REDUCTION IN ENERGY CONSUMPTION BY AIR-CONDITIONER IN RESIDENCES UNDER HOT AND HUMID CLIMATES Tomoko UNO Dr.Eng. 1 Shuichi HOKOI Dr.Eng. 2 Sri Nastiti N. EKASIWI 3 1 Department of Architecture and Environmental Design, Kyoto University, KyotoDaigaku-Katsura, Nishikyou ku, Kyoto 615-8246, Japan, be.uno@ archi.kyoto-u.ac.jp 2 Department of Architecture and Environmental Design, Kyoto University, KyotoDaigaku-Katsura, Nishikyou ku, Kyoto 615-8246, Japan, hokoi@ archi.kyoto-u.ac.jp 3 Institute of Technology Sepluh November Republic of Indonesia, Institut Teknologi Sepuluh Nopember Surabaya, Kampus ITS Sukolilo, Surabaya 60111, Indonesia, titibs@indosat.net.id Summary The purpose of this paper is to propose strategies of reducing energy consumption for cooling in residences under hot and humid climate such as Indonesia. Based on the results of field survey, a simulation of the indoor thermal environment considering the operation of an air-conditioner was carried out, in order to evaluate energy consumption by the air-conditioner. This simulation program takes into account both heat and moisture transports in the walls. The effects of air tightness and thermal insulation were examined. The results show that an increase in insulation on ceilings or roofs is essential to reduce the heat flow caused by the strong solar radiation. This is also true for the houses without air-conditioners. Increase in air tightness of only the air-conditioned room can effectively reduce electricity consumption, mainly due to the latent heat load. Since energy consumption for cooling is expected to increase rapidly in hot and humid areas such as Southeast Asia, an introduction of high insulation and air tightness suitable to the local area will be required for energy saving. 1. Introduction The countries under tropical climate such as Indonesia, air-conditioners have been prevailing not only in offices but also in residences for a comfortable indoor thermal condition 1), 2). Traditionally, the houses in Southeast Asia used to have many openings and be open to the outside for ventilation. When air-conditioners are introduced, however, the residents close the openings to prevent the cool air from flowing outside. Unfortunately, the current air tightness of the residences is not usually enough and the energy consumption for cooling has been increasing. We have been investigating the indoor thermal conditions of the existing residences in Indonesia 3), 4). The measurement of the thermal environment and the questionnaire survey for the residents were carried out. The results of the field survey showed that the energy consumption of the residences installed with an air-conditioner was nearly twice as much as that in the house without an air-conditioner. In the houses with air-conditioners, at least one air-conditioner was installed in the bedroom, and the residents usually used it during night to have a comfortable sleep. Since the residents keep the air-conditioner on all night until they get up in the morning, the room temperature falls down around 23 degrees C during nighttime. Such a way of using the air-conditioner for sleeping will probably cause health problems like a cooling disorder, although not being recognized yet. This low temperature is the result of the low set point temperature. The temperatures reported by residents were from 18 to 26 degrees C, lower than the realized temperatures. Because the thermal resistance of houses is not sufficient, the room air cannot be reduced efficiently. Thus, the residents were obliged to set a lower target temperature, which resulted in a very low room temperature, along with long use of the air-conditioner. In order to both improve the indoor environment under the use of air-conditioners and decrease energy consumption for cooling, an effective use of the air-conditioners along with the design of the house suitable for cooling are highly required. In hot and humid climate, not only temperature but also moisture influences the energy consumption by air-conditioners. Since porous materials are used as building elements, the adsorption/desorption by the wall surfaces should be considered to evaluate the latent cooling load, which has a significant effect on energy consumption of air-conditioner. In this paper, using a simulation program that takes into account the operation of the air-conditioner and the adsorption and desorption of moisture by the building elements, the room temperature and humidity are calculated from viewpoints of energy consumption and indoor thermal comfort.
2. Area and climate The surveyed area is in Surabaya City (7 o S 113 o E) (Figure 1), which is located in the east part of Jawa Island in Indonesia. There are dry and wet seasons. The dry season is from April to November, while the wet season is from December to May. Figure 2 shows the monthly average temperature and relative humidity 5). The temperature ranges from 26 to 28 degrees C, with the annual mean temperature of 27.1 degrees C. The hottest months are October and November. The monthly average of the relative humidity is from 60 to 85%. This paper mainly reports the measured and surveyed results in February, the wet season. Equator Surabaya N Figure 1 Location of Surabaya, Indonesia Figure 2 Monthly average temperature and relative humidity (2001) 5) 3. Analysis of Thermal and Moisture conditions 3.1 Outline of Simulation The typical plan of the measured houses is shown in Figure 3. Two houses, one with and another without airconditioners are analyzed in this paper, the details of which are shown in Table 1. There are a living room (Room 2), a kitchen (Room 1), a bathroom (Room 4) and two bedrooms (Rooms 3 and 5). Also there is an attic space (Room 6). The materials of the building elements are listed in Table 1. The insulation is attached neither to the ceilings nor the roofs. In the house with air-conditioners, they are installed in the bedroom (Room 5) and the living room (Room 2). First, the heat balance of the rooms and building elements is simulated, and the energy consumption of the compressor is calculated. Then several methods to reduce the energy consumption for cooling are discussed. Five rooms and an attic (Room 6) are dealt with simultaneously in this calculation. Table 1 Material of building element Material (thickness) Clay tile (3cm) Plaster board (2cm) Finish (thickness) Roof Ceiling Wall Brick (12cm) Mortar (1cm) Floor Concrete (10cm) Ceramic tile (1cm) Figure 3 Typical plan of surveyed house 3.2 Mathematical model (1) Fundamental equations of heat and moisture transfer in porous materials Fundamental equations in the porous materials are equations (1) and (2) 6). These are the conservation equations for energy and moisture in a porous material that consists of solid, liquid water, vapor and dry air. It is assumed that the moisture transfer in liquid phase is negligible because of the low moisture content of the building walls. By making use of equations (3) and (4), equations (1) and (2) are rewritten by using temperature and humidity ratio as potentials. Although κ and ν are not constant, the constant values are used here (Table2). The boundary conditions on the surface of the walls are given as equations (5) and (6).
2 θ θ ω Energy balance: γ λ 2 ω c = + R (1) Moisture balance: γ X λ X c = 2 2 t x t t x t ω θ = κ X ν ω ω (3) and, κ =, ν = (4) t t t X θ θ boundary condition for energy: λ = α( θ θ ) + α sur R ( X Xsur ) + asurj x boundary condition for moisture: λ = α ( X X ) sur X x sur sur (2) (5) (6) t: time [s], θ : temperature [degrees C], c: heat capacity of material [J/kgK], γ : density of material [kg/m 3 ], λ : thermal conductivity [W/mK], R: enthalpy for phase change of adsorbed water [J/kg], ω : moisture content [kg/m 3 ], X: humidity ratio [kg/kg(da)], c : porosity [m 3 /m 3 ], γ : air density [kg/m 3 ], λ : vapor conductivity [kg/ms(kg/kg(da))], κ : moisture capacity to variation of humidity ratio [kg/m 3 (kg/kg(da))], ν : moisture capacity to variation of temperature [kg/m 3 K], a: solar absorptivity [-], J: solar radiation [W/m 2 ], α : film coefficient of heat transfer [W/m 2 K], α : film coefficient of moisture transfer [kg/m 2 (kg/kg(da))] Subscript sur: wall surface (2) Basic equations for energy and moisture balance of room The governing equations for the temperature and humidity ratio are equations (7) and (8), respectively. In calculating a room temperature (equation (7)), the following heat fluxes into the room are considered; the heat flux from walls (equation (9)), the heat flow by air exchange with outside or other rooms (equations (10) and (11)), the solar radiation (equation (12)), the internal heat generation by human bodies (equation (13)), and cooling by the air-conditioner (equation (14)). Regarding the moisture balance of the room (equation (8)), the vapor fluxes from walls (equation (15)), the vapor fluxes from the outside and the connecting rooms (equations (16) and (17)), the moisture generation from human bodies (equation (18)) and the dehumidification by the air-conditioner (equation (19)) are considered. θro 1 ρavro 1 = Qw + Qvo + Qvr + Qso + Qh + Qac t (7) X ro1 γ avro 1 = Mw + Mvo + Mvr + Mh + Mac t (8) where, Qw = α( θsur θro 1) A w (9) Qvo = ρavr vo( θo θro 1) (10) Qvr = ρavr vr ( θro2 θro 1) (11) Qso = Awi SC J (12) Qh = SH N h (13) Qac = ρav sup ( θsup θro1) (14) ( ) = α M w Xsur Xro 1 A w (15) vo = γ a vo1 o ro1 M = LH N (18) M = γ VR ( X X ) (19) h h M VR ( X X ) (16) Mvr = γ avrro ( Xro2 X ro1) (17) ac a sup sup ro ρ : volumetric specific heat [J/m 3 K], V: volume of room [m 3 ], Q: heat flux [W], M: moisture flux [kg/s], VR: amount of ventilation [m 3 /s], SC: shading coefficient [-], A: surface area [m 2 ], N: number [-], SH: sensible heat load [W/number of human], LH: moisture load [kg/number of human], Subscript a: air, ro: room air, o: outdoor, w: wall, 1, 2 : room number vo: ventilation between outside and room, vr: ventilation between rooms, so: solar, h: human, ac: air-conditioner, sup: supplied air, wi: window, (3) Mathematical Model for Air-conditioner Figure 4 illustrates the schematic diagram of an air-conditioner. Based on the heat and moisture balances of the refrigeration cycle, the air-conditioner is mathematically formulated 7). A heat balance of the heat pump is given as equation (20). The heat exchange at the evaporator (q E ) and the energy consumption by the compressor (L com ) are approximated as linear functions of the evaporation temperature ( θ r E ) and the condensing temperature ( θ r C ) (equations (21) and (22)). At the same time, q E and the heat exchange at the condenser (q C ) are expressed in another forms based on the heat exchange between the coil surface and the inlet air (equations (23) and (24)). The values, q E, q C, L com, θr E and θr C are obtained by solving equations (20)-(24) simultaneously. The supplied air temperature and humidity ratio are give by equations (27) and (29). Here, reheat of the inlet air is assumed. To simplify the expression, it is assumed that the supplied air is reheated by the coil of the condenser (equation (28)). qc = qe + Lcom q loss (20) qe = A1 θr + A2 θr + A 3 (21) L = B θ + B θ + B (22) q = G c ε ( θ θ ) (23) com 1 re 2 rc 3 E C ac C rc adc qe = Ga ζ [ ( 1 θ + 2)] E E hab C E as C (24) q = α ( θ θ ) E E r SI E E ase re (25) qc = α r SI ( θ θ ) C C asc r (26) θ = ζ θ + (1 ζ ) θ C sup E ase E ro (27) θ = θ + α SO ( θ θ ) (28) X = ζ X + (1 ζ ) X (29) sup sup ac C asc sup sup E ase E ro C
q: heat flux [W], L com: energy consumption by compressor [W], G a: air flow [kg/s], ε : temperature efficiency [-], ζ : contact factor [-], h ab: enthalpy of inlet air to heat exchanger [J/kg], α r : heat transfer coefficient on refrigerant side of heat pump [J/m 2 sk], θ r : saturation temperature of refrigerant [degrees C], θ as : saturation temperature of heat exchanger surface [degrees C], SI: inside area of heat exchanger [m 2 ], SO: outside area of heat exchanger [m 2 ], θ ad : dry-bulb temperature of inlet air [degrees C], A i, B i, C i(i=1,2,3): coefficients [-], Subscript C: condenser, E: evaporator, loss: heat loss Figure 4 Air-conditioning system 3.3 External Conditions The external temperature, humidity and the global solar radiation measured from 17th to 23rd February in 2001, are used as the input outdoor conditions (Figure 5). The measured solar radiation is separated into the direct and diffused components by assuming Bouguer and Berlage equations. The input data are assumed to change with a weekly cycle. The calculation is repeated until the ground temperature shows a cycle change. The outdoor temperature and humidity averaged over the measured period are used as initial conditions of the building elements, while the average outdoor temperature is used as the ground temperature at the depth of 5 m. heat capacity [J/ m 3 K] thermal conductivity [J/mK] X 10 3 Table 2 Material properties 7 porosity * air density [(m 3 /m 3 )*(kg/m 3 )] moisture conductivity [kg/ms(kg/kg(da))] X 10-6 κ (=dw/dx) [kg/m 3 (kg/kg(da))] X 10 3 ν ν (=-dw/dt) [kg/m 3 K] Concrete 1.6 1946 0.039 0.47 6.908 2.961 Mortar 1.4 2282.6 0.052 2.16 8.141 3.489 Plaster 0.22 975.63 0.065 0.47 3.97 1.702 board Soil 0.073 1587.6 0.039 0.47 6.908 2.961 Asbestos 0.062 27.6 0.0195 0.42 1.250 0.536 Tile 1.3 2616 0.052 0.45 8.141 3.489 Brick 0.31 1337.6 0.143 7.50 0.9 1.2 Insulation 0.045 84.9 0.845 0.87 2.77 0.002 Table 3 Air exchanges rate (a) Infiltration rate (a) Ventilation rate * House with air-conditioner House without airconditioneconditioneconditioner House with air- House without air- outside other rooms outside other rooms outside other rooms outside other rooms Room 1 2 20 6 20 Room 1 2 20 6 20 Room 2 3 9 8 12 Room 2 5 11 4 10 Room 3 2 2.8 5 5.7 Room 3 2 4.2 3 2.8 Room 4 1 8.5 2 8.5 Room 4 1 8.5 1 8.5 Room 5 2 1.4 5 5.7 Room 5 2 6.1 3 2.8 Room 6 3 0 3 0 * This value added that in (a) during the ventilation period. (a) Outdoor temperature (b) Outdoor relative humidity (c) Global solar radiation Figure 5 Input outdoor conditions
4. Simulated Results 4.1 Comparison between measured and calculated room temperature and humidity The material properties and the air exchanges rates used in the computation are given in Tables 2 and 3. The values of the air exchange rate were adjusted so that an agreement between the measured and calculated temperatures (not humidity) is obtained. The air-conditioners are installed in the living room (Room 2) and the bedroom (Room 5), if the house is air-conditioned. (1) House without air-conditioner First of all, the calculation for the house without air-conditioner is curried out to clarify the influence of the hygroscopicity (absorption/desorption) of building materials, for two cases. In Case A, the hygroscopicity is taken into account, while not considered in Case B. Figures 6 and 7 show the comparison between the measured and calculated temperatures and humidity ratios in Room 5 (bedroom) of the house without an air-conditioner. Since the values of the air exchange rate is decided so as to get a good agreement between the measured and the calculated temperatures in Case A, the calculated room temperature in case A is closer to the measured results than that in Case B. During daytime, the air temperature calculated in Case B is higher than that in Case A by 0.8 degrees K. This is because the ceiling temperature rises up during daytime due to the solar radiation, and also because the moisture evaporates at the ceiling surface and decreases the surface and room temperatures. Figure 6 Comparison between measured and calculated temperatures in Room 5 without AC Figure 7 Comparison between measured and calculated humidity ratios in Room 5 without AC Figure 8 Comparison between measured and calculated temperatures in Room 2 With AC Figure 9 Comparison between measured and calculated humidity ratio in Room 2 with AC Figure 10 Comparison between measured and calculated temperatures in Room 5 with AC Figure 11 Comparison between measured and calculated humidity ratio in Room 5 with AC
The humidity ratio calculated in Case A is also close to the measured value during daytime, while that in Case B is rather closer to the outdoor one. This is because that the ventilation between the room and the outdoor is dominant in determining the room condition in Case B, where the absorption/desorption is not considered. Also, a better agreement of the humidity ratio in Case A supports the validity of the present calculation. (2) House with air-conditioner Next, a house with air-conditioners is examined. Figures 8 and 9 show the room temperatures and humidity ratios in the living room (Room 2), and those in the bedroom (Room 5) are given in Figures 10 and 11. The temperatures of both Room 2 and Room 5 in Case B are higher than those in Case A due to the same reason as in the cases of the house without air-conditioners. On the other hand, the humidity ratio in Room 5 differs only slightly between Case A and Case B. This is because the operation of the air-conditioner is the determining factor of the room condition. Furthermore, the humidity ratio of Room 2 in Case A is closer to the measured value during daytime when the air-conditioner is not operated. This shows the influence of the hygroscopicity of the wall. (3) Influence of hygroscopicity From these results, it can be concluded that the calculated result considering the hygroscopicity of the walls can give a reasonable agreement with the measured results regarding both the temperature and the humidity ratio. The simulation considering the absorption/desorption in this section will be called Case 0 hereafter. 4.2 Improvement of Indoor Thermal Environment (1) Calculation conditions In order to improve the present situation, several simulations were carried out with the insulation and the air tightness changed, although the measured houses were neither insulated nor airtight. As criterion for an improvement, the energy consumption by the compressor is evaluated. Based on the surveyed results, it is assumed that the air-conditioner is used from 14:00 to 16:00 and from 21:00 to 5:00 AM, when the residents are assumed to sleep in the bedroom. The room temperature is controlled between 24.5 and 25.5 degrees C during air-conditioning period. An airconditioner is used only in Room 5 (bedroom). The air exchange rates in Table 3 are used. The infiltration rate is corresponding to the air exchange rate when the all openings are closed. From 6:00 AM to 18:00 PM, the openings are open for ventilation and the ventilation rates in Table 3 (b) are added to the values in Table 3 (a). The openings in Room 5 are closed when the air-conditioner is operated. In order to reduce energy consumption for the air-conditioner, the effect of the thermal insulation and the air tightness are examined for both cases where all rooms and the only air-conditioned room (Room 5) are changed. The simulated cases are listed in Table 4. For increasing insulation, an insulation with 5cm-thickness is put on the ceilings in Cases 1, 2 and 5~8. An improvement of the air tightness is assumed to be expressed as a reduction in the air infiltration rate. The air infiltration rates between the room and outdoor and between the rooms are decreased down to 0.5 times/hour during the nighttime and the operating period of the air-conditioning system. In Cases 3 to 8, even though the air-conditioner is used in Room 5, doors and windows in the other rooms are assumed to be open during daytime, in order to mimic the current situation in Indonesia. (2) Effect of thermal insulation (comparison between Cases 0, 1 and 2) Table 4 Simulated Cases Case No. Insulation Infiltration Room 5 Other rooms Room 5 Other rooms 0 1 X X 2 X 3 X X 4 X 5 X X X X 6 X X 7 X X X 8 X X X Figures 12 and 13 show the calculated room temperature and humidity ratio in Rooms 2 and Room 5 (Cases 0, 1 and 2). In Case 1, the insulation is put on the ceiling of the whole house, while to the ceiling only in Room 5 in Case 2. The temperatures in both Room 2 and Room 5 in Case 1, and that in Room 5 in Case 2 are kept lower than that in Case 0 (Figure 12), because of the insulation effect. The humidity ratio of Room 5 during an operation period of the air-conditioner in Cases 1 and 2 are higher than that in Case 0 by 0.3 g/kg(da). This can be explained as follows. The air-conditioner controls only the room air temperature, not the humidity ratio. By increasing the thermal insulation, the heat flow into the room decreases. Thus, the operating time
of the air-conditioner becomes shorter, and the amount of the moisture dehumidified from the room also decreases. As a result, the sensible heat load is reduced by 17 ~ 21 % while 15 ~ 20 % of the latent heat load (Figure 16). (3) Effect of air tightness (comparison between Cases 0, 3 and 4) Figures 14 and 15 show the calculated room temperatures and humidity ratios in Room 2 and Room 5 in Cases 0, 3 and 4. In Case 3, the infiltration rates between the room and the outdoor are decreased in all the rooms, while in Case 4, only the infiltration rates between the Room 5 and other rooms and between Room 5 and the outdoor are partially decreased. The temperature in Room 2 during nighttime is higher than those in the other cases. Although the outdoor temperature drops during nighttime, the room temperature can not fall down when the air exchange ratio is decrease. In Case 3 the air exchange rate between Room 5 and Room 2 is the same as that in Case 0, it leads the heat load of Room 5, and thus the sensible heat load is reduced only few percent in Case 3. Therefore, to reduce the heat lord, reduction in the air exchange rate of the air-conditioned room and an increase in the air exchange rate between the air-conditioned room are effective. In Case 3, the humidity ratio in Room 2 during nighttime is higher than other cases. This is because the air tightness causes the reduction of the moisture exhaust by the air exchange. In Case 4, the humidity ratio of Room 2 is slightly higher than that in Case 0. Since, the moisture in Room 2 cannot flow into Room 5 due to the increase in the air tightness of Room 5. The humidity ratio in Room 5 during the operating of the air-conditioner in Case 3 is lower than that in the other cases. This is caused by a longer operation of the air-conditioner. The temperature in non air-conditioned room becomes high in Case 3, and which makes the heat load in Room 5 larger. Then the air-conditioner must be operated longer, and it causes the humidity ratio lower. To increase the air tightness between the air-conditioned room and the outdoor leads to the reduction in the latent heat load by preventing the high humidity outdoor air from entering into the room. But, during nighttime, it is against reducing energy consumption by the air-conditioner to decrease the air exchange rates of all rooms without improving the air tightness between the air-conditioned room and the other rooms, since it is equivalent to air-condition all rooms. Although the air tightness is effective in the daytime, whether the air tightness should be increased or not must be decided in the night, taking the balance between the outside and set point temperatures into consideration. Figure 12 Calculated temperatures Figure 13 Calculated humidity ratios in Room 2 and Room 5 in Room 2 and Room 5 Figure 14 Calculated temperatures Figure 15 Calculated humidity ratios in Room 2 and Room 5 in Room 2 and Room 5
(4) Combined effect of insulation and high air tightness (Cases 5 to 8) Cases 5 to 8 are to examine the combined effect of the improved insulation and air tightness. Figure 16 shows the reduction rate in the electric power consumed by compressor, the sensible and the latent heat loads from the values of Case 0. The reduction of the energy consumption is small in Cases 5 and 7. Even though the air-conditioned room is insulated, a large air exchange between the air-conditioned room and the non air-conditioned room causes the high latent and sensible heat loads. Thus the energy consumption cannot be decreased. The reduction rates in Case 6 and Case 8 clarify that the improvement in the air tightness only in the air-conditioned room can reduce the latent heat load significantly. This is also seen in Case 4. The reduction by the combined insulation and partial air tightness amounts to 30 % in Case 6 (partial insulation) and 33 % in Case 8 (whole insulation). Figure 16 Reduction rate from Case 0 in sensible and latent heat loads, electricity consumption by compressor 5. Conclusion The thermal environment of the residences and the residents consciousness to the use of air-conditioner were investigated in Surabaya, Indonesia. Then the thermal environment of the air-conditioned rooms was numerically analyzed in order to evaluate and reduce the energy consumption. The simulation program takes into account the operation of the air-conditioner. To evaluate the influence of the moisture on the cooling load, the absorption and desorption by the building materials are considered. By considering the hygroscopicity of the building elements, the simulated temperature and humidity agreed well with the measured values in both houses with and without airconditioners. The simulated results showed that an addition of the thermal insulation to the ceiling was very effective in reducing the heat flow from the ceiling. In addition to insulation, increasing air tightness of the air-conditioned room could reduce an electric consumption by the air-conditioner, which is mainly caused by a decrease in the latent heat load. Even if the air tightness of the whole houses is increased, the latent heat lord is not decreased so much without the improvement in the air tightness between the air-conditioned room and the surrounding rooms. By the 5-cm-thick insulation on the ceiling and the partial reduction of the air infiltration rate of the air-conditioned room down to 0.5 times/hour, 33 % of the energy consumption is reduced. In hot and humid areas such as Southeast Asia, cooling energy consumption in residences is expected to increase rapidly in the near future. The typical Indonesian houses are designed poorly airtight and not insulated. This causes large energy consumption when an air-conditioner is used in the house. In order to save energy, not only the high insulation but also the partial air tightness are effective. Acknowledgements : This research was partially supported by Heiwa Nakajima Foundation, 2003. References 1) International Energy Agency IEA Energy Balances of Non-OECD Countries. 2000. 2) Statistics Indonesia http://www.bps.go.id/index.shtml, 2004. 3) Uno T., Hokoi S., Nastiti E. and Funo S. A survey on thermal environment in residential houses in Surabaya, Indonesia, Journal of architecture, planning and environmental engineering. - Architectural institute of Japan, No.564, pp.17-24, 2003. 4) Uno T., Hokoi S. and Nastiti E., Survey on Thermal Environment in Residences in Surabaya, Indonesia, Use of Air Conditioner, Journal of Asian Architecture and Building Engineering, Vol.2, No.2, pp.15-21, 2003.11 5) Japan Meteorological Agency (JMA) Monthly Report: From January to December 2001, Japan Meteorological Agency (JMA) 6) Hokoi S., Ikeda T. and Nitta K., Building environmental engineering Heat transfer, moisture transfer and ventilation-, Asakura, pp.103-112, 2002. 3 7) Ito K., Ohkouchi K. and Shibata K. Multiobjective Optimal Design of a Heat Pump System by Considering Partial Load for Air-Conditioning, Transactions of the Society of Heating, Air-Conditioning and Sanitary Engineers of Japan.- the Society of Heating, Air-Conditioning and Sanitary Engineers of Japan, No.29, pp.51-61, October 1985.