EXPERIMENTAL AND CFD STUDIES ON SURFACE CONDENSATION

Similar documents
Modeling of Ceiling Fan Based on Velocity Measurement for CFD Simulation of Airflow in Large Room

STACK EFFECT IN LIGHT WELL OF HIGH RISE APARTMENT BUILDING

Shuzo Murakami, Shinsuke Kato, and Taeyeon Kim Institute of Industrial Science, University of Tokyo Tokyo, Japan

Numerical Simulation of Ventilation Efficiency in Commercial Kitchen

MODELLING AND SIMULATION OF A ROOM WITH A RADIANT COOLING CEILING. Technicka 4, Prague 6, Czech Republic

Heat transfer and heating rate of food stuffs in commercial shop ovens

AIRFLOW PATTERN AND PERFORMANCE ANALYSIS OF DIFFUSE CEILING VENTILATION IN AN OFFICE ROOM USING CFD STUDY

SIMULATION ANALYSIS ON THE FRESH AIR HANDLING UNIT WITH LIQUID DESICCANT TOTAL HEAT RECOVERY

INFLUENCE OF SOLAR RADIATION AND VENTILATION CONDITIONS ON HEAT BALANCE AND THERMAL COMFORT CONDITIONS IN LIVING-ROOMS

developed, and parametric studies are conducted with the model. Based on the parameter study results, a dehumidification performance diagram is propos

Reducing energy consumption of airconditioning systems in moderate climates by applying indirect evaporative cooling

ZONE MODEL VERIFICATION BY ELECTRIC HEATER

Open and Closed Door Moisture Transport and Corresponding Energy Consumption in Household Refrigerator

INDOOR CLIMATE IN HEATING CONDITION OF A LARGE GYMNASIUM WITH UNDER-FLOOR SUPPLY/RETURN SYSTEM

Feasibility study of the passive solar room dehumidifying system using the sorption property of a wooden attic space through field measurement

Evaluation of a dynamic model for a cold climate counter flow air to air heat exchanger

The Research of Performance Comparison of Displacement and Mixing Ventilation System in Catering Kitchen *

power-saving period in summer, in which one of the indoor units was forced to change from a cooling mode to a fan mode, was introduced, and the effect

Control of temperature and humidity surrounding the stone chamber of Takamatsuzuka tumulus during its dismantlement

Numerical investigation on the effect of channelled and unchannelled screens on smoke contamination in atriums upper balconies with open upstand

Healthy Buildings 2017 Europe July 2-5, 2017, Lublin, Poland

EFFECT OF PAG OIL CIRCULATION RATE ON THE HEAT TRANSFER PERFORMANCE OF AIR-COOLED HEAT EXCHANGER IN CARBON DIOXIDE HEAT PUMP SYSTEM

Computer Simulation Investigation on the Effect of Channelled and Unchannelled Screens on Smoke Contamination in Atriums Upper Balconies

Energy-Saving Technology for Multi Split-Type Air-Conditioning Systems for Buildings

A Numerical study of the Fire-extinguishing Performance of Water Mist in an Opening Machinery Space

Air Distribution and Ventilation Effectiveness in a room with Floor/Ceiling Heating and Mixing/Displacement Ventilation

OPTIMIZATION OF VENTILATION MODE OF SMOKE CONTROL SYSTEM IN HIGH-RISE BUILDING FIRE

Healthy Buildings 2017 Europe July 2-5, 2017, Lublin, Poland

Simple Equations for Predicting Smoke Filling Time in Fire Rooms with Irregular Ceilings

FREQUENCY ENHANCEMENT OF DUAL-JUNCTION THERMOCOUPLE PROBES

The Experimental Validation of Numerical Modeling of the Air Distribution in the Indoor Ice Rink Arena

NUMERICAL SIMULATION OF FIRE SPREAD IN TERMINAL 2 OF BELGRADE AIRPORT. PO Box 522, Belgrade, Serbia and Montenegro

Some Modeling Improvements for Unitary Air Conditioners and Heat Pumps at Off-Design Conditions

Heat Transfer in Evacuated Tubular Solar Collectors

A Study of Drying Uniformity in a New Design of Tray Dryer

Numerical Analysis of Water Temperature Distribution in the Tank of. ASHPWH with a Cylindrical Condenser

STUDY ON TEMPERATURE, RH AND AIR FLOW VELOCITY DISTRIBUTION INSIDE THE GREENHOUSE EFFECT SOLAR DRYER

Smoldering Propagation Characteristics of Flexible Polyurethane Foam under Different Air Flow Rates

Experimental investigation of Hybrid Nanofluid on wickless heat pipe heat exchanger thermal performance

Numerical Simulation of Thermal Comfort Degree in Radiant Floor Cooling Room. Architecture, Beijing , China

Finned Heat Sinks for Cooling Outdoor Electronics under Natural Convection

4th International Conference on Sensors, Measurement and Intelligent Materials (ICSMIM 2015)

COMPARING AIR COOLER RATINGS PART 1: Not All Rating Methods are Created Equal

Effect of the Use Pattern on Performance of Heat Pump Water Heater

American Society of Heating, Refrigerating and Air-Conditioning Engineers

Thermal comfort investigation on a naturally ventilated two- storey residential house in Malaysia

Analysis of freeze protection methods for recuperators used in energy recovery from exhaust air

Aalborg Universitet. Diffuse Ceiling Inlet Systems and the Room Air Distribution Nielsen, Peter Vilhelm; Jensen, Rasmus Lund; Rong, Li

Compression of Fins pipe and simple Heat pipe Using CFD

AMOUNT OF MOISTURE PRODUCTION AND FIELD MEASUREMENT IN DRESSING ROOM

Study of Hot-air Recirculation around Off-road Tier-4 Diesel Engine Unit Using CFD Abbreviations Keywords Abstract Introduction and Background

Numerical study of heat pipe application in heat recovery systems

Global Journal of Engineering Science and Research Management

HOW TO REDUCE ENERGY CONSUMPTION OF BUILT-IN REFRIGERATORS?

Performance of an Improved Household Refrigerator/Freezer

NUMERICAL STUDIES ON BARE CABIN FIRES WITH OPERATION OF SMOKE EXTRACTION SYSTEM

EXPERIMENTAL STUDY OF AIR FLOW RATE EFFECTS ON HUMIDIFICATION PARAMETERS WITH PREHEATING AND DEHUMIDIFICATION PROCESS CHANGING

Open Cycle Liquid Desiccant Air Conditioning Systems Theoretical and Experimental Investigations

Leakage of Mildly Flammable Refrigerants into a Room

Effect of domestic storage and cooking conditions on the risk distribution in ready to cook meat products

PRELIMINARY STUDIES ON MECHANICAL SMOKE EXHAUSTS IN LARGE SPACE BUILDING FIRES

INTERNATIONAL JOURNAL OF APPLIED ENGINEERING RESEARCH, DINDIGUL Volume 1, No 4, 2011

Influence of temperature and drying air velocity on the kinetics of convective drying in the food industry

Simulation of Full-scale Smoke Control in Atrium

Numerical analysis of diffuse ceiling ventilation and its integration with a radiant ceiling system

New Convection Correlations for Cooled Ceiling Panels in Room with Mixed and Stratified Airflow

Analysis of Constant Pressure and Constant Area Mixing Ejector Expansion Refrigeration System using R-1270 as Refrigerant

Comparison of Thermal Comfort by Radiant Heating and Convective Heating

Numerical Studies On The Performance Of Methanol Based Air To Air Heat Pipe Heat Exchanger

An experimental study of the impact of tunnel suppression on tunnel ventilation

CHAM Case Study Numerical Simulation of a Air-to-air Cross-flow Heat Exchanger

STUDY ON THE EFFECTIVENESS OF AIR-CONDITIONING AND VENTILATION SYSTEMS BY CFD ANALYSIS IN HOUSES

Optimized Finned Heat Sinks for Natural Convection Cooling of Outdoor Electronics

Experimental Analysis of Open, Simple and Modified Greenhouse Dryers for Drying Potato Flakes under Forced Convection

Yan Xue 1 and Qingyan Chen 2,1* Abstract

Performance Comparison of Ejector Expansion Refrigeration Cycle with Throttled Expansion Cycle Using R-170 as Refrigerant

Feasibility of Controlling Heat and Enthalpy Wheel Effectiveness to Achieve Optimal Closed DOAS Operation

THE EFFECTS OF LEAKAGES IN ROOFS WITH VENTILATED AIR LAYERS - A CFD APPROACH. Zbynek Svoboda

Numerical analysis of diffuse ceiling ventilation and its integration with a radiant ceiling system

Implementation and testing of a model for the calculation of equilibrium between components of a refrigeration installation

PERFORMANCE MONITORING OF A HIGH-TEMPERATURE AIR-TO-WATER HEAT PUMP WITH INJECTION CYCLE INSTALLED IN A LOW-INSULATED SINGLE-FAMILY HOUSE IN BELGIUM

AR/IA/UP 241 Lecture 5: Psychrometrics

VENTILATIVE COOLING CONTROL STRATEGIES APPLIED TO PASSIVE HOUSE IN ORDER TO AVOID INDOOR OVERHEATING

Hot Water Making Potential Using of a Conventional Air- Conditioner as an Air-Water Heat Pump

Performance Evaluation and Design Optimization of Refrigerated Display Cabinets Through Fluid Dynamic Analysis

STUDY FOR SAFETY AT A RELATIVELY SHORT TUNNEL WHEN A TUNNEL FIRE OCCURRED

The Effect of Quantity of Salt on the Drying Characteristics of Fresh Noodles

A STUDY ON THE DEVELOPMENT OF A DEODORIZATION UNIT FOR THE TOILET BIDET

Don t Turn Active Beams Into Expensive Diffusers

CHAPTER I INTRODUCTION. In the modern life, electronic equipments have made their way

Comparison Simulation between Ventilation and Recirculation of Solar Desiccant Cooling System by TRNSYS in Hot and Humid Area

FROSTING BEHAVIOR OF FIN-TUBE HEAT EXCHANGER ACCORDING TO REFRIGERANT FLOW TYPE

Effects of Latent/Sensible Heat Separation Air-Conditioning and Natural Ventilation on Indoor Thermal Environment in Environment-Friendly Office

CHOOSING A FIRE VENTILATION STRATEGY FOR AN UNDERGROUND METRO STATION

THERMAL PERFORMANCE ASSESSMENT OF GREENHOUSE SOLAR DRYER UNDER PASSIVE MODE

Residential ventilation concepts based on the idea of displacement airflow distribution

IMPLEMENTATION OF DISPLACEMENT VENTILATION SYSTEM BY USING A WALL-MOUNTED AIR CONDITIONER

Experimental Study on Compact Heat Pump System for Clothes Drying Using CO 2 as a Refrigerant. Abstract

Scientific Principals and Analytical Model. Charcoal Cooler. Lisa Crofoot MECH 425, Queens University

The Use Of Attic Space For Cooling and Dehumidification

Transcription:

Eighth International IBPSA Conference Eindhoven, Netherlands August 11-14, 2003 EXPERIMENTAL AND CFD STUDIES ON SURFACE CONDENSATION Liu Jing 1, Yoshihiro Aizawa 2, Hiroshi Yoshino 3 1 School of Municipal and Environmental Engineering, Harbin Institute of Tech, Harbin, China 2 Technical Research Institute, Tokyo Gas Co., Ltd., Tokyo, Japan 3 Tohoku University, Sendai, Japan ABSTRACT Condensation and mold problems have been identified as one of the severest IAQ problems in Japan. Especially in the wintertime, moisture condenses on cold wall surfaces where it can cause deterioration of the building materials and mold growth related to allergic symptoms. This paper discusses the possibility of using the CFD method to solve condensation problems. Firstly, a CFD model for simulating condensation is developed, and then the validity of this model is examined experimentally. The results indicated that there is a good agreement between the experimental results and the model predictions. Then, the effect of ventilation on condensation risk is discussed using this model, and it is found that the condensation performance is significantly affected by the ventilation design. INTRODUCTION Condensation and mold problems have been identified as one of the severest IAQ problems in Japan. The reduction of ventilation levels for energy saving has increased these problems in many cases. Especially in the wintertime, moisture condenses on cold wall surfaces where it can cause deterioration of the building materials and mold growth related to allergic symptoms (Nielsen et al., 2000; Ekstrand-Tobin et al., 2000). To date, various studies have been carried out on the non-contact methods of measuring moisture condensation (Kubo et al., 1997), but complicated experimental apparatus and fairly skilled users are needed. Therefore, a computational simulation tool with acceptable accuracy would be very useful for solving these problems. However, when studying condensation by simulation, two very important points should be noted. 1) Many researches use multizone network models to study moisture-related problems (Ikeda et al., 1995; TenWolds, 1993), and do not take into account the temperature and moisture distributions which are very important considerations to investigate where condensation forms and its performance, and 2) For judging whether and when condensation occurs, the time-dependent condensation rate is needed in most cases, so an unsteady-state simulation method is necessary rather than a steady-state one. Based on the above, in this paper, a CFD model for simulating condensation is developed, and then is validated with experimental data. Although the effect of ventilation on condensation risk has long been recognized, excessive ventilation may increase the heating load and produce uncomfortably dry air in cold winter climates. This paper also discusses how ventilation affects condensation risk. VALIDATION EXPERIMENT ON CONDENSATION USING A TEST CHAMBER Figure 1 shows a schematic drawing of the test chamber with the measuring instruments for the validation experiment. The chamber was located in an environmental room, and was made of poly-vinyl chloride, which can be considered without adsorption/desorption effects. There was a lower (Vent1: FL +250 mm) and an upper vent (Vent2: FL +1250 mm) on the two opposite sides of walls. Air was heated prior to being supplied from Vent 1 into 1500 Vent1 1220 P1-7 -6-5 -4-3 -2-1 P2-7 -6-5 -4-3 -2-1 Vent2 1210 Measured point Measured Section Y=605 Figure 1: Schematic of the validation experiment within a test chamber (Unit: mm) - 577 585 -

the chamber, and exhausted to the outside by a fan which was located at Vent2. Hot wire type anemometers were used to measure the airflow rates through the vents. Water vapor was produced by an electrical immersion heater from a tray. A sensor was put into the water to control water temperature and the vapor generation rate. The weight of vapor was measured and calculated by an electronic balance. The time-dependent temperature and relative humidity were measured at 14 points within the chamber, by temperature-humidity sensors which were accurate to 0.5 degrees and 3.0%. Note that the measured section of temperature & humidity and the location of the tray are in the middle of the Y-axis (Y=605mm), differing from the section of the vents and fan (Y=970mm). The measurement conditions are summarized in Table 1. The experiment was divided into the following two periods, Period 1: About 240 min. The fan was run on to supply 25.2 degrees air into the chamber until the air temperature rose close to the steady state. During this period, the tray was covered to keep a steady vapor emission rate and heat flux when the next period started. Period 2: About 30min after Period 1. The cover of the tray was removed and vapor was released to the free stream air. Table 1: Measurement conditions Air temperature and 20 degrees humidity outside the 6.2g/kg (50%RH) chamber Vapor generation rate 101.3g/h Water temperature 70 degrees Ventilation rate 8.0m 3 /h (3.8h -1 ) Supply air temperature 25.2 degrees SIMULATION METHODS CFD Model The commercial Japanese CFD software STREAM4.0 was used in this study. A non-uniform mesh system was used with the finer mesh located in the near-wall region. The boundary and calculation conditions are summarized in Table 2. The simulation was divided into two parts according to the experiment, Table 1 Boundary & calculation conditions Turbulence model Standard k ε Model CFD grid points 39(X) * 47(Y) * 39(Z)=71487 Numerical QUICK schemes Exhaust The measured air velocity of the fan is used Supply Calculated with mass balanced Wall Vel.: Standard log-law Heat: Fixed convective heat transfer rate Moisture 2.6*10-5 m 2 /s diffusion coefficient D m Initial conditions The measured data Condensation model Surface condensation is assumed to form when the absolute humidity of ambient air next to the wall surface W sur is higher than the saturated absolute humidity according to the temperature of the wall surface W a1. The effect of adsorption and desorption is not considered in this model. The time-dependent condensation rate per unit area on a wall surface CON(s, t 1 ) and the accumulative condensation rate of the total wall surface SUMCON (t 1 ) at time t 1 are defined as: CON ( s, t1 ) = h [ Wsur ( s, t) Wa1( s, t)] dt (1) D t = t1 SUMCON ( t1 ) = CON( s, t1) ds (2) s In this paper, h D is calculated using the Lewis relation. h D ht 1 = (3) 0.67 ρc ( L ) p e The combined simulation method is shown in Figure 2. START CFD (calculate flow and temperature, moisture fields) Part 1: Steady-state simulation according to Period 1. Part 2: Unsteady-state simulation according to Period 2, whose initial conditions within the chamber were the results obtained by Part 1. Convergence W sur >W a1 Yes calculate CON (s, t1) and SUMCON (t1) No END Figure 2 Flow chart of combined simulation of airflow, moisture and condensation - 578 586 -

Case study Firstly, CFD prediction was carried out using the measurement conditions as shown in Table 1 for validation (Case1). In addition, to assess the effect of ventilation on reducing condensation risk, two parameter studies (Cases 2, 3) were carried out. Heat transfer due to moisture transfer was set as 500W/m 2 for all the three cases according to other experiments that will be reported hereafter. Computations were time-dependent, and the time interval was set as 0.5s. The total simulation time for each case was about 5h. 1) Case1: Validation with the experiment in the test chamber. 2) Case2: Discussion of the influence of ventilation rate on condensation performance. In this case, ventilation rate increases from 7.9 to 9.4m 3 /h (3.8h -1 to 4.5h -1 ) compared with Case1. Other simulation conditions are the same as those of Case1. 3) Case3: Discussion of the influence of ventilation strategy on condensation performance. In this case, air is exhausted from Vent1 and supplied from Vent2. Other simulation conditions are the same as those of Case1. RESULTS AND DISCUSSION Comparison between measured and predicted results (Case1) Firstly, Figure 3 shows the measured results of three vertical points at Positions 1 and 2 for Period 1. Note that because the tray was not covered completely, some vapor was released and resulted in the rise of humidity. Then this figure shows the comparison between the predicted and measured results for Period 2. The rise of temperature and humidity is due to the simultaneous temperature and humidity transfer. Because of the upward movement of supply air due to the exhaust fan and buoyant plume from the water surface, a vertical distribution with lower values near the floor and higher values near the ceiling can be observed for not only temperature but also humidity. There are differences of about 1.0 degrees and 1.4g/kg at the end of Period 2. After about 20 min, both measured and predicted humidity at the ceiling reached saturation point, indicating that surface condensation is likely to happen in this area. In general, the predicted results are in reasonable agreement with the measurements for temperature and humidity for Position 1 (the average relative difference between the simulated predictions and experimental measurements for temperature and humidity at 30min range from 0.9% to 4.8%, respectively), but some discrepancies can be seen for Position 2. Especially at the floor, both the predicted temperature and humidity is lower than the measured ones, and the relative difference is up to about 7%. Although velocity vectors were not measured, it can be concluded that compared with the experimental results, supply air can not reach the region of Position 2 in the prediction. This suggests that the effect of buoyancy on streamline curvature is over-estimated in the CFD model. Simulation of condensation by CFD (Case1) Figure 4 shows the CON(s, t 1 ) contours at t 1 =20, 30, 45 and 60min from the start of vapor production. In 24 Period 1 Period 2 24 Period 1 Period 2 Temperature[degree] 22 20 Temperature[degree] 22 20 18 18 0 120 240 250 260 270 0 120 240 250 260 270 18 Condensation happened at the ceiling 18 Condensation happened at the ceiling Period 1 Period 2 Period 1 Period 2 Absolute humidity[g/kg'] 15 12 9 Absolute humidity[g/kg'] 15 12 9 6 0 120 240 250 260 270 Time [min] 6 0 120 240 250 260 270 Time[min] Meas. (P1-1) Pred. (P1-1) Meas. (P1-4) Pred. (P1-4) Meas. (P1-7) Pred. (P1-7) Figure 3 Comparison between measured and predicted temperature and moisture variations (Case1) - 579 587 -

20min 30min CON(s,t 1 ) 45min (a) 60min (b) (c) (d) Figure 4 Predicted CON(s, t 1 ) contours for Case1 this paper, it is assumed that if CON(s, t 1 ) is below 1g/m 2 h (3*10-4 kg/m 2 s), it cannot cause significant damage to the wall surface. Although surface condensation was not measured directly, considering the reasonable agreement between the measured and predicted temperature and humidity distributions mentioned before, the prediction of condensation is expected to be acceptable. The results show that condensation happens in the corner near the ceiling firstly, then expands along the ceiling and the vertical walls. After about 45 min, the area of condensation does not change significantly. Because of the air movement by heated supply air, the temperatures of the wall surfaces near the fan and vents (i.e., the wall Y= max and X= min) are higher than those of other walls, and result in a lower condensation rate. Indeed, at the end of the experiment, significant water droplet condensation and frost buildup were observed at the regions corresponding to the simulation. Discussion of ventilation on condensation performance Figures 5 and 6 show the predicted CON(s, t 1 ) contours at 60 min after the start of vapor production for Cases 2 and 3 (compare with Figure 4 (d)). For Case2, as expected, CON(s, 60min) decreases as the supply flow rate increases. For Case3, CON(s, 60min) decreases significantly due to the change of ventilation strategy. Because the exhaust vent is moved to near the moisture source, moisture can be extracted directly to the outside instead of moving through the whole space, thus reducing the humidity levels near the ceiling. Figure 7 shows SUMCON (60min) at each wall and the total value of CON (60min) for all the cases. The total SUMCON (60min) value of Case2 and Case3 is only 26% and 20% compared with Case1, respectively. - 580 588 -

CONCLUSIONS A CFD model for simulating surface condensation has been developed and discussed. Based on the results and discussions, the following conclusions can be drawn: 1) The CFD model gives good agreement with the experimental results for simulating temperature and moisture distributions. It has been proved to be a powerful tool for studying the condensation risk and evaluating the impact of various parameters. 2) Except for the sufficient supply flow rate, the ventilation strategy has a marked effect on the moisture distribution and condensation performance. By placing the air inlet and extract positions appropriately, the condensation risk can be reduced significantly. REFERENCES Aizawa, Y., Liu, J., Yoshino, H. 2002. Study on Indoor Humidity Distributions, The 23rd Conference of the AIVC and the 3rd European Conference on Energy Performance & Indoor Climate in Buildings, pp.201-206 ASHRAE. 1997. ASHRAE handbook - fundamentals, pp.5.11-5.12, Atlanta Ekstrand-Tobin, A., Lindgren, S. 2000. Indoor Environment and Allergic Parameters before and after Renovation of Moisture Damaged Constructions, Proceedings of Healthy Buildings, Vol.3 Ikeda, T., Imanaka, M. 1995. Properties of Condensation and Effects of Hygroscopic Materials in a Dwelling House under Door Open and/or Close conditions, Nol.473, pp15-24 (in Japanese) Kuba, T., Miyamura, H., Tarumi, H., Okazaki, T. 1997. Measurement of Surface Condensation Using Multi-spectral Scanner, The 6th International Symposium on Building and Urban Environment Engineering and Management, pp.53-59 Liu, J., Aizawa, Y., Yoshino, H. 2002. Experimental and Numerical Study on Simultaneous Temperature and Humidity Distributions, 8th International Conference on Air Distribution in Rooms, Roomvent'02, pp.169-172 Nielsen, K. F., Nielsen, P. A., Holm, G. 2000. Growth of Moulds on Building Materials under Different Humidities, Proceedings of Healthy Buildings 2000, Vol.3 TenWolde, A. 1993. Ventilation, Humidity, and Condensation in Manufactured Houses During Winter, ASHRAE Transactions 99(1), pp.103-115 Figure 6 Predicted CON(s, t 1 ) contours for Case3 (t 1 =60min) CON[kg] 0.016 0.014 0.012 0.01 0.008 0.006 0.004 0.002 0 CON(s,t 1 ) Figure 5 Predicted CON(s, t 1 ) contours for Case2 (t 1 =60min) CON(s,t 1 ) Wall2 Wall4 Wall5 Wall6 Wall1 Wall3 Case1 Case2 Case3 Wall1 Wall2 Wall3 Wall4 Wall5 Wall6 Total Figure 7 SUMCON (t 1 ) and the total value for the three cases (t 1 =60min) NOMENCLATURE c p = specific heat at constant pressure, kj/(kg*k) - 581 589 -

CON (s, t 1 ) = condensation rate per unit area on a wall surface at time t 1, kg/m 2 s SUMCON (t 1 ) = accumulative condensation rate on a wall surface at time t 1, kg/s D m = moisture diffusion coefficient, m 2 /s h D = moisture transfer coefficient, m/s h T = heat transfer coefficient, W/(m 2 K) Le = Lewis number, dimensionless W a1 = absolute humidity of the air close to the wall surface, kg/kg W suf = saturated absolute humidity according to the temperature of the wall surface, kg/kg γ = latent heat of moisture vapor, kj/kg ρ = air density, kg/m 3-582 590 -