Dual analysis for heat exchange: application to thermal bridges. (English) Zbl 1419.65124

Summary: The research presented in this article is a contribution to the characterization of thermal dual analysis.
The aim of a dual analysis based on two complementary numerical methods is to calculate the stationary temperature field. The two methods are respectively the classical Kinetically Admissible (KA) finite element or temperature method, and the Statically Admissible (SA) flow method.
The originality of this work is twofold. First, it uses a flow approach (SA) in 2D and 3D that naturally respects flow conservation (in contrast to the KA method). Second, calculating the dissipation energy allows the exact solution of a problem to be enclosed, with the lower and upper bounds being calculated respectively by the KA and SA methods. Thermal bridges are areas of risk in the building walls, because they can give rise to uncontrolled increments in heat transfer. A number of studies have looked at thermal bridges, but much of the numerical code for building energy simulations uses heat transfer models based on one-dimensional heat flow analysis. F. Ascione et al. [“Experimental validation of a numerical code by thin film heat flux sensors for the resolution of thermal bridges in dynamic conditions”, Appl. Energy 124, 213–222 (2014; doi:10.1016/j.apenergy.2014.03.014)] showed that this can lead to unreliable results. The originality of this paper is to consider 2D and 3D thermal bridges using dual analysis with mesh sizes smaller than those used in conventional finite element approaches.


65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
80M10 Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer
80A20 Heat and mass transfer, heat flow (MSC2010)
35Q79 PDEs in connection with classical thermodynamics and heat transfer
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