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

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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.

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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

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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

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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

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3-D Unsteady Conduction

27

Example