×

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.

MSC:

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
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Dhatt, Gouri; Touzot, Gilbert; Lefrançois, Emmanuel, Finite eelement method, (2012), John Wiley & Sons · Zbl 1386.65002
[2] Veubeke, De; Fraeijs, B. M.; Hugge, M. A., Dual analysis for heat conduction problems by finite elements, Internat. J. Numer. Methods Engrg., 5, 1, 65-82, (1972) · Zbl 0251.65061
[3] Martin Kempeneers, (2006) Eléments finis statiquement admissibles et estimation d’erreur par analyse duale. Mémoire de thèse doctorat Université de Liège Faculté des Sciences Appliquées, Vol. 31.
[4] Kempeneers, Martin; Debongnie, Jean-François; Beckers, Pierre, Pure equilibrium tetrahedral finite elements for global error estimation by dual analysis, Internat. J. Numer. Methods Engrg., 81, 4, 513-536, (2010) · Zbl 1183.74284
[5] Debongnie, Jean-François; Zhong, H. G.; Beckers, Pierre, Dual analysis with general boundary conditions, Comput. Methods Appl. Mech. Engrg., 122, 1, 183-192, (1995) · Zbl 0851.73057
[6] Maunder, E. A.W.; Zhong, H. G.; Beckers, P., A posteriori error estimators related to equilibrium defaults of finite element solutions for elastostatic problems, Finite Elem. Anal. Des., 26, 3, 171-192, (1997) · Zbl 0917.73074
[7] Jean-François Debongnie, A general theory of dual error bounds by finite elements. Universite de liege, Faculte des sciences appliquees, Laboratoire de Methodes de fabrication (http://orbi.ulg.ac.be/bitstream/2268/16349/1/GeneralTheoryDualErrorBounds1983.pdf), Rapport LMF/D5 1983.
[8] Bramble, J. H.; Payne, L. E., A priori bounds in the first boundary value problem in elasticity, J. Res. Natl. Bur. Stand., 65, 269-276, (1961) · Zbl 0104.35102
[9] Beckers, Pierre; Beckers, Benoit, A 66 line heat transfer finite element code to highlight the dual approach, Comput. Math. Appl., 70, 10, 2401-2413, (2015)
[10] De Veubeke, Upper and lower bounds in matrix structural analysis (Upper and lower bounds in matrix structural analysis). 1964, 1964, pp. 165-201. · Zbl 0131.22903
[11] De Veubeke, B Fraeijs; Zienkiewicz, O. C., Strain-energy bounds in finite-element analysis by slab analogy, J. Strain Anal. Eng. Des., 2, 4, 265-271, (1967)
[12] Ascione, Fabrizio; Bianco, Nicola; De Masi, Rosa Francesca; Mauro, Gerardo Maria; Musto, Marilena; Vanoli, Giuseppe Peter, 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)
[13] Quinten, Julien; Feldheim, Véronique, Dynamic modelling of multidimensional thermal bridges in building envelopes: review of existing methods, application and new mixed method, Energy Build., 110, 284-293, (2016)
[14] Clarke, Joe A, Chapter 1 to 7, (Energy Simulation in Building Design, (2001), Routledge), 1-280
[15] Viot, H.; Sempey, A.; Pauly, M.; Mora, L., Comparison of different methods for calculating thermal bridges: application to wood-frame buildings, Build. Environ., 93, 339-348, (2015)
[16] Zalewski, Laurent; Lassue, Stéphane; Rousse, Daniel; Boukhalfa, Kamel, Experimental and numerical characterization of thermal bridges in prefabricated building walls, Energy Convers. Manage., 51, 12, 2869-2877, (2010)
[17] Aguilar, F.; Solano, J. P.; Vicente, P. G., Transient modeling of high-inertial thermal bridges in buildings using the equivalent thermal wall method, Appl. Therm. Eng., 67, 1, 370-377, (2014)
[18] Babuska, Ivo; Aziz, Abdul Kadir, Part 1 survey lectures on the mathematical foundations of the finite element method, (The Mathematical Foundations of the Finite Element Method with Applications To Partial Differential Equations, (1972), Academic Press New York and London), 3-360
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.