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Sensitivity Analysis applied to Hygrothermal Simulation of a Brick Building in Hot and Humid Climate
Available Available online online at at www.sciencedirect.com www.sciencedirect.com
ScienceDirect
Available online at www.sciencedirect.com Procedia Procedia Engineering Engineering 00 00 (2017) (2017) 000–000 000–000
ScienceDirect
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Procedia Engineering 205 (2017) 665–671
10th International Symposium on Heating, Ventilation and Air Conditioning, ISHVAC2017, 1922 October 2017, Jinan, China
Sensitivity Analysis applied to Hygrothermal Simulation of a Brick Building in Hot and Humid Climate
b,c GUO Xing-guoaa，LUO Hongtaoaa, ZHANG Jingxinaa, LIU Xiang-weiaa，*，CHEN Guo-jieb,c aa
School School of of Civil Civil Engineering Engineering and and Architecture，Nanchang Architecture，Nanchang University，Nanchang University，Nanchang 330031，P.R.China; 330031，P.R.China; b bCollege of Civil Engineering, University of South China, Hengyang 421001, P.R.China; College of Civil Engineering, University of South China, Hengyang 421001, P.R.China; cc College College of of Civil Civil Engineering Engineering ,, Hunan Hunan University, University, Changsha Changsha 410082, 410082, P.R.China) P.R.China)
Abstract Based on the Fourier law, Fick law and Darcy law, a coupled heat and moisture transfer model for porous media was established. Relative humidity and temperature were chosen as the driving potentials. The effects of sorption capacity, water vapor permeability, liquid water conductivity, specific heat, and thermal conductivity on the coupled heat and moisture transfer in porous media were investigated under hot-humid climate. The results show that liquid water permeability and thermal conductivity have greater effects on the coupled heat and moisture transfer, and the average errors are 2% and 2.2%. The effects of other parameters are negligible, and the average errors are less than 0.1%.
© © 2017 2017 The The Authors. Authors. Published Published by by Elsevier Elsevier Ltd. Ltd. © 2017 The Authors. Published by Elsevier Ltd. committee of the 10th International Symposium on Heating, Ventilation and Air Peer-review under responsibility of the scientific Peer-review under responsibility of the scientific committee of of the the 10th 10th International International Symposium Symposium on on Heating, Heating, Ventilation Ventilationand and Air Peer-review under responsibility of the scientific committee Conditioning. Conditioning. Air Conditioning.
Keywords: porous wall; coupled heat and moisture transfer; relative humidity; temperature; Sensitivity analysis.
1. INTRODUCTION In hot and humid climate regions, temperature changes frequently which intensifies the moisture migration. Walls are normally subjected to both thermal and moisture gradients. The heat and moisture transfer through the walls has an important effect on the building energy consumption, thermal performance of walls. In addition, too high levels of indoor relative humidity can cause mould growth on the inside surfaces of the * * Corresponding Corresponding author. author. Tel.: Tel.: +86-153-9791-3323. +86-153-9791-3323. E-mail E-mail address: address: [email protected] [email protected] 1877-7058 1877-7058 © © 2017 2017 The The Authors. Authors. Published Published by by Elsevier Elsevier Ltd. Ltd. Peer-review Peer-review under under responsibility responsibility of of the the scientific scientific committee committee of of the the 10th 10th International International Symposium Symposium on on Heating, Heating, Ventilation Ventilation and and Air Air Conditioning. Conditioning.
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 10th International Symposium on Heating, Ventilation and Air Conditioning. 10.1016/j.proeng.2017.09.838
Guo Xing-guo et al. / Procedia Engineering 205 (2017) 665–671 Author name / Procedia Engineering 00 (2017) 000–000
666 2
walls which lead to indoor air quality problems[1]. Therefore, it is necessary to study on the heat and moisture transfer behaviors in the walls. It is time-consuming and complex to simulate the heat and moisture transfer phenomenon in porous media, since the mass transfer and heat transfer is simultaneous and the dependent variables are highly coupled. Many studies have been carried out to investigated the heat and moisture transfer behavior in porous media[2-3]. Most of the models are based on the work by Philip and Luikov[4] and De Vries[5] who developed transient models that used moisture content as the driving potential for moisture transport. However, parameters of models are functions of temperature and moisture content which leads to highly nonlinear of the governing equations. Abahri et al.[6] developed a model based on the theory of Luikov which take all parameters as constants and they used the transfer function method to solve the partial differential equations. According to the Fourier law, Fick law and Darcy law, Qin et al.[7] developed a two-dimensional hygrothermal model with variable physical properties. Wang et al.[8] proposed a dynamic mathematical model with which they studied effect of moisture migration on the heat conduction through walls. . It is obvious that the way to deal with the parameters of the walls will affect the solution of the governing equations directly. Therefore, the purpose of this paper is to investigate the effects of the parameters on the coupled heat and moisture transfer within the walls. Nomenclature
ξ Dv Ps Dl Pw R M Cm Pm
λ
Cpl Cpv L
sorption capacity water vapor permeability (s) saturation vapor pressure (Pa) liquid water permeability (s) density of liquid water (kg/m3) general gas constant (8.314J/(mol·k)) molar weight of water vapor (0.018kg/mol) specific heat capacity of the material (J/(kg·k)) density of the dry material (kg/m3) thermal conductivity (W/(m·k)) specific heat capacity of the water liquid (J/(kg·k)) specific heat capacity of the vapor (J/(kg·k)) vaporization latent heat (J/kg)
2. Mathematical model Most building materials are porous and composed of solid matrices and pores. A hygrothermal model for the porous materials has been developed according to the mass and energy conservation laws. Assumptions are as follows:1) water vapor is an ideal gas; 2) The material is homogenous. 3) The effect of temperature on equilibrium moisture content is negligible. Neglecting the effect of airflow[9-10], energy and mass transfer equations can be expressed as:
ξ
∂Ps ρ R ρ R T ∂ϕ ∂ϕ ∂ ∂T = + Dl w ln ϕ + Dv Ps + Dl w Dvϕ M ∂t ∂x M ϕ ∂x ∂T ∂x
（1）
Guo Xing-guo et al. / Procedia Engineering 205 (2017) 665–671 Author name / Procedia Engineering 00 (2017) 000–000
ρ R ∂P ∂T λ + C plTDl w ln φ + Dv ( L + C pvT )φ s ∂T ∂ M ∂T ∂x = Cm ρ m ∂t ∂x + C TD ρ w R T + D ( L + C T ) P ∂φ v pv s pl l M φ x ∂
667 3
（2）
The boundary conditions are given as follows:
g = hm ( Pswφw − Ps∞φ∞ ) q = h(Tw − T∞ ) + hm ( Pswφw − Ps∞φ∞ ) L
（3） （4）
3. Mathematical model The governing equations are highly nonlinear and coupled. To ensure the stability of numerical solution, the governing equations were discrete by finite volume method with implicit forward differences. The discrete equations were solved by using MTDMA[11] (MultiTriDiagonal-Matrix Algorithm). N. The presented model is validated by comparing the simulation results with the results of the benchmarks of the HAMSTAD project [12], which was initiated to develop a platform to assess computational modeling of heat, moisture and air transport mechanism in building physics. There, the benchmark two in which the thick of the “ homogeneous wall ” is 200mm is displayed. The initial conditions are 20 ℃ and 95% (w=84.7687kg/m3). Suddenly, the outdoor and indoor relative humidity is changed to 45% and 65%, respectively. The temperature is kept constant at 20℃. The heat and mass transfer coefficients for both surfaces are 25W/(m2·K) and 1×10-3s/m, respectively. The detail material properties are given in table 1. Table 1 Parameters of material
Parameter ω Sorption isothermal(kg/m3)
Value w=
116 1 (1 − ln(ϕ )) 0.869 0.118
Vapor diffusion(s)
1×10-15
Moisture diffusivity (m2/s)
6×10-10
Thermal conductivity (W/m·K)
0.15
Specific heat capacity (J/m3·K)
800
Density (kg/m3)
525
The comparison results are shown in Fig. 1. The simulation result of the developed model agrees well with that of benchmark two.
Guo Xing-guo et al. / Procedia Engineering 205 (2017) 665–671 Author name / Procedia Engineering 00 (2017) 000–000
668 4
Fig.1 Moisture distribution within the wall
4. Sensitivity analysis of parameters The wall in benchmark two is selected the object of study. The hygrothermal properties of brick are prepared in Fig. 2.
(a)
(c)
(b)
(d)
Guo Xing-guo et al. / Procedia Engineering 205 (2017) 665–671 Author name / Procedia Engineering 00 (2017) 000–000
669 5
(e)
Fig.2 Typical moisture and thermal transport properties curves
In order to analyze the effects of parameters on the coupled heat and moisture transfer of the walls, Table 2 summarizes the models derived from basic model in which all parameters are the functions of temperature and relative humidity. In the process of simulations, the indoor air temperature and relative humidity offset as 24℃ and 50%, respectively. The outdoor air temperature and relative humidity are 30℃ and 80% respectively. Table 2 Summary of the sub-models
Basic model Model 1 Dv
√
Model 2
Model 3
Model 4
Model 5
Model 6
×
√
√
√
√
×
Dl
√
√
×
√
√
√
×
ξ
√
√
√
×
√
√
×
cm λ
√ √
√ √
√ √
√ √
× √
√ ×
× ×
Note: “√” represents the parameters which are the functions of temperature and relative humidity, “×” represents the parameters which are constants.
The simulation results are shown in Fig.3 to Fig.5. As shown in Fig. 3, the average errors of relative humidity between the basic model and sub-models in which the liquid water permeability and thermal conductivity are assumed constants are 2% and 2.2%, respectively. The other sub-models’ results are close to the basic model and the errors are less than 0.1%. Fig. 4 shows the similar results as those shown in Fig.3. As shown in Fig. 5, the differences between the seven curves are relatively larger. The average errors of temperature between the basic model and sub-models in which the liquid water permeability and thermal conductivity are assumed constants are 0.3% and 1.5%, respectively. When all parameters are considered as constants, the error of temperature distribution compared with basic model is 1.7% and the error of relative humidity is 1.5%.
670 6
Guo Xing-guo et al. / Procedia Engineering 205 (2017) 665–671 Author name / Procedia Engineering 00 (2017) 000–000
Fig.3 Relative humidity distribution in the wall
Fig.4 Moisture content distribution in the wall
Fig.5 Temperature distribution in the wall
5. Sensitivity analysis of parameters In this paper, a coupled heat and moisture transfer model which considers the vapor diffusion and liquid water transfer is developed based on the energy and mass conservation laws. The temperature and relative humidity are selected as driving potentials. The mathematic model is solved by using the MTDMA method.
Guo Xing-guo et al. / Procedia Engineering 205 (2017) 665–671 Author name / Procedia Engineering 00 (2017) 000–000
671 7
And the model is validated by comparing with HAMSTAD benchmark two. Six sub-models are put forward. The simulation results of sub-models are compared with the basic model’ s. The results show that the difference between the basic model and sub-model is relatively large, when the liquid water permeability and thermal conductivity are assumed constants. The effect of changes in vapor permeability and specific heat on the distribution of temperature and relative humidity within walls is negligible. Therefore, the liquid water permeability and thermal conductivity should be set as the functions of moisture content and temperature, while the other parameters can be set as constants. 6. Acknowledgment
The authors would like to express their gratitude for the support from the National Nature Science Foundation of P. R.China (No.51208247, 51408294). References
[1] HU Min. The research on analysis method of moiture transport in buildings and its influence on indoor environment [D]. Hunan: Hunan university, 2006. (in Chinese) [2] Glaser H. Graphical method for investigation of diffusion process [J]. German: Kalteohnik, 1958,35-67. [3] Shakun W. The causes and control of mold and mildew in hot and humid climates . ASHRAE Transactions, 1992, 98 (1):1282-1292. [4] Luikov A W. Heat and Mass Transfer in Capillary-Porous Bodies[M]. Pergamon Press. Oxford, 1966, chap. 6. [5] Philip J,De Vries D. Moisture movement in porous materials under temperature gradients. Transaction of American Geophysical Union, 1957, 38(2):222-232. [6] ABAHRI K, BELARBI R, TRABELSI A. Contribution to analytical and numerical study of combined heat and moisture transfers in porous building materials[J]. Building and Environment, 2011, (46): 1354-1360. [7] Qin Meng-hao, AIT-MOKHTAR A,BELARBI R. Two-dimensional hygrothermal transfer in porous building materials[J]. Applied Thermal Engineering, 2010, (30): 2555-2562. [8] Wang Yingying, Liu Yanfeng, Liu Jiaping. Analysis on the effect of moisture migration through walls on heat transfer[J]. Journal of Civil,Architectural & Environmental Engineering, 2012, 34(6):109-114.(in Chinese) [9] Hugo Hens. Building Physicis-Heat,Air and Moisture[M]. Germany:Ernst & Sohn, 2007. 120-134 [10] Tariku F, Kumaran K, Fazio P. Transient model for coupled heat, air and moisture transfer through[J]. International Journal of Heat and Mass Transfer, 2010, (53): 3035-3044 [11] dos Santos G H, Mendes N. Heat, air and moisture transfer through hollow porous blocks[J]. International Journal of Heat and Mass Transfer, 2009, (52): 2390-2398 [12] Hagentoft C E, HAMSTAD– Final report: methodology of HAM-modeling, Report R-02:8, Gothenburg, Department of Building Physics, Chalmers University of Technology, 2002
ScienceDirect
Available online at www.sciencedirect.com Procedia Procedia Engineering Engineering 00 00 (2017) (2017) 000–000 000–000
ScienceDirect
www.elsevier.com/locate/procedia www.elsevier.com/locate/procedia
Procedia Engineering 205 (2017) 665–671
10th International Symposium on Heating, Ventilation and Air Conditioning, ISHVAC2017, 1922 October 2017, Jinan, China
Sensitivity Analysis applied to Hygrothermal Simulation of a Brick Building in Hot and Humid Climate
b,c GUO Xing-guoaa，LUO Hongtaoaa, ZHANG Jingxinaa, LIU Xiang-weiaa，*，CHEN Guo-jieb,c aa
School School of of Civil Civil Engineering Engineering and and Architecture，Nanchang Architecture，Nanchang University，Nanchang University，Nanchang 330031，P.R.China; 330031，P.R.China; b bCollege of Civil Engineering, University of South China, Hengyang 421001, P.R.China; College of Civil Engineering, University of South China, Hengyang 421001, P.R.China; cc College College of of Civil Civil Engineering Engineering ,, Hunan Hunan University, University, Changsha Changsha 410082, 410082, P.R.China) P.R.China)
Abstract Based on the Fourier law, Fick law and Darcy law, a coupled heat and moisture transfer model for porous media was established. Relative humidity and temperature were chosen as the driving potentials. The effects of sorption capacity, water vapor permeability, liquid water conductivity, specific heat, and thermal conductivity on the coupled heat and moisture transfer in porous media were investigated under hot-humid climate. The results show that liquid water permeability and thermal conductivity have greater effects on the coupled heat and moisture transfer, and the average errors are 2% and 2.2%. The effects of other parameters are negligible, and the average errors are less than 0.1%.
© © 2017 2017 The The Authors. Authors. Published Published by by Elsevier Elsevier Ltd. Ltd. © 2017 The Authors. Published by Elsevier Ltd. committee of the 10th International Symposium on Heating, Ventilation and Air Peer-review under responsibility of the scientific Peer-review under responsibility of the scientific committee of of the the 10th 10th International International Symposium Symposium on on Heating, Heating, Ventilation Ventilationand and Air Peer-review under responsibility of the scientific committee Conditioning. Conditioning. Air Conditioning.
Keywords: porous wall; coupled heat and moisture transfer; relative humidity; temperature; Sensitivity analysis.
1. INTRODUCTION In hot and humid climate regions, temperature changes frequently which intensifies the moisture migration. Walls are normally subjected to both thermal and moisture gradients. The heat and moisture transfer through the walls has an important effect on the building energy consumption, thermal performance of walls. In addition, too high levels of indoor relative humidity can cause mould growth on the inside surfaces of the * * Corresponding Corresponding author. author. Tel.: Tel.: +86-153-9791-3323. +86-153-9791-3323. E-mail E-mail address: address: [email protected] [email protected] 1877-7058 1877-7058 © © 2017 2017 The The Authors. Authors. Published Published by by Elsevier Elsevier Ltd. Ltd. Peer-review Peer-review under under responsibility responsibility of of the the scientific scientific committee committee of of the the 10th 10th International International Symposium Symposium on on Heating, Heating, Ventilation Ventilation and and Air Air Conditioning. Conditioning.
1877-7058 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 10th International Symposium on Heating, Ventilation and Air Conditioning. 10.1016/j.proeng.2017.09.838
Guo Xing-guo et al. / Procedia Engineering 205 (2017) 665–671 Author name / Procedia Engineering 00 (2017) 000–000
666 2
walls which lead to indoor air quality problems[1]. Therefore, it is necessary to study on the heat and moisture transfer behaviors in the walls. It is time-consuming and complex to simulate the heat and moisture transfer phenomenon in porous media, since the mass transfer and heat transfer is simultaneous and the dependent variables are highly coupled. Many studies have been carried out to investigated the heat and moisture transfer behavior in porous media[2-3]. Most of the models are based on the work by Philip and Luikov[4] and De Vries[5] who developed transient models that used moisture content as the driving potential for moisture transport. However, parameters of models are functions of temperature and moisture content which leads to highly nonlinear of the governing equations. Abahri et al.[6] developed a model based on the theory of Luikov which take all parameters as constants and they used the transfer function method to solve the partial differential equations. According to the Fourier law, Fick law and Darcy law, Qin et al.[7] developed a two-dimensional hygrothermal model with variable physical properties. Wang et al.[8] proposed a dynamic mathematical model with which they studied effect of moisture migration on the heat conduction through walls. . It is obvious that the way to deal with the parameters of the walls will affect the solution of the governing equations directly. Therefore, the purpose of this paper is to investigate the effects of the parameters on the coupled heat and moisture transfer within the walls. Nomenclature
ξ Dv Ps Dl Pw R M Cm Pm
λ
Cpl Cpv L
sorption capacity water vapor permeability (s) saturation vapor pressure (Pa) liquid water permeability (s) density of liquid water (kg/m3) general gas constant (8.314J/(mol·k)) molar weight of water vapor (0.018kg/mol) specific heat capacity of the material (J/(kg·k)) density of the dry material (kg/m3) thermal conductivity (W/(m·k)) specific heat capacity of the water liquid (J/(kg·k)) specific heat capacity of the vapor (J/(kg·k)) vaporization latent heat (J/kg)
2. Mathematical model Most building materials are porous and composed of solid matrices and pores. A hygrothermal model for the porous materials has been developed according to the mass and energy conservation laws. Assumptions are as follows:1) water vapor is an ideal gas; 2) The material is homogenous. 3) The effect of temperature on equilibrium moisture content is negligible. Neglecting the effect of airflow[9-10], energy and mass transfer equations can be expressed as:
ξ
∂Ps ρ R ρ R T ∂ϕ ∂ϕ ∂ ∂T = + Dl w ln ϕ + Dv Ps + Dl w Dvϕ M ∂t ∂x M ϕ ∂x ∂T ∂x
（1）
Guo Xing-guo et al. / Procedia Engineering 205 (2017) 665–671 Author name / Procedia Engineering 00 (2017) 000–000
ρ R ∂P ∂T λ + C plTDl w ln φ + Dv ( L + C pvT )φ s ∂T ∂ M ∂T ∂x = Cm ρ m ∂t ∂x + C TD ρ w R T + D ( L + C T ) P ∂φ v pv s pl l M φ x ∂
667 3
（2）
The boundary conditions are given as follows:
g = hm ( Pswφw − Ps∞φ∞ ) q = h(Tw − T∞ ) + hm ( Pswφw − Ps∞φ∞ ) L
（3） （4）
3. Mathematical model The governing equations are highly nonlinear and coupled. To ensure the stability of numerical solution, the governing equations were discrete by finite volume method with implicit forward differences. The discrete equations were solved by using MTDMA[11] (MultiTriDiagonal-Matrix Algorithm). N. The presented model is validated by comparing the simulation results with the results of the benchmarks of the HAMSTAD project [12], which was initiated to develop a platform to assess computational modeling of heat, moisture and air transport mechanism in building physics. There, the benchmark two in which the thick of the “ homogeneous wall ” is 200mm is displayed. The initial conditions are 20 ℃ and 95% (w=84.7687kg/m3). Suddenly, the outdoor and indoor relative humidity is changed to 45% and 65%, respectively. The temperature is kept constant at 20℃. The heat and mass transfer coefficients for both surfaces are 25W/(m2·K) and 1×10-3s/m, respectively. The detail material properties are given in table 1. Table 1 Parameters of material
Parameter ω Sorption isothermal(kg/m3)
Value w=
116 1 (1 − ln(ϕ )) 0.869 0.118
Vapor diffusion(s)
1×10-15
Moisture diffusivity (m2/s)
6×10-10
Thermal conductivity (W/m·K)
0.15
Specific heat capacity (J/m3·K)
800
Density (kg/m3)
525
The comparison results are shown in Fig. 1. The simulation result of the developed model agrees well with that of benchmark two.
Guo Xing-guo et al. / Procedia Engineering 205 (2017) 665–671 Author name / Procedia Engineering 00 (2017) 000–000
668 4
Fig.1 Moisture distribution within the wall
4. Sensitivity analysis of parameters The wall in benchmark two is selected the object of study. The hygrothermal properties of brick are prepared in Fig. 2.
(a)
(c)
(b)
(d)
Guo Xing-guo et al. / Procedia Engineering 205 (2017) 665–671 Author name / Procedia Engineering 00 (2017) 000–000
669 5
(e)
Fig.2 Typical moisture and thermal transport properties curves
In order to analyze the effects of parameters on the coupled heat and moisture transfer of the walls, Table 2 summarizes the models derived from basic model in which all parameters are the functions of temperature and relative humidity. In the process of simulations, the indoor air temperature and relative humidity offset as 24℃ and 50%, respectively. The outdoor air temperature and relative humidity are 30℃ and 80% respectively. Table 2 Summary of the sub-models
Basic model Model 1 Dv
√
Model 2
Model 3
Model 4
Model 5
Model 6
×
√
√
√
√
×
Dl
√
√
×
√
√
√
×
ξ
√
√
√
×
√
√
×
cm λ
√ √
√ √
√ √
√ √
× √
√ ×
× ×
Note: “√” represents the parameters which are the functions of temperature and relative humidity, “×” represents the parameters which are constants.
The simulation results are shown in Fig.3 to Fig.5. As shown in Fig. 3, the average errors of relative humidity between the basic model and sub-models in which the liquid water permeability and thermal conductivity are assumed constants are 2% and 2.2%, respectively. The other sub-models’ results are close to the basic model and the errors are less than 0.1%. Fig. 4 shows the similar results as those shown in Fig.3. As shown in Fig. 5, the differences between the seven curves are relatively larger. The average errors of temperature between the basic model and sub-models in which the liquid water permeability and thermal conductivity are assumed constants are 0.3% and 1.5%, respectively. When all parameters are considered as constants, the error of temperature distribution compared with basic model is 1.7% and the error of relative humidity is 1.5%.
670 6
Guo Xing-guo et al. / Procedia Engineering 205 (2017) 665–671 Author name / Procedia Engineering 00 (2017) 000–000
Fig.3 Relative humidity distribution in the wall
Fig.4 Moisture content distribution in the wall
Fig.5 Temperature distribution in the wall
5. Sensitivity analysis of parameters In this paper, a coupled heat and moisture transfer model which considers the vapor diffusion and liquid water transfer is developed based on the energy and mass conservation laws. The temperature and relative humidity are selected as driving potentials. The mathematic model is solved by using the MTDMA method.
Guo Xing-guo et al. / Procedia Engineering 205 (2017) 665–671 Author name / Procedia Engineering 00 (2017) 000–000
671 7
And the model is validated by comparing with HAMSTAD benchmark two. Six sub-models are put forward. The simulation results of sub-models are compared with the basic model’ s. The results show that the difference between the basic model and sub-model is relatively large, when the liquid water permeability and thermal conductivity are assumed constants. The effect of changes in vapor permeability and specific heat on the distribution of temperature and relative humidity within walls is negligible. Therefore, the liquid water permeability and thermal conductivity should be set as the functions of moisture content and temperature, while the other parameters can be set as constants. 6. Acknowledgment
The authors would like to express their gratitude for the support from the National Nature Science Foundation of P. R.China (No.51208247, 51408294). References
[1] HU Min. The research on analysis method of moiture transport in buildings and its influence on indoor environment [D]. Hunan: Hunan university, 2006. (in Chinese) [2] Glaser H. Graphical method for investigation of diffusion process [J]. German: Kalteohnik, 1958,35-67. [3] Shakun W. The causes and control of mold and mildew in hot and humid climates . ASHRAE Transactions, 1992, 98 (1):1282-1292. [4] Luikov A W. Heat and Mass Transfer in Capillary-Porous Bodies[M]. Pergamon Press. Oxford, 1966, chap. 6. [5] Philip J,De Vries D. Moisture movement in porous materials under temperature gradients. Transaction of American Geophysical Union, 1957, 38(2):222-232. [6] ABAHRI K, BELARBI R, TRABELSI A. Contribution to analytical and numerical study of combined heat and moisture transfers in porous building materials[J]. Building and Environment, 2011, (46): 1354-1360. [7] Qin Meng-hao, AIT-MOKHTAR A,BELARBI R. Two-dimensional hygrothermal transfer in porous building materials[J]. Applied Thermal Engineering, 2010, (30): 2555-2562. [8] Wang Yingying, Liu Yanfeng, Liu Jiaping. Analysis on the effect of moisture migration through walls on heat transfer[J]. Journal of Civil,Architectural & Environmental Engineering, 2012, 34(6):109-114.(in Chinese) [9] Hugo Hens. Building Physicis-Heat,Air and Moisture[M]. Germany:Ernst & Sohn, 2007. 120-134 [10] Tariku F, Kumaran K, Fazio P. Transient model for coupled heat, air and moisture transfer through[J]. International Journal of Heat and Mass Transfer, 2010, (53): 3035-3044 [11] dos Santos G H, Mendes N. Heat, air and moisture transfer through hollow porous blocks[J]. International Journal of Heat and Mass Transfer, 2009, (52): 2390-2398 [12] Hagentoft C E, HAMSTAD– Final report: methodology of HAM-modeling, Report R-02:8, Gothenburg, Department of Building Physics, Chalmers University of Technology, 2002