一拖二熱泵型空調(diào)器（KFR-30GW×2）設(shè)計(jì),一拖二熱泵型空調(diào)器（KFR-30GW×,2）設(shè)計(jì),一拖二熱泵型,空調(diào)器,kfr,30,gw,設(shè)計(jì) ORIGINAL O. Kaynakli E. Pulat M. Kilic Thermal comfort during heating and cooling periods in an automobile Received: 9 September 2003/Published online: 17 September 2004 C211 Springer-Verlag 2004 Abstract Most vehicles have a heating, ventilation and air conditioning (HVAC) device to control the thermal environments of interior of the vehicle. But, under hot summer season or cold winter conditions, it is dicult to achieve and maintain thermal comfort in an automobile from the start up to the steady-state conditions. During these transition periods, an understanding of human thermoregulatory processes facilitates the design and development of improved heating and cooling systems. This study presents a model of thermal interactions between a human body and the interior environment of an automobile. The model is based on the heat balance equation for human body, combined with empirical equations defining the sweat rate and mean skin tem- perature. Simulation has been performed by the use of transient conditions. The eects of both heating and cooling processes on the thermal comfort inside the automobile are investigated. Results are compared with the present measurements and available experimental data in the literature. It is shown that the agreement between the experimental data and the model is very good. List of symbols A surface area, m 2 c p specific heat, J/(kg K) CSIG cold signal f correction factor h heat transfer coefficient, W/(m 2 K) i segment number j air or fabric layers number k conductiveheattransfercoefficient,W/(m K) L heat load, W/m 2 m body mass, kg _m mass flow rate from per unit area, kg/(s m 2 ) M metabolic heat production rate, W nl number of layers covering segment p water vapor pressure, kPa Q heat transfer rate, W r outer radius of fabric layer R thermal or evaporative resistance, (m 2 K)/W or (m 2 kPa)/W S heat storage, W t time, s (unless specified in minutes) T temperature,C176C TS thermal sensation V air velocity, m/s w skin wettedness W humidity ratio, kgH 2 O/kg dry air _W external work rate accomplished, W WSIG warm signal x thickness, mm Greek symbols a ratio of skin layer mass to total body mass g permeation efficiency Subscripts a air al air layer b body bl blood cd conduction cl clothing cr core cv convection dif diffusion e exposed to convective and radiant environment ev evaporation O. Kaynakli E. Pulat M. Kilic (sk i C0C1 1 S sk iQ cr;sk iC0 Q cd iQ cv iQ rd iQ ev i 2 where, M rate of metabolic heat production, 7pt _W rate of mechanical work accomplished, Q res total rate of respiratory heat loss, Q cr,sk rate of heat transport from core to skin, Q cn ,Q cv ,Q rd rate of heat loss from skin to environment by conduction, convection and radiation respectively. S cr and S sk that denotes stored energies in core and skin layer causes instantaneous temperature changes in these compartments. These eects are ex- pressed with following equations: dT cr i dt S cr i 1C0 a mic p;b C0C1 3 dT sk i dt S sk i amic p;b C0C1 4 where m is the body segment mass, c p,b is the specific heat of the body. Q cv and Q rd terms in Eq. 2 are the heat transfers with convection and radiation and can be cal- culated with following relation: Q cv Q rd i T sk iC0T o iA e i R cl i 1=h cv ih rd f cl iC138 5 where, A e is the surface area of the body segments exposed to the environment (total area minus the area in contact with seat, back support, etc.), f cl is the ratio of the surface areas of the clothed body and the nude body. Operative temperature value (T o ) that includes average radiation and ambient air temperature is given as follows: T o i h rd C22 T rd h cv iT a h rd h cv i 6 For radiative heat transfer coecient the value of 4.7 W/(m 2 K) is used since it is suciently accurate for internal conditions 3 and convective heat transfer coecient values of each segment of the body are taken Table 2 Surface areas of the body segments 15 Body segments Segment number Surface area m 2 Fraction of total body surface area % Left foot 1 0.062 3.5 Right foot 2 0.062 3.5 Left fibula 3 0.140 8.0 Right fibula 4 0.140 8.0 Left thigh 5 0.160 9.1 Right thigh 6 0.160 9.1 Pelvis 7 0.080 4.6 Head 8 0.180 10.4 Left hand 9 0.050 2.9 Right hand 10 0.050 2.9 Left forearm 11 0.062 3.5 Right forearm 12 0.062 3.5 Left upperarm 13 0.077 4.4 Right upperarm 14 0.077 4.4 Chest 15 0.185 10.6 Back 16 0.204 11.7 The whole body 1.751 100.0 Table 3 Mass of the body segments 17 Body segments Segment number Mass (kg) Fraction of total body mass (%) Foot 12 1.16 1.45 Fibula 34 3.72 4.65 Thigh 56 8.00 10.00 Pelvis 7 6.78 8.48 Head 8 6.48 8.10 Hand 910 0.48 0.60 Forearm 1112 1.28 1.60 Upperarm 1314 2.24 2.80 Trunk 1516 32.98 41.22 The whole body 80.00 100.00 452 as described in de Dear et al. 8. The total latent heat loss from the skin due to evaporation, Q ev , is given by Q ev i wi p sk;s iC0p a C0C1 Ai R cl i=g cl LR1=h cv i f cl i LR 7 where, w is the wettedness ratio, p sk,s is the saturated water vapor partial pressure at the skin temperature and p a is the water vapor partial pressure in the ambient air, g cl is permeation eciency of the clothing and LR is the Lewis Relation which is the ratio of the evaporative heat transfer coecient to the convective heat transfer coecient. McCullough et al. 14 have been found an average value of g cl =0.34 for common indoor clothing. The total skin wettedness (w), includes wettedness due to regulatory sweating (w sw ) and to diusion through to skin (w dif ) is given by w sw i h fg _m sw i Q ev;max i 8 w dif i0:06 1C0w sw i 9 wiw sw iw dif i10 Maximum evaporation potential, Q ev,max occurs when the skin surface is completely wetted (w=1). In an automobile, a significant portion (1520%) of the body surface area is in contact with a seat, back support and steering wheel 5. This portion does not lose heat by convection and radiation. The heat loss from the skin due to conduction is given by Q cd i T sk iC0T int R cl i A cd i11 In the two-node model, heat exchange between the core and the skin occurs by direct contact and through the skin blood flow. A constant average thermal conductance, K cr,sk =5.28 W/(m 2 K) is as- sumed over the body. The heat flow from core to skin is as follows: Q cr;sk i K cr;sk c p;bl _m bl C0C1 T cr iC0T sk iAi12 The specific heat of the blood, c p,bl is 4,187 J/(kg K). Respiratory heat loss is approximately 10% of total heat loss 9. The heat loss due to respiration is given by Q res _m res c p;a T ex C0T a h fg W ex C0W a C2C3 A b 13 where _m res is the mass flow rate of air inhaled, T ex and T a are the exhaled air and the ambient air temperatures, respectively. W ex and W a are the exhaled air and the ambient air humidity ratio, respectively. The heat of vaporization (h fg ) is 2.4310 6 J/kg. _m res 2:58C210 C06 C0C1 M 14 T ex 32:60:066T a 32W a 15 W ex 0:02770:000065T a 0:2W a 16 The ratio of the skin mass to total body mass (a)is modeled as the following function of core to skin blood flow: a 0:0418 0:745 3;600 _m bl 0:585 17 The blood flow between the core and the skin per unit of skin area is expressed as _m bl 6:3200WSIG cr = 10:5CSIG sk C138 3;600 18 The rate of sweat production per unit of skin area is estimated by _m sw 4:7C210 C05 WSIG b exp WSIG sk 10:7 C18C19 19 The average temperature of human body can be pre- dicted by the weighted average of the skin and core temperatures: T b aT sk 1C0 aT cr 20 The neutral body temperature is calculated from the neutral skin and core temperatures in the same man- ner. The body is divided into 16 segments which are uni- formly clothed. The total thermal resistance and the total evaporative resistance for each segments are as follows 14: R t iR a i ri;0 ri;nl X nl j1 R al i;j ri;0 ri;jC01 R f i;j ri;0 ri;j C20C21 21 R ev;t iR ev;a i ri;0 ri;nl X nl j1 R e;al i;j ri;0 ri;jC01 R e;f i;j ri;0 ri;j C20C21 22 It is assumed that heat transfer through air layers between clothing layers occurs by conduction and radi- ation. In this case, thermal resistance of an air layer is given by R al 1 h rd k=x a 23 where x a is air layer thickness. The values of h rd and k were taken as h rd =4.9 W/(m 2 K) and k=0.024 W/(mK) 14. Similar equation can be written for the evaporative resistance. Evaporative resistance of an air layer is given by: 453 R ev;al a 1C0exp C0 x a b C16C17hi 24 where a and b are constants. The values of a and b are 0.0334 (m 2 kPa)/W and 15 mm, respectively 14. The outer surface exposed to the environment is treated a little dierently. The thermal resistance of the outer layer is then: R a 1 h cv h rd 25 The evaporative resistance of the outer layer can be determined from the convective heat transfer coecient and the Lewis Relation: R ev;a 1 h cv LR 26 2.2 Prediction of thermal sensation The above equations describe thermal exchange between the human body and the environment and thermoregu- latory control mechanisms. Combination of the thermal energy on the body, thermal load, aects the human thermal comfort in the thermal energy exchange (tran- sition) between the body and its environment. If the thermal load (L) on the body is nearly zero, then neu- trality or thermal comfort is achieved. Combinations of activity, clothing and the four environmental variables (air temperature, mean radiant temperature, air velocity and humidity) all aect thermal comfort. The most widely used thermal comfort index is the thermal sen- sation (TS) value is given by Eq. 27. TS 0:303exp C00:036M A b C18C19 0:028 C20C21 L 27 where A b is the total surface area of the body. The TS scale is given in the Table 4. 2.3 Assumptions and initials conditions Nude body surface area is taken as A b =1.751 m 2 . Body mass (m) is 80 kg and initial values of core and skin temperatures are taken as 36.8 and 33.7C176C respectively 3. Summer clothing insulation, winter clothing insula- tion, clothing area factor for summer clothing, clothing area factor for winter clothing and metabolic activity are taken as 0.5 clo, 1.5 clo, f cl = 1.1, f cl = 1.15 and 75 W/m 2 , respectively 5, 6. Table 4 Scale of TS values 0 thermal neutrality 1 slightly warm C01 slightly cool 2 warm C02 cool 3 hot C03 cold 4 very hot C04 very cold 5 painfully hot C05 painfully cold Fig. 1 Automobile interior air temperature during heating process Fig. 2 Temperatures inside the automobile and human body contact surfaces Fig. 3 Relative humidity values during cooling process inside the automobile 454 Local air velocities on the body is given in the Table 1 and mean air temperature (T a ) for heating and cooling processes is taken as given in Figs. 1 and 2. Relative humidity in heating period is taken as 0.35 5 and in cooling period it is taken as given in Fig. 3.Mean radiant temperature in heating period is taken as C22 T rd 0:94T a C01:38 and in cooling period is taken as C22 T rd C00:007752T 2 a 1:625778T a C06:879288: Surface temperatures of solids in contact with the body (T int ) in heating period (t is time from start-up in minutes) were 5: Seat T int 41 1C0exp C0t 4 C16C17C16C17 C020 for t C20 15 T int 200:367t C015 for t 15 Clothed area in contact with seat: 0.07 m 2 Back support T int C02030t for t C20 1 T int 14:61C0exp C0 t C01 5 C18C19 10 for 1t10 T int 22:20:065t C010 for t C21 10 Clothed area in contact with back support: 0.07 m 2 Steering wheel T int 40 1C0exp C0t 6 C16C17C16C17 C020 Clothed area in contact with steering wheel: 0.01 m 2 . In cooling period, surface temperatures of solids in contact with the body (T int ) are found as follows as a result of performed experiments. (where t is in minutes) (Table 5). T int at 2 bt c 28 3 Results and discussions In order to investigate the eects of automobile interior conditions resulted by heating and cooling process, the equations given in Mathematical model section are conducted to computer medium by using the program- ming language Delphi 6. For heating period, required experimental input data such as automobile interior air temperature and humidity, mean radiant temperature, seat, back support and steering wheel surface tempera- tures are taken from Burch et al. 5. In their experi- mental studies, interior air has been heated from C020 to 20C176C as seen from Fig. 1. Table 5 Constants in the Eq. 28 For t 2 For t2 ab c a b c Seat 3.10 C015.30 65.20 0.0051 C00.3870 46.0496 Back support 2.55 C013.65 62.10 0.0049 C00.3306 43.7763 Steering wheel 2.50 C016.00 67.00 0.0064 C00.4618 44.6285 Fig. 4 Comparison of body heat losses in heating process Fig. 6 Average body skin temperature in heating process Fig. 5 Comparison of thermal sensation during heating process 455 Required experimental data for cooling process are measured in 1991 Toyota Corona Sedan automobile equipped with a 2,000-cc engine. Automobile is parked in the sun and it is observed that the increase of tem- perature inside car is 64C176C with the ambient temperature of about 30C176C. Later, standard cooling process is started by running the air conditioning unit. During this process temperature inside car, relative humidity, seat, back support and steering wheel surface temperatures are measured. Measured parameters are shown Figs. 2 and 3. Since relative humidity decreases from 50 to 11% during the increase of temperature inside car to 64C176C, relative humidity in cooling process is started from 11%. Heat losses from body to the environment during warm-up process are given in Fig. 4 comparatively. Since the model of Burch et al. 5 and the present model exhibit some principal dierences (e.g., the body is divided into four segments in Burchs et al. 5 model, whereas it is divided into 16 segments in our model.), some discrepancies appear at the beginning period. Apart from this relatively small time interval, the agreement between the results can be acceptable range. Conduction heat losses to the seat, back support and steering wheel is rather low in comparison to the total value of convective and radiative heat losses because the areas of body segments in contact with solid surfaces are smaller than other body surfaces. In the beginning of warm-up process, conductive, convective and radiative heat losses are high since the temperature inside the automobile and the interior surface temperatures are rather low. Even total of these heat losses are higher than metabolic heat generation. For this reason, core and skin temperatures of the body a little decreases. But, the decrease in skin temperature is higher than the de- crease in core temperature. It is observed that rapid decrease in these heat losses due to increase in the tem- perature inside the automobile. In this process, body tries to keep respiration and evaporation heat losses in minimum to balance heat losses. Comparative variation of TS values in warm-up period is given in Fig. 5. By inspection of Fig. 5, there is a good agreement with the study of Burch et al. 5. These calculations are performed by considering the same conditions described in the experimental and analytical studies of Burch et al. 4, 5. In their experi- ments, TS values were obtained by using jury data, and the mean TS and standard deviation (r) of the jury data were calculated versus time. The present study calcula- tions are fall within the range of TS1r, and the value of r is given as 0.62. In the beginning, time heat losses from the body to the environment is very high due to low temperature inside the car. For this reason, TS indices that considers thermal load on the body has been started from very low values. And then, TS has improved with increasing inside temperature and interior surface temperatures. One of the parameters that indicate the eects of environmental conditions on human comfort during the warm-up period of automobile cabin is mean body skin temperature and its variation with time is shown in Fig. 6. In early minutes, average skin temperature instantly decreases due to very low temperatures of both inside the car and interior surfaces. Since temperature inside car increases with time, mean skin temperature increases after its values drops a minimum value of Fig. 7 Temperature of body parts that contact with solid surfaces in heating process Fig. 8 Heat flow between body and environment in cooling process Fig. 9 Variation of thermal sensation during cooling process 456 32C176C. Although average skin temperature gives an idea about the human comfort condition, it must be paid attention local discomforts on human body. The tem- peratures of back, thigh and hand of the body that contact with solid surfaces are given in Fig. 7. The temperatures of back and thigh are not much more aected from inside temperatures, and so they dont vary importantly. But the hand-skin temperature decreases to a value of 17.5C176C that can be evaluated as a rather low temperature. In literature, it is mentioned that hand-skin temperature of 20C176C causes a report of uncomfortably cold; and 15C176C, extremely cold 3. Heat transfer from the body in cooling process is given in Fig. 8. Since inside temperature and interior surface temperatures are high at the beginning, sensible heat flow (conduction, convection and radiation) occurs from environment to the body. This situation contrib- utes to increase in core and skin temperatures. To con- tinue vital functions and in addition to ensure comfort conditions, the heat from environment to body and metabolic heat generation of body must be emitted to environment. For this reason, body increases the sweat generation, and then a large portion of the body is covered by sweat. In this way, evaporative heat loss in- creases as shown in Fig. 8. Whereas respiration loss is not aected by ambient conditions and it stays about 10 W. The variation of TS for cooling period is given comparatively with Chakroun and Al-Faheds 7 study in Fig. 9. In Chakroun and Al-Faheds 7 paper, detailed ambient conditions were not given, so our model could not be applied directly to their measurement conditions. Therefore, this figure presents only a qualitative comparison. In their study, it is ensured the temperature inside car reaches up to approximately 65C176C by parking in the sun. Then, cooling process is investigated by running the A/C unit. But experiments are performed in relatively hot climate and ambient temperature is about 45C176C. However it is about 30C176C in our experiments. And the radiation from the sun is also stronger than our cases. For this reason, temperature profile inside the car is dierent and depending on this TS values are also dierent. In early minutes, due to high inside tem- peratures, heat is transferred from environment to the body by conduction, convection and radiation. For this reason, since the body has a significant thermal load, TS starts from very high values. Then, thermal load decreases with decreasing the temperature inside car and the surface temperatures and comfort condi- tion gets better. The variation of mean body, feet, and hand-skin temperatures during the cooling process is given in Fig. 10. In early times, since the temperature inside the car is very high (C2464C176C), the temperatures of the all body segments rise. But, the temperature rise of the hand that directly contacts with air is higher than other segments. Since inside the car cools with time this rise decreases. Hands are most aected from ambient conditions, so obvious decrease in tempera- ture occurs on hand. Similar situation is valid for head. Since shoes are important insulation element, feet are not aected from the interior temperature variations. For this reason, the highest temperature at the end of cooling process occurs at feet. Mean skin temperature of the body varies between hand and feet temperatures. One of the important parameters that aect the comfort sensation is skin wettedness and its variation with time is given in Fig. 11. At the early stage of cooling process, since temperature inside car is high, sweat generation rate is increased to increase heat loss from body. So skin wettedness on the body increases.