Thermal comfort during heating and cooling periods in an automobile.pdf

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 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 diffi cult 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 defi ning the sweat rate and mean skin tem perature Simulation has been performed by the use of transient conditions The eff ects 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 Asurface area m2 cp specifi c heat J kg K CSIGcold signal fcorrection factor h heat transfer coeffi cient W m2K isegment number jair or fabric layers number k conductiveheattransfercoeffi cient W m K Lheat load W m2 mbody mass kg m mass fl ow rate from per unit area kg s m2 Mmetabolic heat production rate W nlnumber of layers covering segment pwater vapor pressure kPa Qheat transfer rate W router radius of fabric layer Rthermal or evaporative resistance m2K W or m2kPa W Sheat storage W t time s unless specifi ed in minutes Ttemperature C TSthermal sensation Vair velocity m s wskin wettedness Whumidity ratio kgH2O kg dry air Wexternal work rate accomplished W WSIGwarm signal xthickness mm Greek symbols aratio of skin layer mass to total body mass g permeation effi ciency Subscripts aair alair layer bbody blblood cdconduction clclothing crcore cvconvection difdiffusion eexposed to convective and radiant environment evevaporation O Kaynakli E Pulat M Kilic sk i 1 Ssk i Qcr sk i Qcd i Qcv i Qrd i Qev i 2 where M rate of metabolic heat production 7pt W rate of mechanical work accomplished Qrestotal rate of respiratory heat loss Qcr skrate of heat transport from core to skin Qcn Qcv Qrdrate of heat loss from skin to environment by conduction convection and radiation respectively Scrand Sskthat denotes stored energies in core and skin layer causes instantaneous temperature changes in these compartments These eff ects are ex pressed with following equations dTcr i dt Scr i 1 a m i cp b 3 dTsk i dt Ssk i am i cp b 4 where m is the body segment mass cp b is the specifi c heat of the body Qcvand Qrdterms in Eq 2 are the heat transfers with convection and radiation and can be cal culated with following relation Qcv Qrd i Tsk i To i Ae i Rcl i 1 hcv i hrd fcl i 5 where Aeis the surface area of the body segments exposed to the environment total area minus the area in contact with seat back support etc fclis the ratio of the surface areas of the clothed body and the nude body Operative temperature value To that includes average radiation and ambient air temperature is given as follows To i hrd Trd hcv i Ta hrd hcv i 6 For radiative heat transfer coeffi cient the value of 4 7 W m2 K is used since it is suffi ciently accurate for internal conditions 3 and convective heat transfer coeffi cient values of each segment of the body are taken Table 2 Surface areas of the body segments 15 Body segments Segment number Surface area m2 Fraction of total body surface area Left foot 10 062 3 5 Right foot 20 062 3 5 Left fibula 30 140 8 0 Right fibula 40 140 8 0 Left thigh 50 160 9 1 Right thigh 60 160 9 1 Pelvis70 0804 6 Head80 18010 4 Left hand 90 050 2 9 Right hand 100 050 2 9 Left forearm 110 062 3 5 Right forearm 120 062 3 5 Left upperarm 130 077 4 4 Right upperarm140 077 4 4 Chest150 18510 6 Back160 20411 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 Foot1 21 161 45 Fibula3 43 724 65 Thigh5 68 0010 00 Pelvis76 788 48 Head86 488 10 Hand9 100 480 60 Forearm11 121 281 60 Upperarm13 142 242 80 Trunk15 1632 9841 22 The whole body80 00100 00 452 as described in de Dear et al 8 The total latent heat loss from the skin due to evaporation Qev is given by Qev i w i psk s i pa A i Rcl i gclLR 1 hcv i fcl i LR 7 where w is the wettedness ratio psk sis the saturated water vapor partial pressure at the skin temperature and pais the water vapor partial pressure in the ambient air gcl is permeation effi ciency of the clothing and LR is the Lewis Relation which is the ratio of the evaporative heat transfer coeffi cient to the convective heat transfer coeffi cient McCullough et al 14 have been found an average value of gcl 0 34 for common indoor clothing The total skin wettedness w includes wettedness due to regulatory sweating wsw and to diff usion through to skin wdif is given by wsw i hfg msw i Qev max i 8 wdif i 0 06 1 wsw i 9 w i wsw i wdif i 10 Maximum evaporation potential Qev maxoccurs when the skin surface is completely wetted w 1 In an automobile a signifi cant portion 15 20 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 Qcd i Tsk i Tint Rcl i Acd i 11 In the two node model heat exchange between the coreandtheskinoccursbydirectcontactand through the skin blood fl ow A constant average thermalconductance Kcr sk 5 28 W m2K isas sumed over the body The heat fl ow from core to skin is as follows Qcr sk i Kcr sk cp bl mbl Tcr i Tsk i A i 12 The specifi c heat of the blood cp blis 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 Qres mrescp a Tex Ta hfg Wex Wa Ab 13 where mres is the mass fl ow rate of air inhaled Texand Ta are the exhaled air and the ambient air temperatures respectively Wexand Waare the exhaled air and the ambient air humidity ratio respectively The heat of vaporization hfg is 2 43 106J kg mres 2 58 10 6 M 14 Tex 32 6 0 066Ta 32Wa 15 Wex 0 0277 0 000065Ta 0 2Wa 16 The ratio of the skin mass to total body mass a is modeled as the following function of core to skin blood fl ow a 0 0418 0 745 3 600 mbl 0 585 17 The blood fl ow between the core and the skin per unit of skin area is expressed as mbl 6 3 200WSIGcr 1 0 5CSIGsk 3 600 18 The rate of sweat production per unit of skin area is estimated by msw 4 7 10 5WSIGbexp WSIGsk 10 7 19 The average temperature of human body can be pre dicted by the weighted average of the skin and core temperatures Tb aTsk 1 a Tcr 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 Rt i Ra i r i 0 r i nl X nl j 1 Ral i j r i 0 r i j 1 Rf i j r i 0 r i j 21 Rev t i Rev a i r i 0 r i nl X nl j 1 Re al i j r i 0 r i j 1 Re f i j r i 0 r i j 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 Ral 1 hrd k xa 23 where xais air layer thickness The values of hrdand k were taken as hrd 4 9 W m2K 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 Rev al a 1 exp xa b hi 24 where a and b are constants The values of a and b are 0 0334 m2kPa W and 15 mm respectively 14 The outer surface exposed to the environment is treated a little diff erently The thermal resistance of the outer layer is then Ra 1 hcv hrd 25 The evaporative resistance of the outer layer can be determined from the convective heat transfer coeffi cient and the Lewis Relation Rev a 1 hcvLR 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 aff ects 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 aff ect thermal comfort The most widely used thermal comfort index is the thermal sen sation TS value is given by Eq 27 TS 0 303exp 0 036M Ab 0 028 L 27 where Abis 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 Ab 1 751 m2 Body mass m is 80 kg and initial values of core and skin temperatures are taken as 36 8 and 33 7 C 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 fcl 1 1 fcl 1 15 and 75 W m2 respectively 5 6 Table 4 Scale of TS values 0 thermal neutrality 1 slightly warm 1 slightly cool 2 warm 2 cool 3 hot 3 cold 4 very hot 4 very cold 5 painfully hot 5 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 Ta 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 Trd 0 94Ta 1 38 and in cooling period is taken as Trd 0 007752T2 a 1 625778Ta 6 879288 Surface temperatures of solids in contact with the body Tint in heating period t is time from start up in minutes were 5 Seat Tint 41 1 exp t 4 20for t 15 Tint 20 0 367 t 15 for t 15 Clothed area in contact with seat 0 07 m2 Back support Tint 20 30tfor t 1 Tint 14 6 1 exp t 1 5 10for 1 t 10 Tint 22 2 0 065 t 10 for t 10 Clothed area in contact with back support 0 07 m2 Steering wheel Tint 40 1 exp t 6 20 Clothed area in contact with steering wheel 0 01 m2 In cooling period surface temperatures of solids in contact with the body Tint are found as follows as a result of performed experiments where t is in minutes Table 5 Tint at2 bt c 28 3 Results and discussions In order to investigate the eff ects 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 20 to 20 C as seen from Fig 1 Table 5 Constants in the Eq 28 For t 2For t 2 abcabc Seat3 10 15 3065 200 0051 0 387046 0496 Back support2 55 13 6562 100 0049 0 330643 7763 Steering wheel2 50 16 0067 000 0064 0 461844 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 64 C with the ambient temperature of about 30 C 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 64 C 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 diff erences e g the body is divided into four segments in Burch s 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 TS 1r 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 improvedwithincreasinginsidetemperatureand interior surface temperatures One of the parameters that indicate the eff ects 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 fl ow between body and environment in cooling process Fig 9 Variation of thermal sensation during cooling process 456 32 C 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 aff ected from inside temperatures and so they don t varyimportantly Butthehand skintemperature decreases to a value of 17 5 C that can be evaluated as a rather low temperature In literature it is mentioned that hand skin temperature of 20 C causes a report of uncomfortably cold and 15 C 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 fl ow 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 aff ected by ambient conditions and it stays about 10 W The variation of TS for cooling period is given comparativelywithChakrounandAl Fahed s 7 study in Fig 9 In Chakroun and Al Fahed s 7 paper detailed ambient conditions were not given so our model could not be applied directly to their measurement conditions Therefore this fi gure presents only a qualitative comparison In their study it is ensured the temperature inside car reaches up to approximately 65 C by parking in the sun Then cooling process is investigated by running the A C unit But experiments are performed in relatively hot climateandambienttemperatureisabout45 C However it is about 30 C in our experiments And the radiation from the sun is also stronger than our cases For this reason temperature profi le inside the car is diff erent and depending on this TS values are also diff erent 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 signifi cant 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