BEM Utility for Simulation of Linear Thermal Bridges
Werner-Juszczuk Anna, Rynkowski Piotr
Białystok University of Technology
Faculty of Civil and Environmental Engineering, HVAC Department
E-mail: p.rynkowski@pb.edu.pl, a.juszczuk@pb.edu.pl
Received:
Received: 09 December 2015; revised: 03 January 2016; accepted: 29 January 2016; published online: 23 March 2016
DOI: 10.12921/cmst.2016.22.01.003
Abstract:
This paper aims to prove utility of the boundary element method for modelling 2D heat transfer in complex multi- regions, particularly in thermal bridges. It proposes BEM as an alternative method commonly applied in commercial software for simulation of temperature field and heat flux in thermal bridges, mesh methods (FEM, FDM).The BEM algorithm with Robin boundary condition is developed for modelling 2D heat transfer in complex multi-regions. Simulation is performed with the authoring Fortran program. The developed mathematical algorithm and computer program are validated according to standard EN ISO 10211:2007. Two examples of complex thermal bridges that commonly appears in house building are presented. Analysis of two reference cases, listed in standard ISO, confirms utility of the proposed BEM algorithm and Fortran program for simulation of linear thermal bridges. Conditions, quoted in standard ISO, are satisfied with models of a relatively small number of boundary elements. Performed validation constitutes the base for further development of BEM as an efficient method for modelling heat transfer in building components, and for the prospective application in commercial software.
Key words:
boundary element method, heat transfer, linear thermal bridges, multi-region
References:
[1] J. Mackerle, FEM and BEM in the context of information retrieval, Computers and Structures 80, 1595-1604 (2002).
[2] J.T. Katsikadelis, Boundary Elements. Theory and Applica- tions, Elsevier Science, Oxford 2002.
[3] C.A. Brebbia, J.C.F. Telles, and L.C. Wrobel, Boundary Ele- ment Techniques: Theory and Applications in Engineering, Springer-Verlag Berlin, Heidelberg 1984.
[4] M. Ramšak and L. Škerget, 3D multidomain BEM for solving the Laplace equation, Engineering Analysis with Boundary Elements 31, 528-538 (2007).
[5] M. Ramšak and L. Škerget, 3D multidomain BEM for a Pois- son equation, Engineering Analysis with Boundary Elements 33, 689-694 (2009).
[6] J. Chatterjee, D.P. Henry, F. Ma, and P.K. Banerjee, An ef- ficient BEM formulation for three-dimensional steady-state heat conduction analysis of composites, International Journal of Heat and Mass Transfer 51, 1439-1452 (2008).
[7] X.-W. Gao and J. Wang, Interface integral BEM for solv- ing multi-medium heat conduction problems, Engineering Analysis with Boundary Elements 33, 539-546 (2009).
[8] X.-W.GaoandT.G.Davies,3Dmulti-regionBEMwithcor- ners and edges, International Journal of Solids and Structures 37, 1549-1560 (2000).
[9] M.AkifAtalay,E.DilaraAydin,andM.Aydin,Multi-region heat conduction problems by boundary element method, In- ternational Journal of Heat and Mass Transfer 47, 1549-1553 (2004).
[10] E. Majchrzak, Boundary element method in heat transfer, Cze ̨stochowa University of Technology, Cze ̨stochowa 2001, in Polish.
[11] Q.XuandD-S.Yang,Solvingmulti-domain2Dheatconduc- tion problems by the least squares collocation method with RBF interpolation on virtual boundary, Engineering Analysis with Boundary Elements 42, 37-44 (2014).
[12] F.Branco,A.TadeuandN.Simo ̋es,Heatconductionacross double brick walls via BEM, Building and Environment 39, 51-58 (2004).
[13] A. Tadeu, J. Prata and N. Simo ̋es, Dynamic simulation of three-dimensional heat conduction through cylindrical in- clusions using a BEM model formulated in the frequency domain, Applied Mathematics and Computation 261, 397- 407 (2015).
[14] E. Majchrzak, B. Mochnacki and M. Jasin ́ski, Numerical modelling of bioheat transfer in multi layer skin tissue do- main subjected to a flash fire, Computational Fluid and Solid Mechanics II, 1766-1770 (2003).
[15] E. Majchrzak, J. Mendakiewicz and A. Piasecka-Belkhayat, Algorithm of mould thermal parameters identification in the system casting mould environment, Journal of Materials Pro- cessing Technology 164-165, 1544-1549 (2005).
[16] A.BenLarbi,Statisticalmodellingofheattransferforther- mal bridges of buildings, Energy and Buildings 37, 945-951 (2005).
[17] R.Yumrutas ̧,M.Ünsal,andM.Kanoðlu,Periodicsolution oftransientheatflowthroughmultilayerwallsandflatroofs by complex finite Fourier transform technique, Building and Environment 40, 1117-1125 (2005).
[18] G.MaoandG.Johannesson,Dynamiccalculationofthermal bridges, Energy and Buildings 26, 233-240 (1997).
[19] F. Asdrubali, G. Baldinelli, and F. Bianchi, A quantitative methodology to evaluate thermal bridges in buildings, Ap- plied Energy 97, 365-373 (2012).
[20] A. Tadeu, I. Simo ̋es, N. Simo ̋es, and J. Prata, Simulation of dynamic linear thermal bridges using a boundary element method model in the frequency domain, Energy and Build- ings 43, 3685-3695 (2011).
[21] EN ISO 10211:2007, Thermal bridges in building construc- tion – Heat flows and surface temperatures – Detailed calcu- lations.
[22] PN-EN 12831:2006, Heating systems in buildings – method for calculation of the design heat load, in Polish.
[23] PN-EN ISO 6946: Building components and building el- ements – Thermal resistance and thermal transmittance – Calculation method, in Polish.
This paper aims to prove utility of the boundary element method for modelling 2D heat transfer in complex multi- regions, particularly in thermal bridges. It proposes BEM as an alternative method commonly applied in commercial software for simulation of temperature field and heat flux in thermal bridges, mesh methods (FEM, FDM).The BEM algorithm with Robin boundary condition is developed for modelling 2D heat transfer in complex multi-regions. Simulation is performed with the authoring Fortran program. The developed mathematical algorithm and computer program are validated according to standard EN ISO 10211:2007. Two examples of complex thermal bridges that commonly appears in house building are presented. Analysis of two reference cases, listed in standard ISO, confirms utility of the proposed BEM algorithm and Fortran program for simulation of linear thermal bridges. Conditions, quoted in standard ISO, are satisfied with models of a relatively small number of boundary elements. Performed validation constitutes the base for further development of BEM as an efficient method for modelling heat transfer in building components, and for the prospective application in commercial software.
Key words:
boundary element method, heat transfer, linear thermal bridges, multi-region
References:
[1] J. Mackerle, FEM and BEM in the context of information retrieval, Computers and Structures 80, 1595-1604 (2002).
[2] J.T. Katsikadelis, Boundary Elements. Theory and Applica- tions, Elsevier Science, Oxford 2002.
[3] C.A. Brebbia, J.C.F. Telles, and L.C. Wrobel, Boundary Ele- ment Techniques: Theory and Applications in Engineering, Springer-Verlag Berlin, Heidelberg 1984.
[4] M. Ramšak and L. Škerget, 3D multidomain BEM for solving the Laplace equation, Engineering Analysis with Boundary Elements 31, 528-538 (2007).
[5] M. Ramšak and L. Škerget, 3D multidomain BEM for a Pois- son equation, Engineering Analysis with Boundary Elements 33, 689-694 (2009).
[6] J. Chatterjee, D.P. Henry, F. Ma, and P.K. Banerjee, An ef- ficient BEM formulation for three-dimensional steady-state heat conduction analysis of composites, International Journal of Heat and Mass Transfer 51, 1439-1452 (2008).
[7] X.-W. Gao and J. Wang, Interface integral BEM for solv- ing multi-medium heat conduction problems, Engineering Analysis with Boundary Elements 33, 539-546 (2009).
[8] X.-W.GaoandT.G.Davies,3Dmulti-regionBEMwithcor- ners and edges, International Journal of Solids and Structures 37, 1549-1560 (2000).
[9] M.AkifAtalay,E.DilaraAydin,andM.Aydin,Multi-region heat conduction problems by boundary element method, In- ternational Journal of Heat and Mass Transfer 47, 1549-1553 (2004).
[10] E. Majchrzak, Boundary element method in heat transfer, Cze ̨stochowa University of Technology, Cze ̨stochowa 2001, in Polish.
[11] Q.XuandD-S.Yang,Solvingmulti-domain2Dheatconduc- tion problems by the least squares collocation method with RBF interpolation on virtual boundary, Engineering Analysis with Boundary Elements 42, 37-44 (2014).
[12] F.Branco,A.TadeuandN.Simo ̋es,Heatconductionacross double brick walls via BEM, Building and Environment 39, 51-58 (2004).
[13] A. Tadeu, J. Prata and N. Simo ̋es, Dynamic simulation of three-dimensional heat conduction through cylindrical in- clusions using a BEM model formulated in the frequency domain, Applied Mathematics and Computation 261, 397- 407 (2015).
[14] E. Majchrzak, B. Mochnacki and M. Jasin ́ski, Numerical modelling of bioheat transfer in multi layer skin tissue do- main subjected to a flash fire, Computational Fluid and Solid Mechanics II, 1766-1770 (2003).
[15] E. Majchrzak, J. Mendakiewicz and A. Piasecka-Belkhayat, Algorithm of mould thermal parameters identification in the system casting mould environment, Journal of Materials Pro- cessing Technology 164-165, 1544-1549 (2005).
[16] A.BenLarbi,Statisticalmodellingofheattransferforther- mal bridges of buildings, Energy and Buildings 37, 945-951 (2005).
[17] R.Yumrutas ̧,M.Ünsal,andM.Kanoðlu,Periodicsolution oftransientheatflowthroughmultilayerwallsandflatroofs by complex finite Fourier transform technique, Building and Environment 40, 1117-1125 (2005).
[18] G.MaoandG.Johannesson,Dynamiccalculationofthermal bridges, Energy and Buildings 26, 233-240 (1997).
[19] F. Asdrubali, G. Baldinelli, and F. Bianchi, A quantitative methodology to evaluate thermal bridges in buildings, Ap- plied Energy 97, 365-373 (2012).
[20] A. Tadeu, I. Simo ̋es, N. Simo ̋es, and J. Prata, Simulation of dynamic linear thermal bridges using a boundary element method model in the frequency domain, Energy and Build- ings 43, 3685-3695 (2011).
[21] EN ISO 10211:2007, Thermal bridges in building construc- tion – Heat flows and surface temperatures – Detailed calcu- lations.
[22] PN-EN 12831:2006, Heating systems in buildings – method for calculation of the design heat load, in Polish.
[23] PN-EN ISO 6946: Building components and building el- ements – Thermal resistance and thermal transmittance – Calculation method, in Polish.
