CE 318: Transport Process 2 (Heat and Mass Transfer) Lecture 17: Unsteady-State Diffusion (Chapter 27) NSC 210 4/14/2015.
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CE 318: Transport Process 2(Heat and Mass Transfer)
Lecture 17: Unsteady-State Diffusion(Chapter 27)
NSC 2104/14/2015
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).
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
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.
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.
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
dx
dCDJ AAA
dx
dCA
21 AAAA CCkJ )(Re,ScfkA
2
2
x
CD
t
C AA
A
7
General Equation
+
+
• Equimolar counterdiffusion
• Unimolecular diffusion (diffusion through a stagnant layer)
• Pseudo-steady-state diffusion (moving boundary)
• Diffusion with reaction (heterogeneous or homogenous reaction)
8
One-Dimensional Steady State Molecular Diffusion
0, AzA R
dz
dN
zBzAAA
ABzA NNydz
dycDN ,,,
Case I: Equimolar counterdiffusion (NA+NB=0)
Case II: B is stagnant (NB = 0)
9
Binary Diffusion in Gases
zBzAAA
ABzA NNydz
dycDN ,,,
• Basic partial differential equation and conditions
• Example of analytical solutions
• Chart method to obtain solution
10
Outline: Unsteady State Mass Transfer
Overview of Transport Processes
11
Momentum Heat Mass
Profile
Steady state
Non-steady state
dy
dvxyx
dx
dTkqx
dx
dCDJ AAA
2
2
y
v
t
v xx
2
2
x
T
t
T
2
2
x
CD
t
C AA
A
1-D Unsteady State Mass Transfer
12
Initial condition: t=0, CA = CA0
Boundary conditions: t > 0
x = 0, C = CAS
x = L, C = CAS
L L/2
1-D Unsteady State Heat Conduction Negligible Surface Resistance
13
T
Initial condition: t=0, T = T0
Boundary conditions: t > 0
x = 0, T = T1
x = 2H, T = T1
1. Simplify the PDE
2. Try and error to convert PDE to ODE
3. Try and error to determine the constant
4. Boundary conditions
5. Initial condition
14
Separation of Variables
1. Simplify the PDE
2. Try and error to convert PDE to ODE
3. Try and error to determine the constant
4. Boundary conditions
5. Initial condition
15
Separation of Variables
1-D Unsteady State Mass Transfer
16
L L/2
21x
tDX ABD
• Basic partial differential equation and conditions
• Example of analytical solutions
• Chart method to obtain solution
17
Outline: Unsteady State Mass Transfer
18
Unsteady State Transfer
2
2
x
T
t
T
2
2
x
CD
t
C AA
A
Charts for Solution of Unsteady Transport Problems (Appendix F, Page 711)
19
0AAS
AAS
CC
CCY
1xk
Dm
c
AB
1x
xn
Relative temperature change
Relative time
Relative resistance
Relative position
21x
tDX ABD
Unsteady State: Large Flat Plate
20
0AAS
AAS
CC
CCY
1xk
Dm
c
AB
1x
xn
Relative temperature change
Relative time
Relative resistance
Relative position
21x
tDX ABD
Large Flat Plate: Center Concentration
21
0AAS
AAS
CC
CCY
2
1x
tDX ABD
1x
xn
1xk
Dm
c
AB
Long Cylinders
22
0AAS
AAS
CC
CCY
1xk
Dm
c
AB
1x
xn
Relative temperature change
Relative time
Relative resistance
Relative position
21x
tDX ABD
Long Cylinder: Center Temperature
230AAS
AAS
CC
CCY
2
1x
tDX ABD
1x
xn
1xk
Dm
c
AB
Spheres
24
0AAS
AAS
CC
CCY
1xk
Dm
c
AB
1x
xn
Relative temperature change
Relative time
Relative resistance
Relative position
21x
tDX ABD
Sphere: Center Temperature
25 0AAS
AAS
CC
CCY
2
1x
tDX ABD
1x
xn
1xk
Dm
c
AB
26
3-D Unsteady Conduction
27
Example
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