(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

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

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

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

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

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

General Equation + + 7

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

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

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

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

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

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

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

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

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

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

Unsteady State Transfer 18

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

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

Large Flat Plate: Center Concentration 21

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

Long Cylinder: Center Temperature 23

Spheres Relative temperature change Relative time Relative position Relative resistance 24

Sphere: Center Temperature 25

3-D Unsteady Conduction 26

Example 27