Mathematical modelling in industry can help solve problems in many fields such as energy, manufacturing, mining, sports and more. Industrial mathematics modellers attend MISG conferences where industry presents problems on Monday and academics present solutions on Friday. Some example problems included optimizing steel casting, understanding rock blasts, soccer ball design, and more. A key skill of modellers is understanding problems across disciplines and applying appropriate mathematical techniques to gain insight rather than just numeric solutions.

1. Mathematical Modelling in Industry
Nev Fowkes
neville.fowkes@uwa.eu.au
School of Maths an Stats
University of Western Australia
November 10, 2012

2. Industrial Mathematics: MISGs
I am a industrial mathematics modeller.
MISG (Maths in Industry Study Groups)
(www.maths-in-industry.org):
Originated at Oxford 35 years ago. Now worldwide (about 16 each
year) and linked. I have attended/help facilitate more than 50 of
these in Australia, Asia, Africa, Canada, Europe, UK.
The format: problems presented by industry on Monday, results
presented by academics on Friday. Followup: proceedings produced
later.
These are worldwide interconnected activities (about 16 each year).
The next MISG in Australia is at QUT in Feb 2013.

3. Problem Areas
Environmental Areas: fire (home, forests, caused by electric
wires), hydraulics, waste disposal
Energy: wind turbines, alcohol from cellulose, coal extraction,
explosives,
Operations research; optimal ore extraction, scheduling
(airlines), water management.
Medical: Cancer research, epilepsy, lens manufacture (coatings
for lenses, manufacture of plastic lenses), scheduling patients.
Mining/Construction: ore detection, extraction. explosives,
safety (tunnel collapse), corrosion, concrete.

4. Sports and Defence: soccer, badminton racquets, computer
and defence games.
Agriculture: tea drying, sprays for crops, labelling of bottles,
sugar beer production.
Manufacturing: continuous casting of steel, corrosion in sheet
steel, wine bottle labels, icecream manufacture, beer
production, paper (rolls, sheets).
Finance (bidding for energy supply), product differentiation.
Transport: air rail scheduling, noise reduction, mechanical
problems.

5. So what does a industrial mathematical modeller have to
offer?
As a mathematical modeller I can say that I am expert in none of
the disciplines required to understand such problems.
So what skills are offered by a modeller?
Cross disciplinary modelling experience: the ‘same’ problem
arises in many contexts!
Mathematical technique (scaling, computational, asymptotics)
The primary issues are not numeric: the aim is to understand the
science.
Mathematics is just one tool for doing this
Now for a few problems:

6. An Industrial Packer (Inflatable Packers International,
Perth, Enterprise Connect)
Inflatable packers are used for sealing off sections of a drill hole in
the oil and gas and geothermal industries (permeability, sampling).
borehole

7. The reinforced rubber tube
A packer needs to be easily inflated but able to withstand high
pressure once in place.
This is achieved using wire cords are imbedded in rubber.
The cord winding angle changes during inflation.
600mm
60mm

8. Issues: practical and technical
Commercial Issues:
Hand crafted.
Often need to be designed (effective sealing and rupture) for a
particular application.
Need to be reliably designed (strict design specifications).
Practical/Technical Issues:
Winding angle issues
Rubber issues
Scaling issues
Composite material issues
All these issues are subtle (crude computation is useless).
Understanding is essential.

9. Continuous Casting of Steel (BHP/Australia, Voest)
Normally steel is cast into blocks (20cms thick) and then rolled; a
very expensive process.
In continuous steel casting a strand of molten steel moves
downwards under gravity and is cooled by water filled moulds.
The moulds are oscillated. (what amplitude, frequency?)
Flux facilitates the process (insulation, lubrication properties?)
molten steel
flux
a sin wt
5m
0.2m
water
cooled
solid
steel
V

10. Problems
The oscillating mould feeds flux into the gap.
Major problems arise if flux doesn’t fill the gap (thickness 1-2mm).
upstroke: flux drawn into the gap
flux flux
molten molten
water U water
steel steel U
solid solid
V V
downstroke: flux movement blocked
The essence: the molten steel acts as a pump; sucking flux into
the gap (upstroke) and then blocking the flow (downstroke).
Subtle!

11. Steel sheet casting BHP
In this process a thin sheet (1cm) of molten steel is poured onto a
rotating cylinder and a steel sheet is drawn off.
No rolling needed!
What radius is required to ensure solidification without spilling?
2mm
molten steel
solidified steel
3m water
The essence lies in the determination of the long molten tail.

12. Capacitor Dipping: DuPont
Silica ‘slabs’ (1mm by 2mm) are dip coated in metal.
Question: How to reduce mooning (surface tension)?
The essence lies in understanding corner effects; really important
for all industrial coating problems (Blue Steel, lens coatings).
Major understanding issues remain. Computationally difficult.

13. Rock Blast prevention: Thin Spray Liners. (S Africa
mining)
It has been observed that thin (1mm) elastically weak spray liners
help stabilise tunnel walls (prevent rock blasts).
Why?

14. Tunnel collapse: Crack Extension
The essence: The stress singularity at the the crack tip is reduced
by the presence of the liners:
1 1
τij = 1/2 (cos(θ/2), sin(θ/2)) → τij = γ (cos(γθ), sin(γθ))
r r
where r is the distance from the crack tip. γ → 0 for even weak
liners.
Thus cracks don’t extend.
Key stones don’t fall out.
Tunnels don’t collapse under the action of (seismic and
steady) loading.

15. Earthquakes and Mining (S Africa)
Can water draining into the deep (2000m) disused gold mines lead
to increased earthquakes?
The essence:
It takes about 1 year for water to enter available faults.
The effect is to increase the prevalence of earthquakes by
10-20% due to hydrostatic loading and (unexpectedly) the slip
angle range is increased.
Johannesburg look out

16. Concrete Problems
Dam construction: cooling using water pipes (network design)
Maturity (chemistry, cracking)
Concrete cancer (chemistry, cracking)

17. Icecream (Unilever UK)
Icecream is a really quite remarkable composite material: There are
solid ice crystals, water in a viscous sugary liquid, and fat uniformly
spread, and coexisting (liquid, solid, gaseous) in a delicious smooth
and stable product.
One can apply material science techniques to produce the ice
creams of the future (sintering, particle growth).

18. The problem is with stability/commerce
The essence: To make more money one needs to increase the
amount of air and water and decrease the fat content which
compromises stability/taste. Additives (surfactants) are used to
stabilise the ‘foam’.
Problems of interest:
Quality control (additives) under commercial/transport
conditions (excess crystal growth, bubbles bursting).
Designer ice creams. (would like to produce special shapes to
attract customers)
Chocolate coatings

19. Wine Labels (Australia, S Africa): a lubrication problem
How to prevent bubbles in the label?
Figure : Wrinkling of wine labels (Southcorp)

20. Soccer ball design (SAfrican Soccer Assn)
World Soccer Championships 2010 (Johannesburg (2000m))
Can one choose a soccer ball design to advantage S Africa?
Answer: Yes and they did.
It’s all about swerve: reverse and direct Magnus effect.

21. Johannesburg is 2000m above sea level (air density is 20%
below that of sea level.)
Forces acting on a movie ball are gravity and air drag.
Spin produces greater drag on one side of the ball producing
swerve (Magnus effect)
At low speeds there is a transition in the air flow at around
10-15 m/sec which leads to a reverse Magnus effect.
The effect is much greater if the ball is smoother and lighter
and stitching is minimal especially under low density
conditions. Perturbation procedures produce explicit results.
Yes nonlocal players had trouble playing in Johannesburg.