"Moving boundary problems will be studied in the context of two practically important settings: melting of ice in gas flow channels of Proton Exchange Membrane Fuel Cells and plaque build-up in arteries (atherosclerosis). The problems are related in that they involve a liquid layer flowing past the moving solid boundary. As well as being mathematically challenging they also all have immediate and important applications. During the project mathematical models will be developed and analysed for each of these problems. The work will begin with simple one-dimensional models. Approximate analytical solutions will be sought and compared, when possible, against existing exact and numerical solutions. The methods will then be extended to deal with the more complex two and three dimensional formulations where exact solutions are not available. This problem is complicated by the fluid flow which must be coupled to the thermal problem. The work will be linked with experimental research projects involving collaborators of the proposed researcher. These projects will be used to guide the analytical work and verify any results produced. This research proposal is viewed as the starting point for a much broader vision. In the long-term it is hoped to build up an industrial maths (IM) research group within the CRM, with a strong emphasis on heat transfer, fluid flow and phase changes. This group will then develop ties with local and international industry and act as a link between academia and industry."