Computational Research of the Efficiency of Using a Three-Layer Panel Made of Highly Porous Polystyrene Concrete

This paper presents linking computational research of the multilayer structure of the cladding of a three-layer panel made of highly porous polystyrene concrete developed using a new technology in comparison with traditional ones. The calculation of the thermal efficiency of the exterior fence was carried out in three stages, where the thermal regime was calculated from the values of temperature fields in the ELCUT 6.6 system, and the humidity and air modes were determined by the analytical method in the Maple system. The territory of central Kazakhstan (Karaganda) was selected as the research region, where the research showed that equating the thickness by the values of the actual and required heat transfer resistances of traditional multilayer structures to the developed one, the thickness of traditional structures increases from 3.09% to 27.83%. Moisture accumulation relative to the developed one occurs in all the studied structures. Thus, if in some cases of traditional structures moisture is collected by 2.61% and 9.48% less, in others moisture is collected by 27.94% and 119% more. However, the value of evaporated moisture during the drying period showed that all the moisture will evaporate during the specified period. Thus, all the structures meet the conditions for the inadmissibility of moisture for the annual period and the period of moisture accumulation. Moreover, the values of the actual and required permeabilities to air satisfy the condition, which affected the values of the temperature fields taking into account air filtration; the developed structure showed a positive effect for this value, and in traditional structures, the value of τint decreased to 1.35 °C depending on the option. The analytical results of the thermal inertia values of the developed and traditional multilayer structures showed that the developed structure exceeds traditional ones by up to 30.04% depending on the option, which is positive in the cold period. It was also found that the market prices of all traditional structures exceed the developed one by 1.2–2.5 times, depending on the design, which also emphasizes the positive aspects of the new design. Thus, the findings of this research will positively complement the catalog of products of external multilayer cladding structures made of effective materials and can be used by research communities and design organizations in the design of residential buildings.


Introduction
Today, the housing and utilities sector is one of the most energy-intensive industries of the Republic of Kazakhstan, consuming almost 65% of the country's fuel and energy resources [1], where 70% of the total housing sector is made up of apartment buildings, the number of which has exceeded 18 thousand buildings [2].In this regard, the development of new measures aimed at improving the rules for accounting and monitoring energy consumption and maximum energy losses is of particular importance, where one of the priority areas of energy saving in the housing and utilities sector is increasing the energy efficiency of the housing stock [3][4][5][6].Most buildings in the Republic have external cladding structures with inefficient or economically inexpedient indicators that do not correspond to modern trends in the development of enclosures in the context of international experience, which is fraught with excessive consumption of thermal energy [7,8].
Currently, there is a lot of development and research being conducted on outdoor fences on an international scale and on the scale of the Republic of Kazakhstan.The importance of such research around the world is determined by the optimal design of outdoor fences, where engineers and scientists must take into account issues such as economically efficient and energy-efficient structures of outdoor fences, which is extremely difficult.Research in this area on an international scale will help to understand more clearly which of the designs is most acceptable in certain situations.Thus, domestic scientists in [9][10][11] studied the outer shell option using heat-accumulating material for free and forced convection.The efficiency of using this design was up to 44%; however, in multiapartment residential buildings, the use of this enclosure is problematic, and to achieve the specified effect, this design is applicable only for southern Kazakhstan.In studies [12][13][14][15], the authors analyzed the efficiency of curtain facade systems with air gaps in comparison with the traditional one.However, as is known, curtain facade systems with ventilated layers are much more expensive than conventional wet facades, the use of which will affect the pricing of the building [16].
On an international scale, the problem of enclosures also has a significant emphasis, where various enclosure designs and methods for achieving them are studied in order to create an effective comfortable environment for human habitation.Thus, in [17], the authors studied the issue of optimizing traditional external walls, taking into account the orientation of the building to achieve a comfortable environment, where the effect was up to 6.59%.With that, the use of lightweight external walls was studied in [18], but this type of construction is not acceptable for apartment buildings.In the studies [19][20][21], the authors reviewed the possibility of using vacuum insulation panels in outer shells, where they reflected on the disadvantages and advantages of these panels; however, this type of thermal insulation in panels has not yet become widespread, which calls into question the widespread use of this panel in outer shells of apartment buildings [22][23][24].
The conducted review of research indicates the diversity of existing multilayer outer shells used in various climatic conditions.However, the review showed that the research conducted in this direction is insufficient, since there are no comparative studies in the field of thermophysical and economic indicators of external fences in the conditions of the Republic of Kazakhstan (Karaganda), which is a gap that requires additional research in this direction.In this regard, our research is aimed at a theoretical analysis of the thermal and physical and economic indicators of a three-layer panel made of highly porous polystyrene concrete [25,26] developed using a new technology in the climatic conditions of Karaganda, in comparison with existing traditional outer shells.The research is relevant, and its scientific novelty lies in obtaining energy-efficient outdoor fences.

Studied Options of Multilayer Structures of Outer Shells
Our research examined five types of multilayer structures of outer shells, where a three-layer panel made of highly porous polystyrene concrete, obtained using a new technology [25] (Figure 1a), was proposed as a new design in comparison with existing structures of outer shells (Figure 1a,c-e).The main thermal engineering characteristics of the studied multilayer structures of outer shells are presented in Tables 1-5 [27].The main thermal engineering characteristics of the studied multilayer structures of outer shells are presented in Tables 1-5 [27].

Climatic and Internal Boundary Conditions of the Region
The research examined a region located in the central part of the Republic of Kazakhstan.The main climatic indicators were adopted according to the standard [33,34] and are presented in Table 6.Required design resistance according to the degree-day of the heating period 3.2 W/m 2 °C

Climatic and Internal Boundary Conditions of the Region
The research examined a region located in the central part of the Republic of Kazakhstan.The main climatic indicators were adopted according to the standard [33,34] and are presented in Table 6.Required design resistance according to the degree-day of the heating period 3.2 W/m 2 • C

Determination of the Actual Heat Transfer Resistance of the Multilayer Structures of the Outer Shells
Figure 5 shows the analytical results of the actual heat transfer resistances of all the multilayer structures of the outer shells (Figure 1) in comparison with the required one (Table 6), obtained according to [27,34].

Determination of the Actual Heat Transfer Resistance of the Multilayer Structures of the Outer Shells
Figure 5 shows the analytical results of the actual heat transfer resistances of all the multilayer structures of the outer shells (Figure 1) in comparison with the required one (Table 6), obtained according to [27,34].

Calculation of Air Permeability Resistance of the Multilayer Structures of the Outer Shells
Table 7 presents the results of calculating the required and actual air permeability resistances of the multilayer structures of the outer shells.7 presents the results of calculating the required and actual air permeability resistances of the multilayer structures of the outer shells.

Research of Thermal Inertia of the Multilayer Structures of the Outer Shells
Figure 12 shows the results of calculating the values of thermal inertia of the multilayer structures of the outer shells.This paper presents linking computational research of the multilayer structure of the cladding developed using a new technology-a three-layer panel made of highly porous polystyrene concrete (Figure 1a) [25]-in comparison with traditional ones (Figure 1b-e) using the ELCUT 6.6 software package [32] and the Maple computer algebra system.A multivariate analysis of all the multilayer structures of the outer shells was carried out in three stages, where the first stage analyzed the values of the thermal conditions (Figure 2), and the second and third stages analyzed the values of the humidity (Figure 3) and air (Figure 4) conditions.In the research, the main geometric and thermal engineering characteristics are presented in Figure 1 and Tables 1-5 [27,28].The central part of the Republic of Kazakhstan (Karaganda) was chosen as the research region, the main climatic values of This paper presents linking computational research of the multilayer structure of the cladding developed using a new technology-a three-layer panel made of highly porous polystyrene concrete (Figure 1a) [25]-in comparison with traditional ones (Figure 1b-e) using the ELCUT 6.6 software package [32] and the Maple computer algebra system.A multivariate analysis of all the multilayer structures of the outer shells was carried out in three stages, where the first stage analyzed the values of the thermal conditions (Figure 2), and the second and third stages analyzed the values of the humidity (Figure 3) and air (Figure 4) conditions.In the research, the main geometric and thermal engineering characteristics are presented in Figure 1 and Tables 1-5 [27,28].The central part of the Republic of Kazakhstan (Karaganda) was chosen as the research region, the main climatic values of which were adopted according to [33,34].

The Market Value of the Construction of the Studied Multilayer Enclosing Structures
The analysis of the first stage of the research showed (Figure 2) that the required heat transfer resistance (R 2 ) of the specified region is 3.2 W/m 2 • • C, adopted according to the value of the degree-day of the heating period according to the standard [27,28].Taking into account the value of the required heat transfer resistance (R 2 ) in the research, the thickness of the multilayer structures of the outer shells was adopted taking into account R 2 , where the values of the actual resistances (R 1 ) of heat transfer are presented in Figure 5, which vary in the range from 3.5 to 3.55 W/m 2 • • C; these values are almost equal at the specified thicknesses of the multilayer structures.Taking these circumstances into account, with the specified (Figure 5) equal accepted values, the thicknesses of traditional enclosures (Figure 1b-e) relative to the developed one (Figure 1a) increase by 25.77%, 23.71%, 3.09%, and 27.83%, respectively.Thus, due to the equating of the enclosure thicknesses, the analysis of temperature fields showed that the temperature on the inner surface of the enclosure is almost all similar, which is equal to 18.40 • C on average (Figure 6).
The analysis of the second stage of the research showed (Figure 3) that moisture accumulation occurs in all structures (Figure 7).With that, the calculation of the amount of accumulated moisture (Figure 8) showed that the values in traditional enclosure options 2 and 4 are 2.61% and 9.48% less, respectively, and for options 3 and 5 they are 27.94% and 119% more, respectively.However, the calculation of the amount of moisture evaporated in the multilayer structures of the outer shells during the drying period showed that all the accumulated moisture in the structures will evaporate (Figure 9).Thus, the condition for the inadmissibility of moisture accumulation in the multilayer structures of the outer shells was additionally analyzed during the annual period of operation (Figure 10) and during the period of moisture accumulation (Figure 11).In all cases, the condition (R 1 vpc ≥ R 2 vpc ) is fulfilled, which emphasizes the positive aspect of the developed structure despite the significant difference in thickness relative to traditional ones.
The analysis of the third stage of the research showed (Figure 4) that in all the studied multilayer structures of the outer shells, the value of the required and actual resistance to air permeability satisfies the condition (R 2 u ≤ R 1 u ), presented in Table 7.Thus, in the developed structure (Figure 1a) this value is significantly higher than in traditional ones, which had a positive effect on the values of the temperature fields of the enclosure.Thus, in the developed structure (Figure 1a), the temperature of the inner surface (τ int ) remains high, even taking into account filtration (18.41 • C); in traditional structures (Figure 1b-e), the value of τ int decreases to 1.35 • C depending on the option of the traditional multilayer structure, which is an unfavorable factor in the cold period.Moreover, the analytical results of thermal inertia (D) of the developed (Figure 1a) and traditional multilayer structures (Figure 1b-e) showed that the developed structure, according to the value of D, belongs to the high inertia (7 < D) type and exceeds the traditional ones by 6.69%, 8.33%, 30.04% and 15.72%, respectively, which is also a positive moment in the cold period.In conclusion, an analysis of the market value of the studied multilayer structures of external fences was carried out (Figure 13), where it was found that the market prices of all traditional structures (Figure 1b-e) exceed the developed one by 1.2-2.5 times, depending on the design, which also emphasizes the positive aspects of the new design (Figure 1a).
The conducted research on the theoretical study of the developed design of the external fence is part of the research conducted by the authors of [25,31].As noted above, the efficiency in terms of economic indicators is significant, which is due to the minimum consumption of materials [37][38][39] and rapid construction [40,41].Since ready-made three-layer panels during installation do not imply a long construction period, as with the structures of ventilated facades [12][13][14][15] and facades made of block masonry [42,43].In this regard, this type of construction is, by all criteria, the most optimal in the climatic conditions of Karaganda.As a disadvantage of this research, it can be noted that we did not take into account cold joints; however, we will solve and supplement this problem in subsequent research.At the same time, the results obtained in this research will positively complement the catalog of products for multilayer outer shells and can be used by research communities and design organizations in the design of residential buildings.

Conclusions
This paper presented computational research of a multilayer structure of the outer fence consisting of a three-layer panel made of highly porous polystyrene concrete developed using a new technology in comparison with traditional structures.The study covered such areas as thermal engineering indicators and the economic efficiency of the new design.As a result of a comprehensive study, the following was found: -Equating the thickness by the R 1 value taking into account R 2 of traditional multilayer structures to the developed one, the thickness of traditional structures increases from 3.09% to 27.83% depending on the option, which is ineffective from the point of view of the construction estimate.-Moisture accumulation relative to the developed structure occurs in all the studied structures in the range of 2113.6-109,758g/m 2 ; if, in options 2 and 4 of traditional structures, moisture is collected by 2.61% and 9.48% less, respectively, then in options 3 and 5 moisture is collected by 27.94% and 119% more, respectively.However, the value of evaporated moisture during the drying period showed that all moisture will evaporate.At the same time, all structures meet the conditions for the inadmissibility of moisture for an annual period and the period of moisture accumulation.- The values of the actual and required air permeabilities satisfy the condition (R 2 u ≤ R 1 u ), which affected the values of the temperature fields taking into account air filtration, where the developed structure showed a positive effect for this value, and in traditional structures the value of τ int decreased to 1.35 • C depending on the option; this will have an adverse effect in the cold period.The analytical results of the value of D of the developed and traditional multilayer structures showed that the developed structure by its value of D refers to high inertia (7 < D) [25,26] and exceeds traditional ones by up to 30.04% depending on the option, which affected the value of τ int taking into account filtration.It was also found that the market prices of all traditional structures exceed the developed one by 1.2-2.5 times, depending on the design, which also emphasizes the positive aspects of the new design.

Figure 1 .
Figure 1.Options of multilayer structures of outer shells.An explanation of the numbering of the layers is given in Tables 1-5: (a)-three-layer panel made of highly porous polystyrene concrete (option 1); (b)-traditional enclosure made of solid ceramic brick (option 2); (c)-traditional enclosure made of hollow ceramic brick (option 3); (d)-traditional enclosure made of foam block (option 4); (e)-outer shell with a ventilated layer (option 5).

Figure 2 .
Figure 2. Algorithm for calculating the thermal conditions of the multilayer structures of the outer shells [30].

Figure 3 .
Figure 3. Algorithm for calculating the humidity conditions of the multilayer structures of the outer shells [25].

Figure 2 .
Figure 2. Algorithm for calculating the thermal conditions of the multilayer structures of the outer shells [30].

Figure 3 .
Figure 3. Algorithm for calculating the humidity conditions of the multilayer structures of the outer shells [25].

Figure 4 .
Figure 4. Algorithm for calculating the air conditions of the multilayer structures of the outer shells [25].

Figure 4 .
Figure 4. Algorithm for calculating the air conditions of the multilayer structures of the outer shells [25].

Figure 5 .
Figure 5. Values of actual (R1) and required (R2) heat transfer resistances of the multilayer structures of the outer shells: option 1-three-layer panel made of highly porous polystyrene concrete; option 2-traditional enclosure made of solid ceramic brick; option 3-traditional enclosure made of hollow ceramic brick; option 4-traditional enclosure made of foam block; option 5-outer shell with a ventilated layer.

Figure 6
Figure 6 shows an analysis of temperature fields of the outer shells, modeled in the ELCUT 6.6 software package [32-36].

Figure 5 .
Figure 5. Values of actual (R1) and required (R2) heat transfer resistances of the multilayer structures of the outer shells: option 1-three-layer panel made of highly porous polystyrene concrete; option 2-traditional enclosure made of solid ceramic brick; option 3-traditional enclosure made of hollow ceramic brick; option 4-traditional enclosure made of foam block; option 5-outer shell with a ventilated layer.

Figure 6 .
Figure 6.Values of temperature fields of the multilayer structures of the outer shells: (a)-three-layer panel made of highly porous polystyrene concrete (option 1); (b)-traditional enclosure made of solid ceramic brick (option 2); (c)-traditional enclosure made of hollow ceramic brick (option 3); (d)-traditional enclosure made of foam block (option 4); (e)-outer shell with a ventilated layer (option 5).

3. 3 .
Figure7shows the results of the calculation of humidity condensation in the multilayer structures of the outer shells.

3. 3 .
Figure7shows the results of the calculation of humidity condensation in the multilayer structures of the outer shells.

Figure 7 .
Figure 7. Values of humidity condensation of the multilayer structures of the outer shells: (a)-threelayer panel made of highly porous polystyrene concrete (option 1); (b)-traditional enclosure made of solid ceramic brick (option 2); (c)-traditional enclosure made of hollow ceramic brick (option 3); (d)-traditional enclosure made of foam block (option 4); (e)-outer shell with a ventilated layer (option 5).3.3.2.Calculation of the Amount of Moisture Condensing in the Multilayer Structures of the Outer Shells During the Period of Moisture Accumulation Figure 8 shows the results of calculating the values of the amount of moisture condensing in the multilayer structures of the outer shells during the period of moisture accumulation.

Figure 7 .
Figure 7. Values of humidity condensation of the multilayer structures of the outer shells: (a)-three-layer panel made of highly porous polystyrene concrete (option 1); (b)-traditional enclosure made of solid ceramic brick (option 2); (c)-traditional enclosure made of hollow ceramic brick (option 3); (d)-traditional enclosure made of foam block (option 4); (e)-outer shell with a ventilated layer (option 5).

3. 3 21 Figure 8 .Figure 8 . 21 Figure 8 .Figure 9 .
Figure 8 shows the results of calculating the values of the amount of moisture condensing in the multilayer structures of the outer shells during the period of moisture accumulation.Materials 2024, 17, x FOR PEER REVIEW 12 of 21

3. 3 . 4 . 21 Figure 9 .
Figure 9. Values of the amount of moisture evaporated from the multilayer structures of the outer shells during the drying period: option 1-three-layer panel made of highly porous polystyrene concrete; option 2-traditional enclosure made of solid ceramic brick; option 3-traditional enclosure made of hollow ceramic brick; option 4-traditional enclosure made of foam block; option 5-outer shell with a ventilated layer.3.3.4.Conditions for the Inadmissibility of Moisture Accumulation in the Structures of the Outer Shells over the Annual Period of Operation ( ≥  )Figure10shows the calculation of the values of the inadmissibility of moisture accumulation in the multilayer structures of the outer shells over an annual period of operation.

Figure 10 .
Figure 10.Values of the inadmissibility of moisture accumulation in the multilayer structures of the outer shells over an annual period of operation: option 1-three-layer panel made of highly porous polystyrene concrete; option 2-traditional enclosure made of solid ceramic brick; option 3traditional enclosure made of hollow ceramic brick; option 4-traditional enclosure made of foam block; option 5-outer shell with a ventilated layer.

3. 3 . 5 .Figure 10 . 21 Figure 11 .
Figure 11 shows the results of calculating the values of inadmissibility of moisture accumulation in the multilayer structures of the outer shells during the period of moisture accumulation.

Figure 11 .
Figure 11.Values of the inadmissibility of moisture accumulation in the multilayer structures of the outer shells during the period of moisture accumulation: option 1-three-layer panel made of highly porous polystyrene concrete; option 2-traditional enclosure made of solid ceramic brick; option 3-traditional enclosure made of hollow ceramic brick; option 4-traditional enclosure made of foam block; option 5-outer shell with a ventilated layer.

3. 4 .
Calculation of Air Conditions in the Multilayer Structures of the Outer Shells (1.Calculation of Air Permeability Resistance of the Multilayer Structures of the Outer Shells Table

Figure 12 .
Figure 12.Values of thermal inertia of the multilayer structures of the outer shells: option 1-threelayer panel made of highly porous polystyrene concrete; option 2-traditional enclosure made of solid ceramic brick; option 3-traditional enclosure made of hollow ceramic brick; option 4traditional enclosure made of foam block; option 5-outer shell with a ventilated layer.

Figure 13 Figure 12 .
Figure13shows the market values of the construction of the studied multilayer structures of external fences in the city of Karaganda per 1 m 2 .

3. 6 . 21 Figure 13 .
Figure13shows the market values of the construction of the studied multilayer structures of external fences in the city of Karaganda per 1 m 2 .Materials 2024, 17, x FOR PEER REVIEW 16 of 21

Figure 13 .
Figure 13.Market values of multilayer structures of the outer shells per 1 m 2 .
Amount of moisture condensing in the multilayer structure of the outer shell during the period of moisture accumulation, g/m 2 ; e int Actual elasticity of water vapor in the internal air of the cladding structure, Pa; e c Actual elasticity of water vapor in the plane of possible condensation of the cladding structure, Pa; Z con Duration of the condensation period, hours; R vpc Vapor permeability resistance of the cladding structure part from the inner surface to the condensation plane, m 2 •h•Pa/mg; Vapor permeability resistance of the cladding structure part from the inner surface to the condensation plane, m 2 •h•Pa/mg; G u Amount of moisture evaporated from the multilayer structure of the outer shell during the drying period, g/m 2 ; e ext Actual humidity of the outside air during the drying period, Pa; E c Saturated water vapor pressure at the average temperature of the drying period, Pa; Z u Duration of the drying period, hours; R vpcext Resistance to vapor permeability of the part of the cladding structure between the plane of possible condensation and the outer surface of the cladding structure, m 2 •h•Pa/mg; E Elasticity of water vapor in the plane of possible condensation over an annual period, Pa; E 1 , E 2 , E 3 Saturated pressure of water vapor, according to the temperatures of winter, spring-autumn, summer periods, respectively, Pa; Z 1 , Z 2 , Z 3 Duration of winter, spring, autumn, summer periods, respectively, months; γ ω Density of the material of the moistened layer, kg/m 3 ; δ ω Thickness of the moistened layer, m; ∆W ω Maximum permissible increase in the calculated mass ratio of moisture in the material of the moistened layer, %; E o Partial pressure of the condensation zone during the period of moisture accumulation, Pa; Z o Duration of condensation period, months; R req u Required air permeability resistance, Pa•m 2 •h/kg; R f u Actual air permeability resistance, Pa•m 2 •h/kg; ∆p Calculated value of the total pressure difference due to temperature difference and wind, Pa; G H = 0.5 Transverse air permeability for external walls, kg/m 2 •h; γ ext , γ int Density of cold and warm air, respectively, kg/m 3 ; H Building height (from the floor level of the first floor to the top of the exhaust shaft), m; ϑ Maximum of average wind speeds by rhumbs for January, m/s; e Base of natural logarithms; G Amount of air filtered through the structure per unit of time, kg/(m 2 •h); c =1 Specific heat capacity of air; D Thermal inertia; s Heat absorption, W/(m 2 • • C).

Table 1 .
Thermal engineering characteristics of a three-layer panel made of highly porous polystyrene concrete (option 1), shown in Figure1a.

Table 1 .
Thermal engineering characteristics of a three-layer panel made of highly porous polystyrene concrete (option 1), shown in Figure1a.

Table 2 .
Thermal engineering characteristics of the multilayer structure of the outer shell made of solid ceramic brick (option 2), shown in Figure1b.

Table 3 .
Thermal engineering characteristics of the multilayer structure of the outer shell made of hollow ceramic brick (option 3), shown in Figure1c.

Table 4 .
Thermal engineering characteristics of the multilayer structure of the outer shell made of foam block (option 4), shown in Figure1d.

Table 5 .
Thermal engineering characteristics of the multilayer structure of the outer shell with a ventilated layer (option 5), shown in Figure1e.

Table 6 .
Climatic and internal boundary conditions.

Table 6 .
Climatic and internal boundary conditions.

Table 7 .
Values of the required and actual air permeability resistances of the multilayer structures of the outer shells.

Table 7 .
Values of the required and actual air permeability resistances of the multilayer structures of the outer shells.Research of Temperature Distribution at the Boundaries of the Multilayer Structures of the Outer Shells Taking into Account Air Filtration Table8presents the results of calculating the temperature distributions at the boundaries of the multilayer structures of the outer shells.

Table 8 .
Values of temperature distributions at the boundaries of the multilayer structures of the outer shells.
Resistance to heat transfer of the layers of the structure from the internal air to the section under consideration, (m 2• • C)/W; t int Indoor air temperature, • C; t ext Outside air temperature, • C; e x Actual elasticity of water vapor in any section of the cladding structure, Pa; e int Actual elasticity of water vapor in the internal air of the cladding structure, Pa; e ext Actual elasticity of water vapor in the outside air of the cladding structure, Pa; R ovp Resistance to vapor permeability of a single layer or separate layer of a multilayer outer shell, m 2 •h•Pa/mg; R xvp Vapor permeability resistance of layers from the inner surface of the wall to section x; R vp Vapor permeability resistance of a single layer or separate layer of the multilayer cladding structure, m 2 •h•Pa/mg; δ Layer thickness, m; µ Calculated vapor permeability coefficient of the layer material, mg/(m•h•Pa); R vpint , R vpext Vapor permeability resistance of the inner and outer wall surfaces, respectively, m 2 •h•Pa/mg; φ int , φ ext Relative humidity of the indoor and outdoor air, respectively, %; E int , E ext Saturated partial pressure at the temperature of the indoor and outdoor air, respectively, Pa;