ce 318: transport process 2 (heat and mass transfer) lecture 17: unsteady-state diffusion (chapter...
TRANSCRIPT
![Page 1: CE 318: Transport Process 2 (Heat and Mass Transfer) Lecture 17: Unsteady-State Diffusion (Chapter 27) NSC 210 4/14/2015](https://reader033.vdocuments.mx/reader033/viewer/2022042822/5697bfb81a28abf838c9f7f4/html5/thumbnails/1.jpg)
CE 318: Transport Process 2(Heat and Mass Transfer)
Lecture 17: Unsteady-State Diffusion(Chapter 27)
NSC 2104/14/2015
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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).
![Page 3: CE 318: Transport Process 2 (Heat and Mass Transfer) Lecture 17: Unsteady-State Diffusion (Chapter 27) NSC 210 4/14/2015](https://reader033.vdocuments.mx/reader033/viewer/2022042822/5697bfb81a28abf838c9f7f4/html5/thumbnails/3.jpg)
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
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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.
![Page 5: CE 318: Transport Process 2 (Heat and Mass Transfer) Lecture 17: Unsteady-State Diffusion (Chapter 27) NSC 210 4/14/2015](https://reader033.vdocuments.mx/reader033/viewer/2022042822/5697bfb81a28abf838c9f7f4/html5/thumbnails/5.jpg)
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.
![Page 6: CE 318: Transport Process 2 (Heat and Mass Transfer) Lecture 17: Unsteady-State Diffusion (Chapter 27) NSC 210 4/14/2015](https://reader033.vdocuments.mx/reader033/viewer/2022042822/5697bfb81a28abf838c9f7f4/html5/thumbnails/6.jpg)
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
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7
General Equation
+
+
![Page 8: CE 318: Transport Process 2 (Heat and Mass Transfer) Lecture 17: Unsteady-State Diffusion (Chapter 27) NSC 210 4/14/2015](https://reader033.vdocuments.mx/reader033/viewer/2022042822/5697bfb81a28abf838c9f7f4/html5/thumbnails/8.jpg)
• 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 ,,,
![Page 9: CE 318: Transport Process 2 (Heat and Mass Transfer) Lecture 17: Unsteady-State Diffusion (Chapter 27) NSC 210 4/14/2015](https://reader033.vdocuments.mx/reader033/viewer/2022042822/5697bfb81a28abf838c9f7f4/html5/thumbnails/9.jpg)
Case I: Equimolar counterdiffusion (NA+NB=0)
Case II: B is stagnant (NB = 0)
9
Binary Diffusion in Gases
zBzAAA
ABzA NNydz
dycDN ,,,
![Page 10: CE 318: Transport Process 2 (Heat and Mass Transfer) Lecture 17: Unsteady-State Diffusion (Chapter 27) NSC 210 4/14/2015](https://reader033.vdocuments.mx/reader033/viewer/2022042822/5697bfb81a28abf838c9f7f4/html5/thumbnails/10.jpg)
• Basic partial differential equation and conditions
• Example of analytical solutions
• Chart method to obtain solution
10
Outline: Unsteady State Mass Transfer
![Page 11: CE 318: Transport Process 2 (Heat and Mass Transfer) Lecture 17: Unsteady-State Diffusion (Chapter 27) NSC 210 4/14/2015](https://reader033.vdocuments.mx/reader033/viewer/2022042822/5697bfb81a28abf838c9f7f4/html5/thumbnails/11.jpg)
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
![Page 12: CE 318: Transport Process 2 (Heat and Mass Transfer) Lecture 17: Unsteady-State Diffusion (Chapter 27) NSC 210 4/14/2015](https://reader033.vdocuments.mx/reader033/viewer/2022042822/5697bfb81a28abf838c9f7f4/html5/thumbnails/12.jpg)
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
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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
![Page 14: CE 318: Transport Process 2 (Heat and Mass Transfer) Lecture 17: Unsteady-State Diffusion (Chapter 27) NSC 210 4/14/2015](https://reader033.vdocuments.mx/reader033/viewer/2022042822/5697bfb81a28abf838c9f7f4/html5/thumbnails/14.jpg)
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
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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
![Page 16: CE 318: Transport Process 2 (Heat and Mass Transfer) Lecture 17: Unsteady-State Diffusion (Chapter 27) NSC 210 4/14/2015](https://reader033.vdocuments.mx/reader033/viewer/2022042822/5697bfb81a28abf838c9f7f4/html5/thumbnails/16.jpg)
1-D Unsteady State Mass Transfer
16
L L/2
21x
tDX ABD
![Page 17: CE 318: Transport Process 2 (Heat and Mass Transfer) Lecture 17: Unsteady-State Diffusion (Chapter 27) NSC 210 4/14/2015](https://reader033.vdocuments.mx/reader033/viewer/2022042822/5697bfb81a28abf838c9f7f4/html5/thumbnails/17.jpg)
• Basic partial differential equation and conditions
• Example of analytical solutions
• Chart method to obtain solution
17
Outline: Unsteady State Mass Transfer
![Page 18: CE 318: Transport Process 2 (Heat and Mass Transfer) Lecture 17: Unsteady-State Diffusion (Chapter 27) NSC 210 4/14/2015](https://reader033.vdocuments.mx/reader033/viewer/2022042822/5697bfb81a28abf838c9f7f4/html5/thumbnails/18.jpg)
18
Unsteady State Transfer
2
2
x
T
t
T
2
2
x
CD
t
C AA
A
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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
![Page 20: CE 318: Transport Process 2 (Heat and Mass Transfer) Lecture 17: Unsteady-State Diffusion (Chapter 27) NSC 210 4/14/2015](https://reader033.vdocuments.mx/reader033/viewer/2022042822/5697bfb81a28abf838c9f7f4/html5/thumbnails/20.jpg)
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
![Page 21: CE 318: Transport Process 2 (Heat and Mass Transfer) Lecture 17: Unsteady-State Diffusion (Chapter 27) NSC 210 4/14/2015](https://reader033.vdocuments.mx/reader033/viewer/2022042822/5697bfb81a28abf838c9f7f4/html5/thumbnails/21.jpg)
Large Flat Plate: Center Concentration
21
0AAS
AAS
CC
CCY
2
1x
tDX ABD
1x
xn
1xk
Dm
c
AB
![Page 22: CE 318: Transport Process 2 (Heat and Mass Transfer) Lecture 17: Unsteady-State Diffusion (Chapter 27) NSC 210 4/14/2015](https://reader033.vdocuments.mx/reader033/viewer/2022042822/5697bfb81a28abf838c9f7f4/html5/thumbnails/22.jpg)
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
![Page 23: CE 318: Transport Process 2 (Heat and Mass Transfer) Lecture 17: Unsteady-State Diffusion (Chapter 27) NSC 210 4/14/2015](https://reader033.vdocuments.mx/reader033/viewer/2022042822/5697bfb81a28abf838c9f7f4/html5/thumbnails/23.jpg)
Long Cylinder: Center Temperature
230AAS
AAS
CC
CCY
2
1x
tDX ABD
1x
xn
1xk
Dm
c
AB
![Page 24: CE 318: Transport Process 2 (Heat and Mass Transfer) Lecture 17: Unsteady-State Diffusion (Chapter 27) NSC 210 4/14/2015](https://reader033.vdocuments.mx/reader033/viewer/2022042822/5697bfb81a28abf838c9f7f4/html5/thumbnails/24.jpg)
Spheres
24
0AAS
AAS
CC
CCY
1xk
Dm
c
AB
1x
xn
Relative temperature change
Relative time
Relative resistance
Relative position
21x
tDX ABD
![Page 25: CE 318: Transport Process 2 (Heat and Mass Transfer) Lecture 17: Unsteady-State Diffusion (Chapter 27) NSC 210 4/14/2015](https://reader033.vdocuments.mx/reader033/viewer/2022042822/5697bfb81a28abf838c9f7f4/html5/thumbnails/25.jpg)
Sphere: Center Temperature
25 0AAS
AAS
CC
CCY
2
1x
tDX ABD
1x
xn
1xk
Dm
c
AB
![Page 26: CE 318: Transport Process 2 (Heat and Mass Transfer) Lecture 17: Unsteady-State Diffusion (Chapter 27) NSC 210 4/14/2015](https://reader033.vdocuments.mx/reader033/viewer/2022042822/5697bfb81a28abf838c9f7f4/html5/thumbnails/26.jpg)
26
3-D Unsteady Conduction
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27
Example