"In this proposal, we consider the reconstruction of (multi-dimensional) heat transfer coefficients from both steady and transient surface temperature measurement input, and investigate a regularized boundary element method to this inverse problem in a framework that can ultimately be incorporated within industrial computational fluid dynamics codes. The research will be performed by the internationally incoming fellow (visitor, Professor Dinh Nho Hao, Hanoi Institute of Mathematics, Vietnam) in colaboration with the scientisty in charge (host, Professor D. Lesnic, Department of Applied Mathemnatics, University of Leeds, UK). The project combines the efforts of applied mathematicians in collaboration with engineers and industry to impact on solving fundamental inverse problems with practical applications in the reconstruction of heat transfer coefficients. The area of research that this project proposes is fascinating and challenging, with wide applications in the heat transfer and polymer industries, e.g. in cooling of hot steel or glass in fluids or gases, but previously with relatively little theoretical input and numerical computations, especially in higher dimensions. The current state of the art is still very much based on practical experience and technical know-how, despite recent advances in technology. The focus of the present study will be therefore to make progress on such inverse identifications of heat transfer coefficients, which can be time, space or temperature dependent, from all theoretical, numerical, experimental validation and design recommendation aspects. The techniques to be developed will be used to predict the efficiency of industrial devices, based on the inversion of real-life experimental data provided by several laboratories performing heat transfer experiments. This in turn will offer new and revolutionary suggestions for the design of such devices in order to optimize their performance."