{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T16:51:42Z","timestamp":1773161502923,"version":"3.50.1"},"reference-count":55,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2019,12,3]],"date-time":"2019-12-03T00:00:00Z","timestamp":1575331200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Energies"],"abstract":"<jats:p>This paper sets out a three-dimensional (3D) boundary element method (BEM) formulation in the frequency domain to simulate heat transfer through a point thermal bridge (PTB) at a corner in a building envelope. The main purpose was to quantify the dynamic effect of a geometrical PTB in terms of distribution of temperatures and heat fluxes, which is useful for evaluating moisture condensation risk. The numerical model is first validated experimentally using a hot box to measure the dynamic heat behavior of a 3D timber building corner. The proposed model is then used to study the dynamic thermal bridging effect in the vicinity of a 3D concrete corner. Given the importance of the risk of condensation, this study looks at the influence of an insulating material and its position on the temperature and heat flux distribution through the PTB under steady state and dynamic conditions.<\/jats:p>","DOI":"10.3390\/en12234595","type":"journal-article","created":{"date-parts":[[2019,12,3]],"date-time":"2019-12-03T04:58:39Z","timestamp":1575349119000},"page":"4595","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["3D Dynamic Simulation of Heat Conduction through a Building Corner Using a BEM Model in the Frequency Domain"],"prefix":"10.3390","volume":"12","author":[{"given":"Nuno","family":"Sim\u00f5es","sequence":"first","affiliation":[{"name":"ITeCons\u2014Institute for Research and Technological Development in Construction, Energy, Environment and Sustainability; Rua Pedro Hispano, 3030\u2013289 Coimbra, Portugal"},{"name":"ADAI\u2014LAETA, Department of Civil Engineering, FCTUC, University of Coimbra; P\u00f3lo II, Rua Lu\u00eds Reis Santos, 3030\u2013788 Coimbra, Portugal"}]},{"given":"Joana","family":"Prata","sequence":"additional","affiliation":[{"name":"ITeCons\u2014Institute for Research and Technological Development in Construction, Energy, Environment and Sustainability; Rua Pedro Hispano, 3030\u2013289 Coimbra, Portugal"},{"name":"ADAI\u2014LAETA, Department of Civil Engineering, FCTUC, University of Coimbra; P\u00f3lo II, Rua Lu\u00eds Reis Santos, 3030\u2013788 Coimbra, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2535-8458","authenticated-orcid":false,"given":"Ant\u00f3nio","family":"Tadeu","sequence":"additional","affiliation":[{"name":"ITeCons\u2014Institute for Research and Technological Development in Construction, Energy, Environment and Sustainability; Rua Pedro Hispano, 3030\u2013289 Coimbra, Portugal"},{"name":"ADAI\u2014LAETA, Department of Civil Engineering, FCTUC, University of Coimbra; P\u00f3lo II, Rua Lu\u00eds Reis Santos, 3030\u2013788 Coimbra, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,3]]},"reference":[{"key":"ref_1","unstructured":"International Organization for Standardization (2007). Thermal Bridges in Building Construction\u2014Heat Flows and Surface Temperatures\u2014Detailed Calculations, ISO."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/j.apenergy.2013.02.045","article-title":"A building thermal bridges sensitivity analysis","volume":"107","author":"Capozzoli","year":"2013","journal-title":"Appl. Energy"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2083","DOI":"10.1016\/j.enbuild.2008.06.006","article-title":"The impact of thermal bridges on the energy demand of buildings with double brick wall constructions","volume":"40","author":"Theodosiou","year":"2008","journal-title":"Energy Build."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"681","DOI":"10.1016\/S0017-9310(97)00229-9","article-title":"Heat Loss and moisture condensation for wall corners of buildings","volume":"41","author":"Krarti","year":"1998","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"4862","DOI":"10.1016\/j.ijheatmasstransfer.2009.05.026","article-title":"A building corner model for hygrothermal performance and mould growth risk analyses","volume":"52","author":"Santos","year":"2009","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/j.icheatmasstransfer.2014.02.018","article-title":"Hygrothermal bridge effects on the performance of buildings","volume":"53","author":"Santos","year":"2014","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/j.icheatmasstransfer.2015.12.015","article-title":"Predicting building\u2019s corners hygrothermal behavior by using a Fuzzy inference system combined with clustering and Kalman filter","volume":"71","author":"Freire","year":"2016","journal-title":"Int. Commun. Heat Mass Transf."},{"key":"ref_8","unstructured":"Erhorn, H., Erhorn-Klutting, H., Citterio, M., Cocco, M., Orshoven, D., Tilmans, A., Schild, P., Bloem, P., Thomsen, K.E., and Rose, J. (2019, October 20). Available online: https:\/\/www.buildup.eu\/en\/node\/8832."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.apenergy.2015.01.084","article-title":"Thermal inertia and energy efficiency\u2014Parametric simulation assessment on a calibrated case study","volume":"145","author":"Aste","year":"2015","journal-title":"Appl. Energy"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1016\/S0378-7788(00)00128-6","article-title":"Effect of 2D modelling of thermal bridges on the energy performance of buildings: Numerical application on the Matisse apartment","volume":"33","author":"Ollivier","year":"2001","journal-title":"Energy Build."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2236","DOI":"10.1016\/j.enbuild.2008.07.003","article-title":"Dynamical building simulation: A low order model for thermal bridges losses","volume":"40","author":"Gao","year":"2008","journal-title":"Energy Build."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1016\/S0378-7788(01)00122-0","article-title":"Multi-dimensional heat transfer through complex building envelope assemblies in hourly energy simulation programs","volume":"34","author":"Kosny","year":"2002","journal-title":"Energy Build."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1016\/j.buildenv.2015.07.017","article-title":"Comparison of different methods for calculating thermal bridges: Application to wood-frame buildings","volume":"93","author":"Viot","year":"2015","journal-title":"Build. Environ."},{"key":"ref_14","first-page":"249","article-title":"Equivalent wall as a dynamic model of a complex thermal structure","volume":"20","author":"Kossecka","year":"1997","journal-title":"J. Therm. Insul. Build. Envel."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"704","DOI":"10.1016\/j.enbuild.2012.08.024","article-title":"Equivalent wall method for dynamic characterisation of thermal bridges","volume":"55","author":"Martin","year":"2012","journal-title":"Energy Build."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1016\/j.applthermaleng.2014.03.058","article-title":"Transient modeling of high-inertial thermal bridges in buildings using the equivalent thermal wall method","volume":"67","author":"Aguilar","year":"2014","journal-title":"Appl. Therm. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1016\/j.enbuild.2015.07.023","article-title":"Dynamic effect of thermal bridges on the energy performance of a low-rise residential buildings","volume":"105","author":"Ge","year":"2015","journal-title":"Energy Build."},{"key":"ref_18","unstructured":"Bonneau, D., Rongere, F.X., Covalet, D., and Gautier, B. (1993, January 16\u201318). Clim 2000: Modular software for energy simulation in buildings. Proceedings of the IBPSA Third International Conference on Building Simulation\u201993, Adelaide, Australia."},{"key":"ref_19","first-page":"16687","article-title":"A simplified methodology for evaluating the impact of point thermal bridges on the high-energy performance of a passive house","volume":"2","author":"Ramanauskas","year":"2015","journal-title":"Sustainability"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1016\/j.proenv.2017.03.121","article-title":"Analysis of the thermal bridging effect on ventilated facades","volume":"38","author":"Theodosiou","year":"2017","journal-title":"Procedia Environ. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1016\/j.enbuild.2015.10.037","article-title":"Thermal bridging analysis on cladding systems for building facades","volume":"109","author":"Theodosiou","year":"2015","journal-title":"Energy Build."},{"key":"ref_22","unstructured":"International Organization for Standardization (2007). Thermal Bridges in Building Construction\u2014Linear Thermal Transmittance\u2014Simplified Methods and Default Values, ISO."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.buildenv.2017.08.041","article-title":"Study on moisture condensation on the interior surface of buildings in high humidity climate","volume":"125","author":"You","year":"2017","journal-title":"Build. Environ."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/j.apenergy.2014.03.014","article-title":"Experimental validation of a numerical code by thin film heat flux sensors for the resolution of thermal bridges in dynamic conditions","volume":"124","author":"Ascione","year":"2014","journal-title":"Appl. Energy"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"3685","DOI":"10.1016\/j.enbuild.2011.10.001","article-title":"Simulation of dynamic linear thermal bridges using a BEM model in frequency domain","volume":"43","author":"Tadeu","year":"2011","journal-title":"Energy Build."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1130","DOI":"10.1016\/j.enganabound.2005.06.002","article-title":"Fundamental solutions for transient heat transfer by conduction and convection in an unbounded, half-space, slab and layered media in the frequency domain","volume":"29","author":"Tadeu","year":"2005","journal-title":"Eng. Anal. Bound. Elem."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1016\/j.enbuild.2012.03.005","article-title":"Thermal delay simulation in multilayer systems using analytical solutions","volume":"49","author":"Tadeu","year":"2012","journal-title":"Energy Build."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Sim\u00f5es, N., Prata, J., and Tadeu, A. (2014, January 24\u201326). Contribution of linear thermal bridges to the overall thermal performance of buildings\u2019 envelope\u2014Dynamic analysis. Proceedings of the 5th International Conference on Harmonisation between Architecture and Nature (Eco-Architecture 2014), Certosa di Pontignano, Siena, Italy.","DOI":"10.2495\/ARC140281"},{"key":"ref_29","unstructured":"Mao, G. (1995). Thermal Bridges: From Research to Applications. Arbetsrapport 1995:1. Tekn. Lic.. [Ph.D. Thesis, Department of Mechanical Engineering of the Faculty of Sciences and Technology of the University of Coimbra]."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/0378-7788(94)00907-2","article-title":"Effect of interior heat transfer coefficients on thermal dynamics and energy consumption","volume":"22","author":"Kalema","year":"1995","journal-title":"Energy Build."},{"key":"ref_31","first-page":"1997","article-title":"Laboratory Measurements and Modelling of the Dynamic Thermal Performance of a Thermal Bridge","volume":"1","author":"Mao","year":"1998","journal-title":"J. Build. Phys."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1016\/j.apenergy.2011.12.054","article-title":"A quantitative methodology to evaluate thermal bridges in buildings","volume":"97","author":"Asdrubali","year":"2012","journal-title":"Appl. Energy"},{"key":"ref_33","unstructured":"International Organization for Standardization (1994). Thermal Insulation\u2014Determination of Steady State Thermal Transmission Properties\u2014Calibrated and Guarded Hot Box, ISO."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1016\/j.enbuild.2017.09.073","article-title":"Heat transfer measurements of a Linear Thermal Bridge in a wooden building corner","volume":"158C","author":"Prata","year":"2018","journal-title":"Energy Build."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1016\/j.enbuild.2009.10.015","article-title":"Methodology for the calculation of response factors through experimental tests and validation with simulation","volume":"42","author":"Flores","year":"2010","journal-title":"Energy Build."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/j.enbuild.2012.03.028","article-title":"Analysis of a thermal bridge in a guarded hot box testing facility","volume":"50","author":"Martin","year":"2012","journal-title":"Energy Build."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"837","DOI":"10.1016\/j.conbuildmat.2012.09.053","article-title":"Hot box measurements of pumice aggregate concrete hollow block walls","volume":"38","author":"Kus","year":"2013","journal-title":"Constr. Build. Mater."},{"key":"ref_38","unstructured":"Gustavsen, A., Goudey, H., Arasteh, D., Uvsl\u00f8kk, S., Talev, G., Jelle, B.P., and Kohler, C. (2010, January 5\u20139). Experimental and Numerical Examination of the Thermal Transmittance of High Performance Window Frames. Proceedings of the XI International Conference Thermal Performance of the Exterior Envelopes of Whole Buildings, Clearwater, FL, USA."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1016\/j.enbuild.2013.01.028","article-title":"Influence of cavities geometric and emissivity properties on the overall thermal performance of aluminium frames for windows","volume":"60","author":"Asdrubali","year":"2013","journal-title":"Energy Build."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"647038","DOI":"10.1155\/2012\/647038","article-title":"Closed form integration of singular and hypersingular integrals in 3D BEM formulations for heat conduction","volume":"2012","author":"Tadeu","year":"2012","journal-title":"Math. Probl. Eng."},{"key":"ref_41","first-page":"397","article-title":"Dynamic simulation of three-dimensional heat conduction through cylindrical inclusions using a BEM model formulated in the frequency domain","volume":"261","author":"Tadeu","year":"2015","journal-title":"Appl. Math. Comput."},{"key":"ref_42","unstructured":"International Organization for Standardization (2017). Energy Performance of Buildings\u2014Indicators for Partial EPB Requirements Related to Thermal Energy Balance and Fabric Features\u2014Part 1: Overview of Options, ISO."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1016\/j.buildenv.2018.06.009","article-title":"Simulation of heat and moisture flow through walls covered with uncoated medium density expanded cork","volume":"142","author":"Tadeu","year":"2018","journal-title":"Build. Environ."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"843","DOI":"10.1016\/S0017-9310(81)80007-5","article-title":"A formulation of the Boundary Element Method for axisymmetric transient heat conduction","volume":"24","author":"Wrobel","year":"1981","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1016\/S0955-7997(99)00016-8","article-title":"Closed-form integration of singular terms for constant, linear and quadratic boundary elements. Part I. SH wave propagation","volume":"23","author":"Tadeu","year":"1999","journal-title":"Eng. Anal. Bound. Elem."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1061\/(ASCE)0733-9399(1992)118:4(721)","article-title":"Frequency domain analysis of undamped systems","volume":"118","author":"Kausel","year":"1992","journal-title":"J. Eng. Mech."},{"key":"ref_47","unstructured":"Hukseflux Thermal Sensors (2016). User Manual HFP01\/HFP03, Hukseflux."},{"key":"ref_48","unstructured":"Hukseflux Thermal Sensors (2016). User Manual TRSYS01\u2014High-Accuracy Building Thermal Resistance Measuring System with Two Measurement Locations, Hukseflux."},{"key":"ref_49","unstructured":"International Organization for Standardization (2007). Building Components and Building Elements\u2014Thermal Resistance and Thermal Transmittance\u2014Calculation Method, ISO."},{"key":"ref_50","unstructured":"International Organization for Standardization (1991). Thermal Insulation\u2014Determination of Steady State Thermal Resistance and Related Properties\u2014Guarded Hot Plate Apparatus, ISO."},{"key":"ref_51","unstructured":"European Standard (2001). Thermal Performance of Building Materials and Products. Determination of Thermal Resistance by Means of Guarded Hot Plate and Heat Flow Meter Methods. Products of High and Medium Thermal Resistance, CEN."},{"key":"ref_52","unstructured":"European Standard (1997). Thermal Insulating Products for Building Applications. Determination of the Apparent Density, CEN."},{"key":"ref_53","unstructured":"International Organization for Standardization (2012). Hygrothermal Performance of Building Components and Building Elements\u2014Internal Surface Temperature to avoid Critical Surface Humidity and Interstitial Condensation\u2014Calculation Methods, ISO."},{"key":"ref_54","unstructured":"BRE (2001). Assessing the Effects of Thermal Bridging at Junctions and Around Openings, BRE, Building Research Establishment Ltd."},{"key":"ref_55","unstructured":"SIA (2015). W\u00e4rmeschutz, Feuchteschutz und Raumklima in Geb\u00e4uden\u2014Korrigenda C1 zur Norm SIA 180:2014, Schweizerischer Ingenieur-und Architektenverein."}],"container-title":["Energies"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1073\/12\/23\/4595\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:39:38Z","timestamp":1760189978000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1073\/12\/23\/4595"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12,3]]},"references-count":55,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2019,12]]}},"alternative-id":["en12234595"],"URL":"https:\/\/doi.org\/10.3390\/en12234595","relation":{},"ISSN":["1996-1073"],"issn-type":[{"value":"1996-1073","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,12,3]]}}}