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Figure 1: I'm the one with the woolly hat

Tim Myers

Associate Professor in Applied Mathematics, University of Cape Town and …

Visiting Professor, Division of Mathematical Sciences, Korean Advanced Institute of Science and Technology (KAIST)

Degrees: B.Sc. (Leicester, UK); Ph.D. (Leeds, UK)

Email: tim.myers@ymail.com

A good webpage is the sign of someone with too much time on their hands or a lackey to do the page for them.

I have neither, hence the following …

Research interests:

My research interests are basically any nice physical problem susceptible to mathematical modelling. Recently I have focussed on solidification and industrial mathematics.

The flow with solidification work started with a project with a consortium of aircraft companies (British Aerospace, Rolls-Royce, GKN-Westland Helicopters, Dunlop Aviation and Dera/Qinetiq). My lovely mathematical models now form part of the ICECREMO aircraft icing code (note if you are planning to design an aircraft do not mix this up with the Thai ice cream company of the same name). Recently I have been working on improved methods for the mathematical modeling of solidification/melting problems and also their application to the industrial process of contact melting. Contact melting denotes the type of melting that occurs when some force (usually gravity) squeezes out the melt layer; an easy example is to put a piece of ice on a warm surface. I am also interested in the modeling of rotating flows, with applications in the manufacture of CDs and computer disks as well as ice growth on rotating aircraft components.

Industrial maths problems I have looked at recently include: flow of mining slurries, beer bottle label wrinkling, the cooling of large concrete structures, injection moulding, lubricant behaviour during steel rolling, Czochralski crystal growth etc etc. The list continues ad infinitum or ad nauseam, my latin was never good. Perhaps one should instead consult the international study group website.

I have been involved in Industrial Maths meetings since working in Oxford. I was a main organizer of the 1996 European Study Group with Industry and am currently involved in organizing industrial maths meetings in South Africa (MISGSA) and Korea (IMI). I was also a main organizer of the first Canadian meeting (PIMS IPSW) and have been invited to meetings in India, the US and Australia. To spread the word and aid our younger, more innocent academics, I have also participated in Graduate Mathematical Modelling camps in Canada (GIMMC) and Europe.

In case I didn’t have enough to do, I am also on the Editorial Board of the MICS Journal (Mathematical in Industry Case Studies).

Anyway, I have work to do so rather than writing more I shall now attach a list of publications and past and present students …

Post-docs

1) Aug. 2008 – present G. Muchatibaya, UCT/AIMS.

2) Aug. 2006 - Jan. 2008 Dr S. Mitchell, UCT.

3) Sept. 2002 - Sept 2006 Dr J. Charpin, UCT.

4) Mar. 1999 - Mar. 2000 Dr S. Bandakhavai, Cranfield.

5) Jan. 1997 - Dec. 1999 Dr P. Hall, Cranfield.

Ph.D. students (soon to be working at a McDonalds near you)

1) Feb. 2006 - present, K. Colville Industrial applications of the finite element method.

2) April 2005 – May 2008, G. Muchatibaya Mathematical Modelling of Unsteady Contact Melting.

3) April 2002 - present, M.S. Tshehla The flow of variable viscosity fluids in a channel. Part-time PhD expected completion July 2008.

4) Sept. 2003 - April 2006, M. Lombe The behaviour of non-Newtonian rotating thin films.

5) March 2003 - Feb 2006, T. Brakel Fluid Mechanics and Solidification of the Czochralski InSb Crystal

Growth.

6) 1997-2002 J.P.F. Charpin Water flow on accreting ice surfaces.

7) 1996-2002 H.C.W. Anderson Stability effects of heat and mass transfer on thin liquid films.

8) 1995 (- 1996) C.J. Breward The mathematics of foams, main supervisor Dr J.R. Ockendon (FRS), com-

pleted Oct. 99.

Selected publications for a full list click here

1) Mitchell S.L. & Myers T.G. The application of standard and refined heat balance integral methods to one-dimensional Stefan problems. Submitted to SIAM Review August 2008.

2) Myers T.G. Optimizing the exponent in the Heat Balance and Refined Integral Methods. Submitted to Int. Comm. Heat & Mass Trans. July 2008.

3) Myers T.G. & Mitchell S.L. Application of the Heat Balance and Refined Integral Methods to the Korteweg-de Vries equation. To appear Thermal Science Vol. 2, 2009.

4) Myers T.G.& Charpin J.P.F. Modelling the temperature, maturity and moisture content in a drying concrete block. To appear Mathematics in Industry Case Studies, MICS Journal.

5) Mitchell S.L. & Myers T.G. A heat balance integral method for one-dimensional ablation of a finite block. J. Thermophys. & Heat Trans. 22(3): 508 -- 514, Jul.-Sept. 2008.

6) Myers T.G., Mitchell S.L. & Muchatibaya G. Unsteady contact melting of a rectangular cross-section material on a flat plate. To appear Phys. Fluids, October 2008.

7) Ha Y-S. , Kim Y-J. & Myers T.G. A comparison of numerical schemes for convection on a fourth-order diffusion equation. J. Comp. Phys., 227: 7246 – 7263 doi:10.1016/j.jcp.2008.04.007, 2008.

8) Mitchell S.L. & Myers T.G. Approximate solution methods for one-dimensional solidification from an incoming fluid. Applied Maths & Computing, 202(1): 311 -- 326, 2008. doi:10.1016/j.amc.2008.02.031, 2008.

9) Charpin J.P.F., Lombe M., Myers T.G. Spin coating of non-Newtonian fluids with a moving front. Phys Rev E76, DOI: 10.1103/PhysRevE.76.016312, 2007.

10) Myers T.G., Mitchell S.L., Muchatibaya G. & Myers M.Y. A cubic heat balance integral method for one-dimensional melting of a finite thickness layer. Int. J. Heat & Mass Trans. 50(25-26), 5305-5317, 2007. DOI: http://dx.doi.org/10.1016/j.ijheatmasstransfer.2007.06.014.

11) Balmforth N., Ghadge S. & Myers T.G. Surface tension driven fingering of a viscoplastic film. J.non-Newtonian Fluid Mech., 142: 143-149, paper no. JNNFM-D-06-00043, March 2007.

12) Myers T.G. & Lombe M. The importance of the Coriolis force on axisymmetric horizontal rotating thin film flows. Chem. Engng & Procng. 45: 90-98, 2006.

13) Myers T.G. The application of non-Newtonian models to thin film flow. Physical Rev. E, 72: 066302-1-11, 2005.

14) Charpin J.P.F. & Myers T.G. Modelling thin film flow with erosion, deposition and incoming rain. Advances in Water Resources, 28: 761-772, 2005.

15) Myers T.G. & Charpin J.P.F A mathematical model for atmospheric ice accretion and water flow on a cold surface. Int. J. Heat & Mass Trans. 47: 5483-5500, Dec. 2004.

16) Myers T.G. Unsteady laminar flow over a rough surface. J. Engng Math. 46 (2): 111-126, June 2003.

17) Myers T.G., Charpin J.P.F. & Chapman S.J. The flow and solidification of a thin fluid film on an arbitrary three-dimensional surface. Physics of Fluids 14(8) pp2788-2803 2002.

18) Myers T.G. Modelling laminar sheet flow over rough surfaces. Water Resources Research 38(11), 1230 (12 pages), doi:10.1029/2000WR000154, 2002.

19) Myers T.G., Charpin J.P.F. & Thompson C.P. Slowly accreting glaze ice due to supercooled droplets impacting on a cold substrate. Physics of Fluids 14(1) pp240-256 2002.

20) Myers T.G. Extension to the Messinger model for aircraft icing. AIAA J. 39(2) pp211-218, 2001.

21) Myers T.G. & Charpin J.P.F. The effect of the Coriolis force on axisymmetric rotating thin film flows. Int. J. Nonlinear Mech. 36(4) pp629-635 2001.

22) Myers T.G. & Hammond D.W. Ice and water film growth from incoming supercooled water droplets. Int. J. Heat Mass Trans. 42 pp2233-2242 1999.

23) Myers T.G. & Thompson C.P. Modelling the flow of water on aircraft in icing conditions. AIAA J. 36(6) pp1010-1013 1998.

24) Myers T.G. Thin films with high surface tension. SIAM Review 40(3) pp441-462 1998.

25) Myers T.G., editor. Proceedings of the 29th ESGI, OCIAM, Maths Inst., Oxford University, 1996.

26) Myers T.G., Aldis G.K. & Naili S. Ion induced deformation of soft tissue, Bull. Math. Biol. 57(1) pp77-98, 1995.

27) Hill J.M. & Myers T.G. The combined shear and compression of a rectangular rubber block. Z. angew. Math. Phys., 43, pp911-923, 1992.

28) Myers T.G. A series solution method for sharp asymmetric dry contact problems. J. Strain Anal. 26(1), pp39-45, 1991.

29) Myers T.G., Hall R.W. Savage M.D. & Gaskell P.H. The transition region of elastohydrodynamic lubrication. Proc. Roy. Soc. Series A, 432, pp467-479, 1991.

Industrial Reports

1. Investigation of ice growth on a rotating substrate, confidential report for GKN-Westland Helicopters, Dec. 1999 (written with J.P.F. Charpin).
2. A FLUENT-ICECREMO interface, confidential report for GKN-Westland Helicopters, Sept. 1999 (with J.P.F. Charpin).
3. Droplet migration and condensation in Teflonated porous media, confidential report for MITACS-MMSC Workshop, Simon Fraser University/U.B.C. May 1999 (with members of SFU/UBC Maths Depts.).
4. Water droplet transport through a turbofan, for Rolls-Royce Aug. 1998.
5. Combined ice growth and water flow, for ICECREMO Consortium (British Aerospace, Rolls Royce, Westland Helicopters, DERA), to develop a 3-D aircraft ice accretion code, May 1998.
6. Ice growth model, for ICECREMO Consortium, June 1997.
7. Water film model, for ICECREMO Consortium, Jan. 1997.
8. Coating Stability. Rexam Custom, Jan. 1996 (with various OCIAM members).
9. Die Coating. Rexam Custom, Oct. 1995 (with various OCIAM members).
10. Gold wire bonding, surge resistors, bubble and pinhole formation in dip coating and solder spreading. DuPont Electronics, June 1995 (with various OCIAM members).
11. Modelling Radiation from Nuclear Accidents. Royal Agricultural College, March 1995 (with various OCIAM members).
12. Cross-flow Ultrafiltration. Engineering Science, Oxford University, Feb. 1995 (with various OCIAM members).
13. Furrow formation in demisters. DuPont Electronics, Dec. 1994 (with various OCIAM members).
14. Furrowing in demister manufacture, dip coating of capacitors and sintering. DuPont Electronics, Nov. 1994 (with various OCIAM members).
15. Determining vertical on a moving ship. TSS (UK) Ltd, Sept. 1994 (with various OCIAM members).
16. The motion of bubbles in shear and extensional flow. Pilkington Research, Aug. 1994 (with various OCIAM members).
17. Screen printing, capacitor manufacture and sintering in the electronics industry. DuPont Electronics May 1994. Die swell in fibre manufacture. Courtaulds Fibres, Feb 1994 (with various OCIAM members).

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