A new semester

1
A new semester

• From compartment to distributed systems

2
What was ECS About?

• Engineering of COMPARTMENT systems
• Small number of state variables
• Concentration on temporal dynamics
• Examples
• Mass / Spring / Damper
• PID Feedback

3
What is EDS About?

• Engineering of spatially DISTRIBUTED Systems
• Focus on spatial and spatio-temporal systems
• Example
• Spatial Force of gravity vs. height from
  surface, magnetic fields.
• Spatio-Temporal Spread of diseases in a
  geographic population.

4
EDS in Three Acts

• Part 1 Diffusion
• Example (EDS) Spread of heat
• Example (Math) Vector calculus
• Part 2 Fields (Quasi-Statics )
• Example (Physics) Electric Magnetic Fields
• Example (EDS) Magnetic Fields and Forces
• Example (Math) Vector Calculus
• Part 3 Waves
• Example (EDS) Sound, Radio, Water Waves
• Example (Physics) Radio, Optics

5
Tools You Will Use

• Analogy
• Analysis
• Experiment
• Hand-Written Simulation (MATLAB)
• Off-the-Shelf Simulation (Comsol-FEMLAB)

6
What to expect

• Its still Gill and Brian
• Its still lecture and lab format
• Same Ninja format
• More exams
• More simulation (experiments are difficult)
• We have to give grades

7
How to do well in this course

• For us, doing well learning
• Come to class, pay attention.
• Come to lab, pay attention.
• See your Ninja, ask questions.
• Do the labs/homework, ask questions.
• Its mostly a linear system Output (learning) is
  proportional to input (effort)

8
Why start with diffusion?

• Bad
• It will not seem integrated with math/physics.
• Good
• Important in many applications.
• Good system for studying with analysis,
  simulation, and experiments.
• Allows us to introduce tools and concepts in a
  simple problem.
• Provide time for physics to sync up.
• You will see the connections later.

9
Diffusion Lectures 1 2

• Physics, applications, and analysis

10
The diffusion equation

• Mass (Mass diffusivity - Length2/time)
• How should we mix fuel and air in an engine to
  reduce pollution?
• How can gases change the properties of materials
  (semiconductors or carburizing steel) ?
• Electro-chemical reactions in fuel cells can be
  diffusion limited.
• Heat (thermal diffusivity - Length2/time)
• How long do we cook a steak to get medium rare?
• How much heat is wasted out the window?
• How do we keep the Pentium cool?
• Momentum (kinematic viscosity - Length2/time)
• How do we predict the drag on an airplane?
• Why do golf balls have dimples?
• How do very small creatures swim?
• The diffusion eqn. is also used to model the
  spread of disease in populations, models of
  derivatives trading, and more.

11
Questions

• What is diffusion?
• the process whereby particles of liquids, gases,
  or solids intermingle as the result of their
  spontaneous movement caused by thermal agitation.
• If there were only molecular diffusion, how long
  would it take to smell your feet after removing
  your sock?
• 1 year!

12
So why do we smell our feet?
13
Mass diffusion in gases

• Easy to understand gas molecules move and
  collide with neighbors resulting in randomness.
• Mean free path is 100 nm in standard air.
• In air molecules undergoes about 1010 collisions
  per second.
• Kinetic theory can predict everything quite well.
• However, convection dominates most of our
  everyday experience in gases.

14
Particle view of diffusion
15
Assume some fluid flow
16
No molecular diffusion
17
Diffusion is 1/100 of convection
18
Diffusion is 1/20 of convection
19
Without convection, mixing in liquids is slow
20
Mass Diffusion Coefficients

• Time to move distance L t L2/D
• O2 in N2 D 0.18 cm2/s (0.42 cm/sec)
• Caffeine in H2O D 630 µm2/s (25 micron/sec)
• H2 in Fe D 0.25 µm2/s (0.5 micron/sec)
• Al in Cu D 0.5 angstroms2/million years

21
Diffusion of momentum in a fluid
22
Heat conduction in solids

• Lattice vibrations in non-metals.
• Electrons participate in metals similar
  mechanism as electrical conductivity.
• No convection pure diffusion problem.
• Can be understood from continuum formulation.

23
Thermal diffusivity

• Aluminum a 0.9 cm2/s
• Iron a 0.12 cm2/s
• Air a 0.18 cm2/s
• Water a 0.0017 cm2/s
• Brick a 0.005 cm2/s
• Glass a 0.005 cm2/s

24
Fouriers Law

• Empirical Law
• Derivable for gases

K thermal conductivity W/mK
25
Conservation of energy 1-D
26
Energy Balance
where
This is just like last year.
27
Heat equation
balance
rearrange
Fouriers Law
Definition of derivative when dx is small
28
What does it mean?

• Second spatial derivative of temperature equals
  the rate of change of temperature
• If the local curvature of T in space is upward, T
  increases with time at that point.
• If local curvature is downward, T decreases.
• No curvature, T is steady.

29
Heat equation
30
Heat equation
31
Heat equation
T(x,tT)
dT/dt0
temperature
X
32
Quenching
Assume -T is uniform and hot at time0 -At
time0 edges are held at a cold temperature -All
heat flow is 1-D (wall is thin in x compared to y
and z)
33
What happens?
T
X
34
1-D Box model

• Assume
• - For storage, each box has an average, uniform
  T.
• Heat flux assumes linear connections between box
  centers
• T1 and T6 are fixed at the cold temperature
• Length L is broken into equally spaced points

?x
L
35
Rate equation for T2
36
Equations for all nodes
37
Taylor series expansion
PLUS
38
Time integration with Euler
T 011110 dx 1/6 dt 0.01 for j
1NumberOfSteps dT(1) 0 dT(6)
0 dT(25) (T(14) 2T(25)T(36))/dx2
T T dtdT end
39
Implementation for interior w/ MATLAB
T1 T2 T3 T4 - 2(T2 T3 T4 T5)
T3 T4 T5 T6 ---------------
--------------------------------------------------
------------------ dT2/dt dT3/dt dT4/dt
dT5/dt
40
Increase the number of grid points
41
For stability w/ Euler
42
Cooking a steak - medium
Constant temperature heat source
HOT!
Constant temperature heat source
HOT!
43
How long do we cook in order to achieve the same
center temperature when the steak is two times
thicker?
Constant temperature heat source
Meat thermometer
Constant temperature heat source
44
Experimental data
45
Return of the glob of particles
How fast does it spread? How do we measure?
46
Mean distance traveled
47
Histogram of x location
numbers
-3 -2 -1 0 1
2 3
location
How does the std. vary with time ?
48
Particle location histogram on semi-log plot
Probability
location
49
Hot/Cold in contact
----------- Insulated------------------
----------- Insulated------------------
50
Heat flow
dT/dx
Distance
Temp. or temp. gradient
51
Hot/cold (new condition)
52
Heat flow
dT/dx
Distance
Temp. or temp. gradient