Born:         12th April 1941, Hope, Derbyshire.

Education: King Edward VII School, Sheffield.

                    The Queen's College, Oxford.

Degrees:     B.A.(Oxon) 2.I 1963, M.A.(Oxon) 1964.

                     Ph.D.(Hull) 1971.
 
 

Appointments:

1963-1964 Management trainee, S.Osborn & Co., Sheffield.

1964-1965 Assistant to Works Manager, S.Osborn & Co., Sheffield.

1965-1967 Research Fellow, Department of Applied Mathematics, Sheffield University.

1967-1985 Lecturer,
1985-1992 Senior Lecturer,
1992-1999 Reader in Applied Mathematics,
1999- Professor,   Department of Applied Mathematics,  University of Hull, HU7 7RX.
 
 

University Committees:

1973-1975: Elected representative to Board of the Science Faculty,

1975-1976: Member of Senate Committee that designed new degree in Mathematics and Management Sciences.

1975-1978: Warden of Reckitt Hall.

1976-1978: Member of University Court.

1976-1980: Co-ordinator for the Inter-Faculty Degree in Mathematics and Management Sciences.

1978-1979: Member of Senate Committee revising Admissions and Selection Procedures.

1980-1982: Elected member on Board of the Faculty of Science.

1984-1985: Elected as non-Senate member on the Committee to appoint the new Vice-Chancellor.

1984-1985: Secretary to the Faculty Committee formed to report on the provision of Numerical Analysis teaching.

1986-1988: Elected member on Senate.

1987-1988: Elected lecturer representative on University Council.

1987-1989: Chairman of the University Computation Committee.

1988-1989: Re-elected to Senate.

1988-1989 The Lecturer member on the Policy and Resources Committee.

1992-1994 Member of the Board of Studies.

1995-7 Chairman, Academic Approvals Committee,

1995-7 Academic Planning Committee,

1995-7 CMS Implementation Group,

1995-7 Joint Board (for Bishop Grosseteste College.)
 
 

Summary of research.

It is possible to classify my research into different subject areas and identify my contribution to those specific fields, but it seems preferable, because it emphasises my research philosophy, to describe my work with reference to the following categories:

(i) academic problems,

(ii) industrial research,

(iii) collaborative and interdisciplinary research.
 
 

(i) Academic problems.

My early research was undertaken at the University of Sheffield where I worked alongside Professor S.C.R.Dennis on problems of slow viscous flow past inclined plates and aerofoils.

After moving to Hull I started to research phase change phenomena, in particular laminar film condensation and Stefan problems. The work on laminar film condensation culminated in the so-called 'thin-film' and 'thick-film' models [1]. These were developed using perturbation techniques and verified by comparison with numerical solutions; the 'thick-film' model, which treats the vapour phase as a strong suction boundary-layer, is now accepted as the basis for most theoretical work on the subject. The work has subsequently been applied in a variety of different configurations [2,3,5,27] and the theory taught as part of perturbation analysis courses in other universities.

The early work on Stefan problems concerned the solidification of cylinders and spheres, with particular interest in the process towards the time of complete solidification. Here numerical solutions as the known singularity at the time of complete solidification is approached have been accepted for comparative purposes by subsequent researchers who have constructed singular perturbation solutions to this problem. My work on series solutions for Stefan problems [10] is a text book example - A.Aziz, 'Perturbation techniques', McGraw Hill.

Although much of my later work on melting and solidification has concerned industrial applications, I continued to research the fundamentals of the Stefan problems with specific interest in features introduced by internal heating. This developed from research into laser irradiation and though my involvement was stimulated by collaboration with the Applied Physics (University of Hull) Laser research group, my work was self-contained and devoted to the construction of a mathematical theory showing the importance of the so-called 'mushy zone' even for pure metals.

The two papers [9,10] concerning free convection between parallel walls were stimulated by curiosity in the concept of thermal runaway. I discovered some very unusual perturbation solutions, particularly in the neighbourhood of the critical Rayleigh numbers, which together with the numerical solutions show very interesting transitions between the various modes. This research has been taken up again recently because several features of the problem which were unresolved at the time of writing are now identifiable with chaotic development [44].
 
 

(ii) Modelling of industrial processes.

My research into industrial problems spans a period of almost thirty years and can be traced back to 1972 when the universities of Sheffield and Hull jointly launched an MSc in Industrial Applied Mathematics. A partial requirement for that degree was a dissertation based on a four month industrial project and while these projects were initially considered to be of peripheral interest to the industrialists, it soon became clear that the results could offer real benefits; thus we began to tackle problems which were crucial to the needs of industry. The small efforts undertaken as part of the MSc soon became more substantial, and after the MSc was discontinued in 1979 industry became keen to seek our help with direct contracts, research grants and CASE studentships. The industrial work undertaken in the department was formalised by the Senate in 1984 with the creation of the Centre for Industrial Applied Mathematics, CIAM. Most of the work I undertook as a member of CIAM has involved melting and/or solidification; firstly for the British Steel Company, then for the Ministry of Defence and more recently for a range of companies with interests in soldering. The MOD work developed into an ongoing programme to discover the optimal way of de-icing helicopter rotors with the use of electrothermal devices [23,27]; this was supported by three MOD contracts and a joint MOD/SERC research grant. Although the soldering research was deeply integrated with industrial developments, it is better described as interdisciplinary due the need for additional academic expertise in fundamental aspects of engineering – see following section.

(iii) Collaborative and interdisciplinary research.

My knowledge that mathematics can assist across such a wide variety of disciplines has led me to work with colleagues in many science and technology departments within the university. Frequently my contribution has been of insufficient magnitude to warrant my inclusion as co-author, occasionally the interaction has prompted a parallel line of research, e.g. [19,20], but in two major areas my contribution has been considerable and has led to fundamental advances; namely in research into heat transfer aspects of laser soldering with Professor D G Whitehead (Electronic Engineering) and in research into plant respiration with Professor W Armstrong (Applied Biology).

Mathematical modelling of the heat transfer process associated with laser soldering has advanced our understanding of the process to the extent that the Hull group became an acknowledged centre of excellence for this area of research. Early work involved CO₂ lasers and the award of a (ACME) SERC Research Grant for £99,810 reflected the value of this type of collaboration. Subsequently interest was diverted to the use of semiconductor diode lasers for which the group attracted an EPSRC grant for £175,000 (with matching industrial contributions). That program was completed in November 1995 and was reviewed in January 1996 when the ‘Scientific and/or technological merit’ was judged to be of a 4 quality with specific commendation for the mathematical contribution. It is worth noting the research attracted widespread industrial interest to the extent it spawned manufacturing initiatives in three separate UK companies, and that the theoretical modelling played a crucial role in establishing the viability of the processes.

The application of mathematical modelling in biology has been focused on problems of plant aeration; analytical studies and computer simulations of complex root systems have given insight to the possibilities of growth in anoxic conditions for a variety of geometries associated with different plants [21,22,24,26]. The research has also resolved disputes about the relative importance of convection and diffusion in deep water rice [29], provided a fluid dynamical model of aeration in Phragmites australis (which has important applications to biological sewage farming) [30], and provided a mathematical explanation for humidity induced pressurisation phenomena which is believed to be fundamental to plant aeration. The modelling used for these simulations is thought to be unique and has attracted the interest of researchers in many countries; it was also central to a recently completed project supported under the European IVth Framework Initiative. Moreover, the modelling techniques are not confined to the realms of plants since they are also recognised as being relevant to problems in animal physiology [41]

To a lesser extent, research into the atmospheric dispersal of pollen grains in a woodland canopy also shows the value of mathematical modelling in the natural sciences. Here three-dimensional convection and diffusion with discrete sources and sinks is used to simulate pollen production and entrapment in the trees [31]. The same work was subsequently adapted to study particulate emissions from tall chimneys.
 
 
 
 

Current/future research.

In line with suggestions made by respected external reviewers, following a visit to Hull in November 1998, research efforts were focussed on the biological work within a newly established Centre for Mathematical Modelling and Phytopneumatics.

One major project involves the development of a mathematical model that quantifies the potential for the methane transport from flooded soils to the atmosphere and the consequential impact on global warming. This is prompted by an assessment that over 40% of all the methane emission to the atmosphere comes from natural wetlands and rice fields. In the case of one very important plant, namely Phragmites australis, work is in hand to combine the extended study of humidity-induced pressurisation and associated convection [63] with the model for methane diffusion in the plant root and its rhizosphere [62]. In the case of rice, which is responsible for approximately 20% of the total methane load, a model incorporating various types of boundary layer flow past the submerged leaves (and their attendant gas films) is near completion, and there are plans to incorporate this and the general root model [62] into a mathematical simulation of a complete rice plant.

Research also continues into the fundamentals of gas transport in plants, including the analysis of a variety of non-linear respiration models in order to simulate experimental results that exhibit chaotic behaviour, and possibly explain the role of minute levels of haemoglobin that have been detected in plants.

In the knowledge that the dissemination of research plays a vital part in the advancement of science, and particularly in relation to extending an appreciation of the role played by mathematics, I will also continue to be involved in the wider debate that is necessary in order to promote the importance of mathematics in modern society.
 
 
 

Publications. (Listed in chronological order within each category; numbers refer to entire publication list)
 

(a1) Refereed articles in major journals:

1.    ‘Laminar Film Condensation in Forced Flows’, Quarterly Journal of Mechanics and Applied Mathematics, Vol 25, pp 125-152,1972.
        (with G Poots)

2     'Laminar Film Condensation due to Rotating Disc', Journ. of Eng. Math., Vol. 7, pp 63-73, (1973) (with P.C. Hudson and G. Poots)

3     'Similar solutions for laminar film condensation with adverse pressure gradients',  Journ. of Heat Transfer, Vol. 95, pp 268-270 (1973).

4     'Radiative transfer for a cylindrical beam scattered isotropically',  Quart. Journ. of Spectrosc. and Rad. Transfer, Vol. 14, pp 115-125, (1974)
        (with P.J. Foster, V.C.L. Hutson and R.L. Moss)

5     'Laminar film condensation on horizontal flat plates', Mech. Res. Comm, Vol. 2 pp 61-66 (1975)  (with G. Poots).

6     'The effect of a containing sleeve on solidification of a cylindrical bar', Mech. Res. Comm., Vol. 6(3), pp 129-133, (1979).

8     'The effect of shrinkage on the rate of solidification of a cylindrical ingot',  Int. Journ. Heat and Mass Transfer, Vol. 23, pp 433-436, (1980),
        (with N. Hobson).

9     'Combined natural and forced convection between parallel walls',  SIAM Journ. Appl. Math., Vol. 39, pp 372-384, (1980).

10     'On the use of series solutions in solidification problems', Mech. Res. Comm. Vol. 8(3), pp 169-174 (1981).

12     'Strongly implicit algorithm for use in three-dimensional natural convection studies',  Journ. Heat Transfer, Vol. 104, pp 218-219 (1982).

14     'Analytical and numerical solutions to two-dimensional moving interface problems with applications to the solidification of killed steel
        ingots',  Proc. R. Soc. Lond., A385, pp 313-343, (1983) (with H.J.Schulze, J.A.Howarth and G. Poots).

15     'Finite difference solutions of boundary-layer type equations',  Int. Journ. Computer Math., Vol. 14, pp 183-190, (1983).

16     'Combined natural and forced convection between parallel walls: developing flow at higher Rayleigh numbers',
        Int. J. Heat and Mass Transf., Vol. 27, No. 4, pp 611-621, (1984)  (with I.E. Friend).

18     'The Jigsaw Analogy',  IMA Journal Teaching Mathematics and its Applications, Vol. 4, No. 2, pp 45-46, 1985.

19     'Non-linear oscillations of a spherical particle in a rotating fluid',  Int. J. Non-linear Mechanics, Vol. 20, No.4, pp 261-271, 1985.

20     'High-intensity laser induced vaporisation without internal super heating', J. Applied Physics, Vol. 58, No. 8, pp 2943-2948, October, 1985.

21     'Root aeration in unsaturated soil: a multi-shelled mathematical model of oxygen diffusion and distribution with and without sectoral
        blocking of the diffusion path',   New Phytol. Vol. 100, pp 293-311, 1985. (with W. Armstrong).

23     'Mathematical model of an electrothermal de-icing system for helicopter rotors;
          Part 1: One-dimensional transient solutions',
          Math. Engng. Ind., Vol.1, No.2, pp. 123-154 (1987) (with G. Poots, A. Mousavi and R. Gent).

24     'Internal Aeration and the Development of Stelar Anoxia in Submerged Roots.  A multishelled mathematical model combining axial
         diffusion of oxygen in the cortex with radial oxygen losses to the stele, the wall layers and the rhizosphere',
          New Phytol., Vol. 105, pp 221-245, 1987. (with W. Armstrong).

25     'Similar Solutions of the Stefan Problem', Com. App. Num. Anal., Vol. 3, pp 251-254, 1987.  (with G. Poots)

26     'Laminar film condensation on the outside of a vertical circular cylinder; including  surface-tension effects:,
         Journal of Eng. Maths, Vol. 21 pp 23-31 (1987). (with G. Poots)

27     'Mathematical model of an electrothermal de-icing system for a helicopter rotor;
          Part 2. Two dimensional transient solutions',
          Math. Engng. Ind., Vol.2, No.1, pp. 19-49 (1988) (with G. Poots, A. Mousavi and R. Gent),

28     'On the relative importance of convective and diffusive gas-flows in plant aeration',
          New Phytologist, (1988), 110, pp 463-468. (with W. Armstrong, J. Armstrong and S. Justin).

29     ‘Phragmites australis - a critical appraisal of the ventilating pressure concept and an analysis of resistance to pressurised
          gas flow and gaseous diffusion in horizontal rhizomes'. New Phytologist, (1988), 110, 383-389. (with J. Armstrong and W. Armstrong).

30     'Modelling of dispersion and deposition of tree pollen within a forest canopy', Grana, 28, 129-139, 1989.
            (with J.R.Flenley & F.DiGiovanni)

37     'A note on the mathematical modelling of Pollen Dispersal and Deposition',
          Journal of Applied Meteorology, Vol. 29, No. 12, pp 1392-1357, Dec 1990.  (with F. Di-Giovanni.)

38     'Root adaptation to waterlogging', Aquatic Botany, 39, 57-73, 1991.   (With W. Armstrong, S.H.F.W.Justin & S. Lythe)

39     'A note on surface heat transfer coefficient',, International Journal of Heat and Mass Transfer, Vol.34, No.8, pp 2165-2166, 1991.

40     'Phragmites australis: Venturi- and humidity-induced pressure flows enhance rhizome aeration and rhizosphere oxidation',
          New Phytologist (1992), 120, 197-207  (with W.Armstrong & J.Armstrong)

44     'Singular asymptotic expansions for non-linear oscillator problems'   Int. J. of Non-linear Mechanics, Vol.28, No.1, pp 87-93, 1993.

45    Microelectrode and Modelling Study of Oxygen Distribution in Roots', Annals of Botany 74, 287-299, 1994,
        (with W.Armstrong, M.Strange, and S.Cringle)

54. ‘The application of semiconductor diode lasers to the soldering of electrronic components’
        J. Optical and Quantum Electronics, 27,(1995), pp 1303-1311  (with A R Fleming, R J Foster, J M Gilbert and D G Whitehead.)

55.    ‘Internal oxygen transport in plants’, Journal of Experimental Botany, 46: p 23 (1995)
          (with W.Armstrong , J.Armstrong, M.Darwent & M.Strange. )

57.     ‘Pressurised Aeration in Wetland Macrophytes: Some Theoretical Aspects of Humidity-Induced Convection and Thermal Transpiration’,
            Folia Geobot. Phytotax, 31: 25-36, 1996  (With J.Armstrong and W.Armstrong)

58.     ‘Pressurised ventilation in emergent macrophytes: the mechanism and mathematical modelling  of humidity-induced convection’,
            Aquatic Botany 54, 121-135 (1996)  (With W.Armstrong & J.Armstrong

59    ‘Pathways of aeration and the mechanisms and beneficial effects of humidity- and Venturi-induced convections in
         Phragmites australis (Cav.) Trin. Ex Steud’,   Aquatic Botany 54 (1996) 177-197    (With W.Armstrong & J.Armstrong)

60     ‘Pressurised aeration in wetland macrophytes: some theoretical aspects of humidity-induced convection and thermal transpiration.’
          In: Adaptation Strategies in Wetland Plants,  ed. by R.Brandle, H.Cizkova & J.Porkorny. Special Features in Vegetation Science 10,
          Opulus Press, Upsala, 31-42, 1996 (with J.Armstrong & W.Armstrong)

61     ‘The laser in manufacture - its use in the soldering of electronic assemblies’  Trans. Inst. Measurement and Control, Vol.21, No.1, 1999
          (with A.R.Fleming, J.M.Gilbert and D.G.Whitehead.)

62.     A Theoretical Analysis of the potential for localised heating due to a low power focussed laser,
          Math. Engng. Ind., Vol.8, No.1, pp. 65-88, 2000

63.    Oxygen Distribution in Wetland Plant Roots and Permeability Barriers to Gas-exchange with the Rhizosphere:
         a microelectrode and Modelling Study with Phragmites australis, Annals of Botany 86: 687-703, 2000

64.     A modelling approach to the analysis of pressure-flow in Phragmites stands, Aquat.Bot. 69/2-4 (2001), 269-291.
           (with J.Armstrong & W.Armstrong)

65      Mathematical modelling of methane transport by Phragmites: the potential for diffusion within the roots and rhizosphere.,
        Aquatic Botany 69/2-4, (2001)  293-312.  (with J.Armstrong & W.Armstrong)
 
 

(a2) Refereed articles in teaching journals:

7     'Dimensional Analysis Applied to Modelling',   Journ. of Math. Modelling, Vol. 2, No. 2, pp 36-46, (1979).

13     'How mathematical modelling can be used as a source of inspiration',
          Int. Journ. Math. Educ. Sci. Technology, Vol. 13(2), pp 125-132, (1982).
 

(a3) Refereed articles in Trade Journals.

42     'Semiconductor Diodes for Laser Soldering',  Journal of the International Society for Hybrid Microelectronics, No.28, p.4, May 1992.
          (With: D.G.Whitehead & A.V.Polijanczuk).
 
 

(b) Refereed articles presented at conferences and subsequently published.

11     'Numerical treatment of non-linear latent heat boundary conditions at moving interfaces in genuine two-dimensional
          solidification problems',
          Proceedings of NASA Conference on Numerical Boundary Condition Procedures, pp 39-388, NASA publ. 2201, (Oct. 1981).

17     'Laser heating of a solid with change of phase',
        Proc. ASME Heat Transf. Conf. Paper 8A-Ht-6, Niagara 1984.

22     'A multi-shelled approach to root-aeration models',
          In Plant Life under Oxygen Stress: 2nd International Symposium on Plant Anaerobiosis.
          Moscow (UNESCO-Academy of Sciences, USSR.) Collected abstracts pp. 24-25 (1985).
          (with W. Armstrong, S.H.F.W.Justin & S.Lythe).

34     ‘Measurement and modelling of oxygen release from roots of Phragmites australis’,
          in : The Use of Constructed Wetlands in Water Pollution Control, Eds. P F Cooper & B C Findlater, Pergmanon Press, pp 41-52, 1990
          (with W. Armstrong & J. Armstrong)

35     ‘Theoretical modelling of laser soldering’,  HTD-Vol. 143, pp 39-45, Proc. ASME WAGM Dallas, Nov. 1990.
           (with: D G Whitehead and A V Polijanczuk.)

36.     ’Reflow soldering by laser’,  HTD-Vol. 143, pp 47-56, Proc. ASME WAGM Dallas, Nov. 1990.
          (with: D G Whitehead and A V Polijanczuk)

43.     'The application of Solid State Laser Diodes to Soldering',  25th ISATA Silver Jubilee Conference, Florence, June 1992
          (with: D G Whitehead and A V Polijanczuk)

45     ‘Thermal modelling of solder joint formation',
          IEE Conference on "CAD tools for thermal management", Savoy Place, London Feb. 1993.  Digest No. 1993/027
          (with: D G Whitehead and A V Polijanczuk)

47     'Microelectrode and Modelling Studies of Oxygen Distribution in Roots',  XV International Botanical Congress, Tokyo, August 1993.
         (with W.Armstrong and S.Cringle)

48     'An Automated Pick-Place-Laser Soldering Process for Electronics Assembly',
        Proc.ECTC Washington, pp 1079-81, May 1994. (ISBN 0-7803-0914-6),
        (with A.R.Fleming, R.J.Foster, J.M.Gilbert, A.V.Polijanczuk and D.G.Whitehead.)

49 'Thermal Modelling Aspects of Diode Laser Soldering',  Proc 27th ISAATA Conference, pp 311-318, AAchen, Germany, November 1994.

50     'Lser Soldering - A Thermal Modelling Approach',    Proc. 1994 International Symposium on Microelectronics, pp 613-618,
        Boston, USA, November 1994. (ISBN 0-930815-41-6)
        (with A.R.Fleming, R.J.Foster, J.M.Gilbert, A.V.Polijanczuk and D.G.Whitehead.)

56     ‘The laser in manufacture - its use in the soldering of electronic component assemblies’
          Proc AMPST96 Symposium, Bradford UK, 26-27th March 1996; pages 391-397.
          ISBN 0 85298 989 X (with A.R.Fleming, R.J.Foster, J.M.Gilbert and D.G.Whitehead.)
 
 

(c) Refereed chapters in books.

31 ‘Convective gas-flows in wetland plant aeration’,  in Plant Life under Oxygen Deprivation,
        Ed. by M.B.Jackson, D.D.Davies & H.Lambers.  S.P.B. Academic Publishing hv., The Hague. pp 283-302, 1990.
        (with: Armstrong,W., Armstrong,J. & Justin,S.H.F.W.)

32     ‘Modelling, and other aspects of root aeration by diffusion.’
        in Plant Life under Oxygen Deprivation, Ed. by M.B.Jackson, D.D.Davies & H.Lambers.
        S.P.B. Academic Publishing hv., The Hague, pp 267-282, 1990.  (with: Armstrong,W., Justin,S.H.F.W. & Lythe,S.)

41     'The modelling of convection and diffusion-driven aeration in plants'
          Society for Experimental Biology Seminar Series 51, Oxygen Transport in Biological Systems.
          Ed. S.Egginton & H.F.Ross, Cambridge University Press. 1992, pp253-293. ISBN 0-521-41488-1 (With W.Armstrong)
 

(d) Proceedings of conferences (non-reviewed papers).

33     ‘Developments in Laser Soldering for Electronincs Assembly’
          Conference: NEPCON Europe 1990,   National Exhibition Centre, Birmingham, 20-22nd March 1990.
          with: D G Whitehead and A V Polijanczuk

52     'The use of lasers for the soldering of high density interconnects',
         Proc. of "Interconnection Technology" Conference, IEE, November 1994.
         (with A.R.Fleming, R.J.Foster, J.M.Gilbert, and D.G.Whitehead.) [Invited paper]
 

Papers in Hull University Series of 'Mathematical Research Reports'

H1     Theoretical modelling of laser soldering', Vol.IV (1991), No.18. (partially published as [42])

H2     'Singular asymptotic expansions for non-linear oscillator problems', Vol. V (1992), No. 7.

H3     'Heat transfer Analysis of a Laser Irradiated Disc of Solder Mounted on a Copper Disc and FR4
          substrate', Vol.V (1992), No.11 (with D.G.Whitehead and A.V.Polijanczuk)

H4.     'Numerical algorithms for solving radially symmetric heat transfer associated with laser heating
            and melting of a solder disc.', Vol.V (1992), No.12.

H5     'Time dependent heat transfer coefficients', Vol.V (1992), No.13.

H6     'Mathematical modelling: in Plant Biology, Laser Soldering etc',
           Proceedings of Teaching Conference - July 1993.

H7     ‘A Theoretical Analysis of Laser Soldering’. Vol VIII (1995) No.19, ISBN: 085958 924 2
           (with A.R.Fleming, R.J.Foster, J.M.Gilbert and D.G.Whitehead)
 
 

SOLDAT: 'Soldering with Advanced Technology' Report:

E1/53     'Measurements of the Optical Properties of some Common Materials used in Laser Soldering', SOLDAT Report No.108 (199)
            (with A.V.Polijanczuk and D.G.Whitehead.)

Manuscripts submitted or in preparation:

‘Root aeration: a multicylindrical model of radial oxygen diffusion incorporating concentration-dependent respiration’

‘Humidity-induced pressurisation and convection through a micro-porous membrane’

‘A mathematical model of humidity-induced pressurisation and mass transport in Phragmites australis’

'A mathematical model for the respiration of a completely submerged rice plant: the potential for waterlogging',
 

Research Grants and Contracts.

(i)     Mathematical and computer models of electro-thermal deicing systems for a helicopter rotor.
        MOD contract over period 1984-86. (with G.Poots)                                                                                 £39,500

(ii)     Mathematical and computer models of electrothermal de-icing systems for a helicopter rotor
          MOD contract over 6 months January-June 1988, (with G.Poots)                                                       £16,500

(iii)      The aeration of amphibious plants. (with Dept. of Applied Biology, University of Hull)
            NERC grant 1/3/86 - 28/2/89                                                                                                                     £39,980

(v)     Finite Difference Solutions of Free Surface Jet Flow.    NATO Grant 1985-88                                   £3,200

(vi)     Mathematical and computer models of electrothermal de-icing systems for a helicopter rotor
            - phase III.   MOD contract over 6 months October 1988 - March 1989.   (with G.Poots)              £16,500

(vii)     Laser soldering.   SERC Research Grant: 1st June 1989 - 31st May 1992.
            (with D.G.Whitehead - Electronic Engineering, Hull University)                                                       £99,805

(viii)     NATO Collaborative Research Grant CRG/910093
            ‘Connection between Non-linear Oscillations, Bifurcation Theory and Chaos’,                             £2,650

(ix)         Laser Soldering. with Professor D G Whitehead, Electronic Engineering, University of Hull.
              SERC (ACME) research grant GR/H89951:   1st November 1992 to 31st October 1995.                £175,799

(x)         EUREED II - Dynamics & stability of reed-dominated ecosysytems in relation to major
              environmental factors subject to global & regional anthrogenically induced changes.
              with Professor W Armstrong and Dr J Armstrong: - 1996-1999
              IVth Framework grant of 140458ECU, (converted at rate 1.25ECU/£)                                             £112,366
 
 

Journal refereeing:

The International Journal for Heat and Mass Transfer.

The International Journal of Mathematical Engineering with Industrial Applications.

The International Journal of Computer Mathematics.

The ASME Journal of Heat Transfer.

Proceedings of the Institute of Mechanical Engineers.

The Journal of Atmospheric Physics.

The Journal of Chemical Technology and Biotechnology.

1996 Editorial Board: The International Journal of Mathematical Engineering with Industrial Applications. 1
 
 

Teaching

I have presented a wide variety of undergraduate and postgraduate courses to students reading for mathematics degrees. For many I concentrated on service teaching to Engineers, Physicists and Chemists, both in the presentation and course development. As a member of a Senate committee I helped to design the Mathematics and Management Sciences Degree and subsequently was responsible for co-ordinating the teaching of the Mathematics, Operational Research, Economics and Accounting. In recent years I have been at the forefront of using the university computing facilities to aid the teaching and learning of mathematics; in particular I assumed responsibility for a novel first year Computation Course for Honours Mathematics students and designed a module that includes the teaching of basic programming skills (using MathCAD), an appreciation of the use of computer packages and elementary numerical analysis. Most recently, I designed a final year course, for the new Sports Science and Mathematics students, that includes mathematical models of numerous sporting phenomena. The flavour has been strongly influenced by my research work in which the power of numerical analysis and computer simulation have proved to be extremely valuable when solving problems in the real world. My interest in teaching is partly evidenced by two publications related to teaching of mathematics [7,13].

My teaching has not been confined to the campus; I have given many mathematical talks in schools, at education conferences and in careers or admissions conventions. The theme has been consistent - showing why mathematics is so important by using appropriate illustrations; this is another manifestation of the philosophy which has been outlines at the end of the section devoted to ‘Future Research’.
 
 

Post-graduate supervision:

R.L. Moss,     Theoretical Study of Radiative Heat Transfer Between Parallel Plates, in the case of Axial-Symmetry. M.Sc. Thesis 1972.

N.R.Strachan Effects of a Containing Sleeve on the Solidification of a Cylindrical Rod. M.Sc. Thesis 1976

N.Hobson     A Theoretical Investigation into the Solidification of a Cylindrical Steel Ingot. M.Sc. Thesis 1977.

I.E.Friend     Some aspects of forced and natural convection Ph.D. Thesis 1982.

H.J.Schulze   Analytical and numerical solutions to twin dimensional moving interface problems with applications to the
                       solidification of killed steel ingots.   Ph.D. Thesis 1982. (Co-supervisor with G.Poots)

F.DiGiovanni    The mathematical modelling of long-term tree-pollen deposition in mixed woodlands
                            PhD Thesis 1989. (Joint supervisor with J.R.Flenley, Geography Department)

M.Strange        ‘Oxygen stress in roots: development, distribution, consequences and modelling' .MSc Thesis 1992,

M.Darwent       ‘Oxygen stress in roots: development, distribution, consequences and modelling' .PhD Thesis - 1997,
                            (AFRC research studentship).