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Industrial applications of moving boundary problems

Final Report Summary - TMCRM (Industrial applications of moving boundary problems)

1. Work performed

A. Research – My work over the past four years has involved phase change, fluid flow and also more general industrial mathematics problems, such as the motion of a football through the air. Recently I have also moved into modeling nanotechnology. In total I have published 18 articles in ISI journals, with a number of conference proceedings, book and magazine chapters.

B. Organization – I have been involved in organizing various conferences. As main organizer: 27th European Study Group with Industry (CRM 2010); Mathematical modelling of blood flow and the baroreflex sytem (CRM 2010); Nanofluids (CRM 2011); Nanomath (CRM 2012). I was also on the scientific committee for the 2012 European Consortium for Mathematics in Industry (ECMI) conference held in Lund and have organized mini-symposia within various meetings. I am a full council member of ECMI.

C. Hosting visitors – Over the grant period various visitors have come to the CRM to collaborate, give seminars and short courses. These include Prof. James Hill (U. Adelaide), Prof. Sean Bohun (U. Ontario Inst. Tech.), Prof. Andrew Fowler (Oxford/Limerick), Prof. Mark McGuinness (U. Wellington), Prof. Geoff Mercer (Australian National U.), prof. Brian Wetton (U. British Columbia), Prof. Huaxiong Huang (York University), Prof. Lou Kondic & Prof. Linda Cummigs (NJIT), Dr Maria Chiricotto (U. Rome), Dr Sarah Mitchell & Dr Vincent Cregan (U. Limerick), Dr Jon Summers & Prof. Harvey Thompson (U. Leeds).

D. University activities – In addition to the short courses and seminars provided by my visitors, I have taught on undergraduate and graduate courses at the Universitat Politecnica de Catalunya. In 2012 I introduced a series of lectures entitled ‘An introduction to …’, where an applied maths topic is explained from the very basics to undergraduate students. We are looking to expand this initiative to include all final year undergraduate, postgraduate and staff members at UPC. I have advised 2 PhDs and 3 Masters theses during the period.

Currently I am the external examiner for the applied mathematics program at the University of Limerick, I have also examined PhDs and MScs in the UK, Ireland and Spain.

E. Dissemination – together with other IM group members I have authored 18 ISI papers, with a further 4 submitted. My work has also appeared in conference proceedings and books. I have given talks, at conferences and within university departments, throughout the world (Belgium, Ireland, Netherlands, South Africa, Spain, UK and US). I am currently invited as a keynote speaker to the 102nd European Study Group with Industry (to be held in Ireland in July) and Fluidos 2014 (Argentina, November).

2. Main results achieved

A. Research -- The most significant results include:

i. Heat transfer using nanofluids:
There exists a vast literature, involving experiments and theory, demonstrating that nanofluids (fluids containing nanoparticles) significantly enhance heat transfer. This is an extremely important issue since air cooling is no longer sufficient to cool high-power modern electronic devices and nanofluids have been viewed as a frontrunner in the race for new cooling technologies. Our work has shown that in fact nanofluids do not greatly enhance heat transfer (and may even reduce the efficiency). This is the first such theoretical finding. Whilst in direct contradiction with the majority of nanofluid literature, there is now growing experimental evidence to back our finding, including a recent benchmark study carried out at over 30 laboratories world-wide.
ii. Enhanced flow through carbon nanotubes:
This simple theory agrees well with a number of experiments and molecular dynamics studies and has an excellent citation rate for a mathematical paper.

iii. Generalisations to the Stefan problem:
A Stefan problem provides the mathematical description of an object changing phase, such as from solid to liquid. To simplify the analysis assumptions are often made, for example that the material properties (density, specific heat, conductivity) remain constant throughout the process. One of the phases is often neglected, for example by assuming the solid is at the phase change temperature. However, in certain situations these assumptions can lead to large errors. We have developed models for the melting of nanoparticles, where the phase change temperature decreases with the solid particle radius: with a variable phase change temperature the one-phase reduction loses energy. Our work has determined an energy conserving reduction and also demonstrated that the problems encountered by previous authors stem from an incorrect formulation of the model. Finally, we have looked into variable density models which introduce fluid motion into the governing equations (through advection in the heat equation and kinetic energy in the Stefan condition). These advances have all been published in high impact journals, we are also collating our new body of work to be submitted to a review journal such as Reviews of Modern Physics.

B. Re-integration into the local and European community – I have given seminars throughout Spain and Europe, have organized mini-symposia and conferences. I spent July 2013 visiting the mathematics department at the Vrije Universiteit, Amsterdam (and will return there this year). I am a full council member (representing Spain) of the European Consortium for Mathematics in Industry. I am also a member of the editorial board of the Elsevier journal Applied Mathematical Modelling.
I am external examiner for all applied maths courses at the University of Limerick and have examined 3 European PhD theses.

Further details on my work may be found through the CRM webpage

Publications are listed on Google Scholar