Main Article Content
Abstract
The hygrothermal transfer is very important for the design of a building envelope for thermal comfort, economic and energy analysis of the building envelope. The lack of reference materials on models of moisture and temperature behavior in the building, including wooden walls, is a challenge. This paper reviewed the hygrothermal transfer models for building walls. Energy and mass conservation equations with boundary and input conditions were presented in this paper for concrete, bricks, and wooden walls. The review showed the presence of mainly physical-based models, while there is a dearth of data-based models. The influence of the type of wall, orientation, thickness, the density of the material, and climatic variations on the temperature and moisture evolutions within the building materials influenced the model mechanisms. Future research gaps should include shrinkage influence on hygroscopic materials like wood due to their behavior under ambient conditions. Data-based models should be explored too.
Keywords
Article Details
References
- Jang M, T. Hong, C. Ji (2015). Hybrid LCA model for assessing the embodied environmental impacts of buildings in South Korea. Environmental Impact Assessment Review 50 (2015) 143–155
- ONU-environnement, Vers un secteur des batiments et de la construction a emission zero, efficace, et resilient, Bilan mondial (2017) 48pp 2017.
- A.M.E.A. Akata, D. Njomo, B. Agrawal, Assessment of building integrated photovoltaic (BIPV) for sustainable energy performance in tropical regions of Cameroon, Renew. Sustain. Energy Rev. 80 (2017) 1138–1152.
- Chang Y, Ries RJ, Wang Y. Life-cycle energy of residential buildings in China. Energy Policy 2013;62:656–64. http://dx.doi.org/10.1016/j.enpol.2013.07.053.
- Sartori I, Hestnes AG. Energy use in the life cycle of conventional and low-energy buildings: a review article. Energy Build 2007;39(3):249–57. http://dx.doi.org/10.1016/j.enbuild.2006.07.001.
- El-dessouky, H.T., Ettouney, H.M., Bouhamra, W.: A novel air conditioning system membrane air drying and evaporative cooling. Trans IChemE 78(Part A), 999–1009 (2000)
- M. C. Ndukwu · S. I. Manuwa · L. Bennamoun3 · O. J. Olukunle · F. I. Abam. In-Situ Evolution of Heat and Mass Transfer Phenomena and Evaporative Water Losses of Three Agro-Waste Evaporative Cooling Pads: An Experimental and Modeling Study. Waste and Biomass Valorization (2019) 10:3185–3195
- S. Braungardt, V. Burger, J. Zieger, T. Kenkmann, Contribution of Renewable Cooling to the Renewable Energy Target of the EU, Netherlands Enterprise Agency, July 2018 Publication number: RVO-088-1801/RP-DUZA (59p).
- Simo-Tagne M, M C Ndukwu, Y Rogoume (2019). Modelling and numerical simulation of hygrothermal transfer through a building wall for locations subjected to outdoor conditions in Sub-Saharan Africa. Journal of Building Engineering 26 (2019) 100901
- Hong T, Ji C, Park H. Integrated model for assessing the cost and CO2 emission (IMACC) for sustainable structural design in ready-mix concrete. J Environ Manage 2012;103:1–8. http://dx.doi.org/10.1016/j.jenvman.2012.02.034.
- Hong T, Ji C, Jang M, Park H. Assessment model for energy consumption and greenhouse gas emissions during the construction phase. J Manag Eng 2013;30(2):226–35.http://dx.doi.org/10.1061/(ASCE)ME.1943-5479.0000199.
- European Commission, Feuille de route pour une Europe efficace dans l'utilisation des ressources, (2011), p. 31pp.
- L. Benahmed, F.Z. Ben-Mostefa, Integration d’un systeme de rafraichissement solaire au batiment. Faisabilite technico-economique, Master Thesis University of Abou Baker Belkaid Tlemcem (Algeria), 2013, p. 103.
- Shin S, Tae S, Woo J, Roh S. The development of environmental load evaluation system of a standard Korean apartment house. Renew Sust Energ Rev 2011;15(2):1239–49. http://dx.doi.org/10.1016/j.rser.2010.09.036.
- Tae S, Shin S, Woo J, Roh S. The development of apartment house life cycle CO2 simple assessment system using standard apartment houses of South Korea. Renew Sust Energ Rev 2011;15(3):1454–67. http://dx.doi.org/10.1016/j.rser.2010.09.053.
- C. James, C.J. Simonson, P. Talukdar, S. Roels, Numerical and experimental dataset for benchmarking hygroscopic buffering models, International Journal of Heat and Mass Transfer 53 (2010) 3638–3654
- Lelievre D, T. Colinart∗, P. Glouannec . Hygrothermal behavior of bio-based building materials includinghysteresis effects: Experimental and numerical analyses. Energy and Buildings 84 (2014) 617–627
- P. Taylor, R.J. Fuller, M.B. Luther, Energy use and thermal comfort in a rammed earth office building, Energy Build. 40 (2008) 793–800.
- J.C. Damfeu, P. Meukam, Y. Jannot, Modeling and estimation of the thermal properties of clusters aggregates for construction materials: the case of clusters aggregates of lateritic soil, sand, and pouzzolan, Int. J. Heat Mass Transf. 102 (2016) 407–416.
- G. Xingguo, C. Youming, D. Yongqiang, Development and experimental validation of a one-dimensional dynamic hygrothermal modeling based on air humidity ratio, J. Cent. South Univ. 19 (2012) 703–708.
- J.C. Damfeu, P. Meukam, Y. Jannot, Modeling and estimation of the thermal properties of clusters aggregates for construction materials: the case of clusters aggregates of lateritic soil, sand, and pouzzolan, Int. J. Heat Mass Transf. 102 (2016) 407–416.
- W. Simpson, A. TenWolde, Physical Properties and Moisture Relations of Wood, Chapter 3, Forest Products Laboratory, 1999, p. 463 3.1-3.25.
- H. Jafarian, M.H. Demers-Claude, P. Blanchet, V. Laundry, Impact of indoor use of wood on the quality of interior ambiances under overcast and clear skies: case study of the Eugene H. Kruger building, Quebec City. BioResources 11 (1) (2016) 1647–1663.
- M. Watchman, A. Potvin, M.H. Demers-Claude, Wood, and comfort: a comparative case study of two multifunctional rooms, BioResources 12 (1) (2017) 168–182.
- G. Pajchrowski, A. Noskowiak, A. Lewandowska, W. Strykowski, Wood as a building material in the light of environmental assessment of full life cycle of four buildings, Constr. Build. Mater. 52 (2014) 428–436.
- O.F. Osanyintola, C.J. Simonson, Moisture buffering capacity of hygroscopicbuilding materials: experimental facilities and energy impact, Energy andBuilding 38 (2006) 1270–1282.
- Bevan, T. Woolley, Hemp Lime Construction: A Guide to Building with HempLime Composites, IHS/BRE Press, Bracknell, Berkshire, UK, 2008.
- T. Woolley, H. Thompson, T. McGrogan, M. Alexander, The role of low impactbuilding materials in sustainable construction: the potential for hemp, in:Proceeding of Sustainable Building Conference, 13–18 September 2004, Stel-lenbosch, South Africa, 2004.
- T. Pierre, T. Colinart, P. Glouannec, Measurement of thermal properties ofbiosourced building materials, International Journal of Thermophysics (2013),http://dx.doi.org/10.1007/s10765-013-1477-0.
- S. Prétot, F. Collet, C. Garnier, Life cycle assessment of a hemp concrete wall:impact of thickness and coating, Building and Environment 71 (2013) 223–231.
- J. Hildebrandt, N. Hagemann, D. Thran, The contribution of wood-based construction materials for leveraging a low carbon building sector in Europe, Sustainable Cities and Society 34 (2017) 405–418.
- J. Le Dreau, P. Heiselberg, R.J. Lund, A full-scale experimental set-up for assessing the energy performance of radiant wall and active chilled beam for cooling buildings, BUILD SIMUL (2014) 1–13, https://doi.org/10.1007/s12273-014-0190-7.
- T. Busser, A. Piot, M. Pailha, S. Rouchier, M. Woloszyn, Experimental and numerical study of wood-based materials: from material to room scale, Energy Procedia 132 (2017) 747–752.
- D.P. Chen, C.X. Qian, C.L. Liu, A numerical simulation approach to calculating hygrothermal deformation of concrete based on heat and moisture transfer in porous medium, International Journal of Civil Engineerng 8 (4) (2010) 287–291.
- A. Ruuska, T. Hakkinen, Efficiency in the delivery of multi-storey timber buildings, Energy Procedia 96 (2016) 190–201
- N. Mendes, P.C. Philippi, A method for predicting heat and moisture transfer through multilayered walls based on temperature and moisture content gradients, Int. J. Heat Mass Transf. 48 (2005) 37–51.
- Z. Pasztory, P.N. Peralta, S. Molnar, I. Peszlen, Modeling the hygrothermal performance of selected North American and comparable European wood-frame house walls, Energy Build. 49 (2012) 142–147.
- Z. Bing, C. Zhongqing, Z. Liang, Numerical simulation for coupled heat and moisture transfer in building material, 3rd International Conference on Material, Mechanical and Manufacturing Engineering (IC3ME, 2015, pp. 216–221.
- A. Holm, M. Kunzel-Hartwig, Non-isothermal moisture transfer in porous building materials, Materialsweek, Munich, 2000, pp. 1–9 https://www.ibp.fraunhofer.de/ content/dam/ibp/de/documents/non-isothermal_tcm45-35019.pdf , Accessed date:18 August 2018.
- N. Djongyang, R. Tchinda, D. Njomo, A study of coupled heat and mass transfer across a porous building component in intertropical conditions, Energy Build. 41(2009) 461–469.
- A.D. Tran Le, D. Samri, M. Rahim, O. Douzane, G. Promis, T. Langlet, Effect of temperature-dependent sorption characteristics on the hygrothermal behavior of hemp concrete, Energy Procedia 78 (2015) 1449–1454.
- I. Bonefacic, I. Wolf, B. Frankovic, Numerical modeling of thermal comfort conditions in an indoor space with solar radiation sources, J. Mech. Eng. 61 (11) (2015) 641–650.
- Q. Menghao, R. Belarbi, A. Aıt-Mokhtar, A. Seigneurin, An analytical method to calculate the coupled heat and moisture transfer in building materials, Int. Commun. Heat Mass Transf. 33 (2006) 39–48.
- J. Kwiatkowski, M. Woloszyn, J.J. Roux, Modelling of hysteresis influence onmass transfer in building materials, Building and Environment 44 (2009)633–642.
- H. Steeman, M. Van Belleghem, A. Janssens, M. De Paepe, Coupled simulationof heat and moisture transport in air and porous materials for the assessmentof moisture related damage, Building and Environment 44 (2009) 2176–2184.
- P. Talukdar, O.F. Osanyintola, S.O. Olutimayin, C.J. Simonson, An experimentaldata set for benchmarking 1-D, transient heat and moisture transfer modelsof hygroscopic building materials. Part II: Experimental, numerical and ana-lytical data, International Journal of Heat and Mass Transfer 50 (2007) (2007)4915–4926.
- Q.Menghao, R. Belarbi, Development of an analytical method for simultaneous heat and moisture transfer in building materials utilizing transfer function method,Journal of Materials in Civil Engineering 17 (5) (2005) 492–497.
- Q. Menghao, R. Belarbi, A. Aı¨t-Mokhtar, A. Seigneurin, An analytical method to calculate the coupled heat and moisture transfer in building materials, International Communications in Heat and Mass Transfer 33 (2006) 39–48
- D. Kulasiri, I. Woodhead, On modelling the drying of porous materials: analytical solutions to coupled partial differential equations governing heat and moisture transfer, Mathematical Problems in Engineering 3 (2005) 275–291.
- W.J. Chang, C.I. Weng, An analysis solution to coupled heat and mass diffusion transfer in porous materials, Int. J. Heat Mass Transfer 43(2000) 3621–3632
- N.E. Wijeysundera, M.N.A. Hawlader, Effect of condensation and liquid transport on the thermal performance of fibrous insulation, Int. J. Heat Mass Transfer 35 (1992) 2605– 2616
- N.E. Wijeysundera, B.F. Zheng, Numerical simulation of the transient moisture transfer through porous insulation, Int. J. Heat Mass Transfer 39 (1995) 995– 1003..
- Hildebrandta Jakob, Hagemann Nina, Thrän Daniela, The contribution of wood-based construction materials for leveraging a low carbon building sector in europe. Sustainable Cities and Society 34 (2017) 405–418.
- Watchman Mélanie, Potvin André, Demers Claude M. H., Wood and comfort: a comparative case study of two multifunctional rooms. BioResources 12(1), (2017)168-182.
- Poirier Geneviève, Demers Claude M. H., Potvin André, Experiencing wooden ambiences with nordic light : scale model comparative studies under real skies. BioResources 12(1), (2017) 1924-1942.
- Yuan Jihui, Farnham Craig, Emura Kazuo, Optimum insulation thickness for building exterior walls in 32 regions of China to save energy and reduce CO2 emissions. Sustainability (2017), 9, 1711 :1-13; doi:10.3390/su9101711.
References
Jang M, T. Hong, C. Ji (2015). Hybrid LCA model for assessing the embodied environmental impacts of buildings in South Korea. Environmental Impact Assessment Review 50 (2015) 143–155
ONU-environnement, Vers un secteur des batiments et de la construction a emission zero, efficace, et resilient, Bilan mondial (2017) 48pp 2017.
A.M.E.A. Akata, D. Njomo, B. Agrawal, Assessment of building integrated photovoltaic (BIPV) for sustainable energy performance in tropical regions of Cameroon, Renew. Sustain. Energy Rev. 80 (2017) 1138–1152.
Chang Y, Ries RJ, Wang Y. Life-cycle energy of residential buildings in China. Energy Policy 2013;62:656–64. http://dx.doi.org/10.1016/j.enpol.2013.07.053.
Sartori I, Hestnes AG. Energy use in the life cycle of conventional and low-energy buildings: a review article. Energy Build 2007;39(3):249–57. http://dx.doi.org/10.1016/j.enbuild.2006.07.001.
El-dessouky, H.T., Ettouney, H.M., Bouhamra, W.: A novel air conditioning system membrane air drying and evaporative cooling. Trans IChemE 78(Part A), 999–1009 (2000)
M. C. Ndukwu · S. I. Manuwa · L. Bennamoun3 · O. J. Olukunle · F. I. Abam. In-Situ Evolution of Heat and Mass Transfer Phenomena and Evaporative Water Losses of Three Agro-Waste Evaporative Cooling Pads: An Experimental and Modeling Study. Waste and Biomass Valorization (2019) 10:3185–3195
S. Braungardt, V. Burger, J. Zieger, T. Kenkmann, Contribution of Renewable Cooling to the Renewable Energy Target of the EU, Netherlands Enterprise Agency, July 2018 Publication number: RVO-088-1801/RP-DUZA (59p).
Simo-Tagne M, M C Ndukwu, Y Rogoume (2019). Modelling and numerical simulation of hygrothermal transfer through a building wall for locations subjected to outdoor conditions in Sub-Saharan Africa. Journal of Building Engineering 26 (2019) 100901
Hong T, Ji C, Park H. Integrated model for assessing the cost and CO2 emission (IMACC) for sustainable structural design in ready-mix concrete. J Environ Manage 2012;103:1–8. http://dx.doi.org/10.1016/j.jenvman.2012.02.034.
Hong T, Ji C, Jang M, Park H. Assessment model for energy consumption and greenhouse gas emissions during the construction phase. J Manag Eng 2013;30(2):226–35.http://dx.doi.org/10.1061/(ASCE)ME.1943-5479.0000199.
European Commission, Feuille de route pour une Europe efficace dans l'utilisation des ressources, (2011), p. 31pp.
L. Benahmed, F.Z. Ben-Mostefa, Integration d’un systeme de rafraichissement solaire au batiment. Faisabilite technico-economique, Master Thesis University of Abou Baker Belkaid Tlemcem (Algeria), 2013, p. 103.
Shin S, Tae S, Woo J, Roh S. The development of environmental load evaluation system of a standard Korean apartment house. Renew Sust Energ Rev 2011;15(2):1239–49. http://dx.doi.org/10.1016/j.rser.2010.09.036.
Tae S, Shin S, Woo J, Roh S. The development of apartment house life cycle CO2 simple assessment system using standard apartment houses of South Korea. Renew Sust Energ Rev 2011;15(3):1454–67. http://dx.doi.org/10.1016/j.rser.2010.09.053.
C. James, C.J. Simonson, P. Talukdar, S. Roels, Numerical and experimental dataset for benchmarking hygroscopic buffering models, International Journal of Heat and Mass Transfer 53 (2010) 3638–3654
Lelievre D, T. Colinart∗, P. Glouannec . Hygrothermal behavior of bio-based building materials includinghysteresis effects: Experimental and numerical analyses. Energy and Buildings 84 (2014) 617–627
P. Taylor, R.J. Fuller, M.B. Luther, Energy use and thermal comfort in a rammed earth office building, Energy Build. 40 (2008) 793–800.
J.C. Damfeu, P. Meukam, Y. Jannot, Modeling and estimation of the thermal properties of clusters aggregates for construction materials: the case of clusters aggregates of lateritic soil, sand, and pouzzolan, Int. J. Heat Mass Transf. 102 (2016) 407–416.
G. Xingguo, C. Youming, D. Yongqiang, Development and experimental validation of a one-dimensional dynamic hygrothermal modeling based on air humidity ratio, J. Cent. South Univ. 19 (2012) 703–708.
J.C. Damfeu, P. Meukam, Y. Jannot, Modeling and estimation of the thermal properties of clusters aggregates for construction materials: the case of clusters aggregates of lateritic soil, sand, and pouzzolan, Int. J. Heat Mass Transf. 102 (2016) 407–416.
W. Simpson, A. TenWolde, Physical Properties and Moisture Relations of Wood, Chapter 3, Forest Products Laboratory, 1999, p. 463 3.1-3.25.
H. Jafarian, M.H. Demers-Claude, P. Blanchet, V. Laundry, Impact of indoor use of wood on the quality of interior ambiances under overcast and clear skies: case study of the Eugene H. Kruger building, Quebec City. BioResources 11 (1) (2016) 1647–1663.
M. Watchman, A. Potvin, M.H. Demers-Claude, Wood, and comfort: a comparative case study of two multifunctional rooms, BioResources 12 (1) (2017) 168–182.
G. Pajchrowski, A. Noskowiak, A. Lewandowska, W. Strykowski, Wood as a building material in the light of environmental assessment of full life cycle of four buildings, Constr. Build. Mater. 52 (2014) 428–436.
O.F. Osanyintola, C.J. Simonson, Moisture buffering capacity of hygroscopicbuilding materials: experimental facilities and energy impact, Energy andBuilding 38 (2006) 1270–1282.
Bevan, T. Woolley, Hemp Lime Construction: A Guide to Building with HempLime Composites, IHS/BRE Press, Bracknell, Berkshire, UK, 2008.
T. Woolley, H. Thompson, T. McGrogan, M. Alexander, The role of low impactbuilding materials in sustainable construction: the potential for hemp, in:Proceeding of Sustainable Building Conference, 13–18 September 2004, Stel-lenbosch, South Africa, 2004.
T. Pierre, T. Colinart, P. Glouannec, Measurement of thermal properties ofbiosourced building materials, International Journal of Thermophysics (2013),http://dx.doi.org/10.1007/s10765-013-1477-0.
S. Prétot, F. Collet, C. Garnier, Life cycle assessment of a hemp concrete wall:impact of thickness and coating, Building and Environment 71 (2013) 223–231.
J. Hildebrandt, N. Hagemann, D. Thran, The contribution of wood-based construction materials for leveraging a low carbon building sector in Europe, Sustainable Cities and Society 34 (2017) 405–418.
J. Le Dreau, P. Heiselberg, R.J. Lund, A full-scale experimental set-up for assessing the energy performance of radiant wall and active chilled beam for cooling buildings, BUILD SIMUL (2014) 1–13, https://doi.org/10.1007/s12273-014-0190-7.
T. Busser, A. Piot, M. Pailha, S. Rouchier, M. Woloszyn, Experimental and numerical study of wood-based materials: from material to room scale, Energy Procedia 132 (2017) 747–752.
D.P. Chen, C.X. Qian, C.L. Liu, A numerical simulation approach to calculating hygrothermal deformation of concrete based on heat and moisture transfer in porous medium, International Journal of Civil Engineerng 8 (4) (2010) 287–291.
A. Ruuska, T. Hakkinen, Efficiency in the delivery of multi-storey timber buildings, Energy Procedia 96 (2016) 190–201
N. Mendes, P.C. Philippi, A method for predicting heat and moisture transfer through multilayered walls based on temperature and moisture content gradients, Int. J. Heat Mass Transf. 48 (2005) 37–51.
Z. Pasztory, P.N. Peralta, S. Molnar, I. Peszlen, Modeling the hygrothermal performance of selected North American and comparable European wood-frame house walls, Energy Build. 49 (2012) 142–147.
Z. Bing, C. Zhongqing, Z. Liang, Numerical simulation for coupled heat and moisture transfer in building material, 3rd International Conference on Material, Mechanical and Manufacturing Engineering (IC3ME, 2015, pp. 216–221.
A. Holm, M. Kunzel-Hartwig, Non-isothermal moisture transfer in porous building materials, Materialsweek, Munich, 2000, pp. 1–9 https://www.ibp.fraunhofer.de/ content/dam/ibp/de/documents/non-isothermal_tcm45-35019.pdf , Accessed date:18 August 2018.
N. Djongyang, R. Tchinda, D. Njomo, A study of coupled heat and mass transfer across a porous building component in intertropical conditions, Energy Build. 41(2009) 461–469.
A.D. Tran Le, D. Samri, M. Rahim, O. Douzane, G. Promis, T. Langlet, Effect of temperature-dependent sorption characteristics on the hygrothermal behavior of hemp concrete, Energy Procedia 78 (2015) 1449–1454.
I. Bonefacic, I. Wolf, B. Frankovic, Numerical modeling of thermal comfort conditions in an indoor space with solar radiation sources, J. Mech. Eng. 61 (11) (2015) 641–650.
Q. Menghao, R. Belarbi, A. Aıt-Mokhtar, A. Seigneurin, An analytical method to calculate the coupled heat and moisture transfer in building materials, Int. Commun. Heat Mass Transf. 33 (2006) 39–48.
J. Kwiatkowski, M. Woloszyn, J.J. Roux, Modelling of hysteresis influence onmass transfer in building materials, Building and Environment 44 (2009)633–642.
H. Steeman, M. Van Belleghem, A. Janssens, M. De Paepe, Coupled simulationof heat and moisture transport in air and porous materials for the assessmentof moisture related damage, Building and Environment 44 (2009) 2176–2184.
P. Talukdar, O.F. Osanyintola, S.O. Olutimayin, C.J. Simonson, An experimentaldata set for benchmarking 1-D, transient heat and moisture transfer modelsof hygroscopic building materials. Part II: Experimental, numerical and ana-lytical data, International Journal of Heat and Mass Transfer 50 (2007) (2007)4915–4926.
Q.Menghao, R. Belarbi, Development of an analytical method for simultaneous heat and moisture transfer in building materials utilizing transfer function method,Journal of Materials in Civil Engineering 17 (5) (2005) 492–497.
Q. Menghao, R. Belarbi, A. Aı¨t-Mokhtar, A. Seigneurin, An analytical method to calculate the coupled heat and moisture transfer in building materials, International Communications in Heat and Mass Transfer 33 (2006) 39–48
D. Kulasiri, I. Woodhead, On modelling the drying of porous materials: analytical solutions to coupled partial differential equations governing heat and moisture transfer, Mathematical Problems in Engineering 3 (2005) 275–291.
W.J. Chang, C.I. Weng, An analysis solution to coupled heat and mass diffusion transfer in porous materials, Int. J. Heat Mass Transfer 43(2000) 3621–3632
N.E. Wijeysundera, M.N.A. Hawlader, Effect of condensation and liquid transport on the thermal performance of fibrous insulation, Int. J. Heat Mass Transfer 35 (1992) 2605– 2616
N.E. Wijeysundera, B.F. Zheng, Numerical simulation of the transient moisture transfer through porous insulation, Int. J. Heat Mass Transfer 39 (1995) 995– 1003..
Hildebrandta Jakob, Hagemann Nina, Thrän Daniela, The contribution of wood-based construction materials for leveraging a low carbon building sector in europe. Sustainable Cities and Society 34 (2017) 405–418.
Watchman Mélanie, Potvin André, Demers Claude M. H., Wood and comfort: a comparative case study of two multifunctional rooms. BioResources 12(1), (2017)168-182.
Poirier Geneviève, Demers Claude M. H., Potvin André, Experiencing wooden ambiences with nordic light : scale model comparative studies under real skies. BioResources 12(1), (2017) 1924-1942.
Yuan Jihui, Farnham Craig, Emura Kazuo, Optimum insulation thickness for building exterior walls in 32 regions of China to save energy and reduce CO2 emissions. Sustainability (2017), 9, 1711 :1-13; doi:10.3390/su9101711.