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Thermal bridges impact hydrologic cycle fluxes, and lead to the transfer of energy from one side of a thermal bridge to the other. These impacts are of great importance to many engineering projects and infrastructures. This article reviews a large number of modelling tools and techniques used in the field of thermal bridges, including: local energy balance, isotropic or anisotropic heat conduction, thermodynamic properties of the media, local or distributed formulations, and different numerical techniques to solve the equations. In addition, a new model is developed and tested in an industrial context. Finally, important results are reported and some limitations of the available tools are pointed out. Abstract Thermal bridges can have a dramatic impact on the efficiency of many energy- and water-using industries. The authors review a large number of modelling tools and techniques used in the field of thermal bridges, including: local energy balance, isotropic or anisotropic heat conduction, thermodynamic properties of the media, local or distributed formulations, and different numerical techniques to solve the equations. This paper reviews these models and techniques, and more importantly, it proposes a new model which is implemented and tested in an industrial context. This new approach is different than the ones already available in the literature. In particular, it uses local energy balance, and the modelling is performed in a completely three-dimensional domain. All the boundary conditions and heat flow problems are solved by the direct method on the GPU. Then, the results obtained are compared to those obtained by the discrete method, and the numerical solution is validated by a few error indicators. Finally, the results obtained are compared to those obtained by other authors, using both, the discrete and the direct method. The article ends with some conclusions and recommendations for further research. Introduction Thermal bridges (TBs) are discontinuities in the heat flow across the interfaces of two media, which have different thermal conductivities. These interfaces are usually small, and are called thermal bridges, because the thickness of the discontinuity (thermal bridge) is small compared to the characteristic thicknesses of the different layers (Fig. 1). The total thickness of the discontinuity between two media is called thermal bridge thickness, TBTH, and the width of the thermal bridge is usually called thermal bridge width, TBW (Fig. 1). Fig. 1 Possible location of a thermal bridge (TB) in a three-dimensional domain. a TB with a single domain. b TB with

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