

7. General Equation + + 7

8. One-Dimensional Steady State
Molecular Diffusion
Equimolar counterdiffusion
Unimolecular diffusion (diffusion through a stagnant layer)
Pseudo-steady-state diffusion (moving boundary)
Diffusion with reaction (heterogeneous or homogenous reaction) 8

9. Binary Diffusion in Gases
Case I: Equimolar counterdiffusion (NA+NB=0)
Case II: B is stagnant (NB = 0) 9

10. Outline: Unsteady State Mass Transfer
Basic partial differential equation and conditions
Example of analytical solutions
Chart method to obtain solution 10

11. Overview of Transport Processes
Momentum
Heat
Mass
Profile
Steady state
Non-steady state 11

12. 1-D Unsteady State Mass Transfer
Initial condition: t=0, CA = CA0
Boundary conditions: t > 0
x = 0, C = CAS
x = L, C = CAS
L/2 L 12

13. 1-D Unsteady State Heat Conduction Negligible Surface Resistance
Initial condition: t=0, T = T0
Boundary conditions: t > 0
x = 0, T = T1
x = 2H, T = T1 T 13

14. Separation of Variables
Simplify the PDE
Try and error to convert PDE to ODE
Try and error to determine the constant
Boundary conditions
Initial condition 14

15. Separation of Variables
Simplify the PDE
Try and error to convert PDE to ODE
Try and error to determine the constant
Boundary conditions
Initial condition 15

16. 1-D Unsteady State Mass Transfer
L/2 L 16

17. Outline: Unsteady State Mass Transfer
Basic partial differential equation and conditions
Example of analytical solutions
Chart method to obtain solution 17

18. Unsteady State Transfer18

19. Charts for Solution of Unsteady Transport Problems (Appendix F, Page 711)
Relative temperature change
Relative time
Relative position
Relative resistance 19

20. Unsteady State: Large Flat Plate
Relative temperature change
Relative time
Relative position
Relative resistance 20

21. Large Flat Plate: Center Concentration21

22. Long Cylinders Relative temperature change Relative time
Relative position
Relative resistance 22

23. Long Cylinder: Center Temperature23

24. Spheres Relative temperature change Relative time Relative position
Relative resistance 24

25. Sphere: Center Temperature25

26. 3-D Unsteady Conduction26

27. Example 27