Expression of the radiative heat exchange for the human body and its application to modifying the original WBGT for outdoor environment

Transcription

1 Poceeing of Clima 27 WellBeing Inoo Expeion of the aiative heat exchange fo the human boy an it application to moifying the oiginal WBGT fo outoo envionment Kouhei Kuwabaa, Katunoi Nagano, Tohu Mochia an Yauhio Hamaa Hokkaio niveity, Japan Coeponing SMMARY In oe to calculate mean aiant tempeatue in an outoo envionment, we ha to calculate a hypothetical ky tempeatue fom iectly meauement o an empiical fomula of atmopheic aiation expee a function of aily mean ai tempeatue, ou amount, etc. The aim of thi eeach i to popoe new expeion fo imply calculating the aiative heat exchange in an outoo envionment. In thi pape, we efine the long-wave aiation coefficient bae on the atio of atmopheic aiation to long-wave aiation fom the goun to the human boy an eive lineaize aiative heat exchange equation in an outoo envionment to be expee only in the goun tempeatue an ola aiation. We qualitatively analyze the long-wave aiation coefficient an the aiative heat tanfe coefficient. Finally, bae on meaue ata in an outoo envionment, we popoe the empiical fomulae fo calculating the long-wave aiation coefficient uing ola aiation o the goun tempeatue. INTRODCTION It i neceay to epeent accuately heat exchange by long-wave an hot-wave aiation between the human boy an an outoo envionment in oe to evaluate themal an comfot enation of human in outoo envionment. The autho have aleay popoe a eie of effective aiant tempeatue a mean aiant tempeatue in an outoo envionment [] [2]. One i only bae on the iect aiation between the human boy an the uouning [], an the othe i bae on the multiple aiation between the human boy an the uouning [2]. The effective aiant tempeatue bae on the iect aiation equie etemining a hypothetical ky tempeatue by ue of the empiical fomula of ownwa atmopheic aiation efine a function of aily mean ai tempeatue, ou amount, etc. Theefoe, the calculation of the effective aiant tempeatue equie not only meaue ata but the meteoological ata. The effective aiant tempeatue bae on the multiple aiation equie calculating incience facto to ecibe the influence of multiple aiation by ue of linea imultaneou equation. Conequently, it i ifficult fo evaluation of an outoo envionment to calculate thee tempeatue on-ite. In thi eeach, to imply calculate a aiative heat exchange in an outoo envionment, we efine new long-wave aiation coefficient bae on the atio of atmopheic aiation to long-wave aiation fom the goun to the human boy, an popoe new expeion of the heat exchange by aiation between the human boy an an outoo envionment conieing ola aiation an the goun tempeatue. We qualitatively analyze the long-wave aiation coefficient, an popoe concete fomulae fo calculating the long-wave aiation coefficient by ue of meaue ata in an outoo envionment.

2 Poceeing of Clima 27 WellBeing Inoo METHODS In an outoo envionment, heat exchange by long-wave aiation occu between human an the goun, the ky an boy uface uch a builing. Beie, the outoo aiative envionment contain hot-wave aiation, pecifically, iect ola aiation, cattee ola aiation an eflecte ola aiation fom the goun an builing. The heat exchange R between human an the envionment containing hot-wave an longwave aiation i given a Equation (. We aume the builing uface tempeatue i equal to the goun tempeatue an only conie eflecte ola aiation fom the goun. R εg[ ( T ( Tg ]( f ef A ( + ε ε T T f H H ky [( ( ky ] ef ( = a{ f p I DN + I SH + ρ g I TH ( } f ef (2 whee R i aiative heat exchange [W], A i uface aea of othe human [m 2 ], ε i emiivity of othe human boy [N.D.], ε g i emiivity of goun [N.D.], i Stefan- Boltzmann contant (=5.67 * -8 [W/(m 2 K ], T i mean uface tempeatue of othe human [ C], T g i goun tempeatue [ C], i ky view facto fo the human boy [N.D.], f ef i effective aiant aea facto [N.D.], ε ky i emiivity of ky [N.D.], T ky i hypothetical ky tempeatue [ C], H, H an H ae iect, cattee an eflecte ola aiation abobe into boy uface [W/m 2 ], a i aboptivity of human uface [N.D.], f p i pojecte aea facto [N.D.], I DN i iect ola aiation to nomal plane [W/m 2 ], I SH i cattee ola aiation to hoizontal plane [W/m 2 ], ρ g i eflectivity of goun [N.D.], I TH i global ola aiation to hoizontal plane [W/m 2 ]. Figue how atmopheic aiation an the long-wave aiation fom the goun in an outoo envionment. Atmopheic aiation maintain a table conition uing any eaon. Long-wave aiation fom the goun vaie with the imate conition of ay. Boken line in Figue emontate the atio of atmopheic aiation to long-wave aiation fom the goun. The atio i itibute between.5 an.7. Atmopheic aiation Long-wave aiation fom goun (Tky+273/(Tg+273 Long-wave aiation [W/m 2 ] Open pace, aytime 5/9 5/22 5/23 5/2 5/25 5/29 5/292 5/3 7/26 7/262 7/27 7/28 7/282 8/3 8/ 8/5 8/3 8/3 9/ 9/2 9/ (T ky +273 /(T g +273 Figue. Long-wave aiation in an open pace in the aytime of Sappoo city

3 Poceeing of Clima 27 WellBeing Inoo We efine the atio Ω of atmopheic aiation to long-wave aiation fom the goun to the human boy a equation (3, an ty to implify the aiative heat exchange equation( between the human boy an an outoo envionment by ue of the atio Ω. ( Tky Ω = (3 T ( ( g whee Ω i atio of atmopheic aiation to long-wave aiation fom the goun to the human boy [N.D.]. in equation (3 enote configuation facto between the human boy an the ky, an i efee to a ky view facto fo the human boy. RESLTS Subtituting equation (3 into equation ( to eliminate T ky yiel equation (. R ( T {( Tg ( + ( Tky } f ef H A [ ] ( {( T ( + Ω( T ( } f ( H 2 ( T + ( + Ω ( 2 2 ( T g 2 g ( ( ( ( ( T Ω Tg ( T ( ( 273 ( Tg Ω + f ef ( H Defining equation (5 make it poible to efine linea aiative heat tanfe coefficient h in an outoo envionment a equation (6. λ in equation (5 expee the long-wave aiation popetie of the human boy pecific to the egion, ate an time, an i efee to a longwave aiation coefficient. h ( + Ω ( λ ef ( {( T + λ ( T }( { T + λ( T 273 } ε g g + (6 whee λ i long-wave aiation coefficient [N.D.], h i human linea aiative heat tanfe coefficient [W/(m 2 C]. The ue of the aiative heat tanfe coefficient h povie the lineaize aiative heat exchange between the human boy an an outoo envionment a follow: {( T λ( Tg } f ef ( H R = h (7 A Finally, convective an aiative heat exchange equation coniee othing inulation R i hown a follow: C + R = h c ( Tk Ta Ff A k (8 + h T λ T f F f H F f {( k ( g } ef ( whee A k i kin uface aea [m 2 ], C i convective heat lo [W], h c ae human convective heat tanfe coefficient [W/(m 2 C], T k i mean kin tempeatue [ C], T a i ai tempeatue [ C], F i themal efficiency facto [N.D.], f i othing aea facto[n.d.].

4 Poceeing of Clima 27 WellBeing Inoo If the long-wave aiation coefficient λ wee peliminaily calculate in each egion an time, the aiative heat exchange coul be calculate uing ola aiation an goun tempeatue. DISCSSION We qualitatively analyze λ an h. λ mean a coection facto to calculate the heat exchange by long-wave aiation uing goun tempeatue only. Subtituting equation (3 into equation (5 give equation (5. ( Tky ( T λ = (5 g Becaue the tem in bace on the ight-han ie of equation (5 i poitive, the long-wave aiation coefficient λ inceae with the eceae of the ky view facto fo the human boy an i oe to. Figue 2 how the vaiation of λ in epone to the vaiation of an (T ky /(T g. The long-wave aiation coefficient λ eceae with oe to an open pace, which mean the inceae of the ky view facto fo the human boy, an the eceae of (T ky /(T g. Figue 3 how the vaiation of linea aiative heat tanfe coefficient h in epone to that of the goun tempeatue T g an the long-wave aiation coefficient λ. The goun tempeatue T g in an outoo envionment ange appoximately fom to 5 C an the aiative heat tanfe coefficient h vaie with the vaiation of λ. Theefoe, it i ifficult to ega h a a contant value in an outoo envionment unlike an inoo envionment. The limitation of a tempeatue conition coul ega h a a contant value. Long-wave aiation popety λ [N.D.] Raiation ky view facto [N.D.] (T ky +273 (T g +273 = =.8 =.7 =.6 =.5 Figue 2. Vaiation of long-wave aiation coefficient λ Raiative heat tanfe coefficient h [W/(m 2 K] Goun tempeatue T g [K] λ=9 λ=3 T=Tg+5 T=Tg+ T=Tg+5 T=Tg Figue 3. Vaiation of aiative heat tanfe coefficient h We etemine concete fomulae fo calculating the long-wave aiation coefficient λ uing the ata of human expeiment. Human expeiment fo evaluating themal an comfot enation in an outoo envionment wee caie out fom 999 to 2 in Sappoo an Nagoya city of Japan [3]. The expeiment wee conucte on the oof of a ix-toie builing which coul be coniee an open pace, in a coutya uoune by fou builing in Sappoo city, an in a teet pace nea a thee-toie builing in Nagoya city. The ky view facto fo the human boy of the open, coutya an teet pace i, epectively,.5,.6 an.. Expeimental time wa 2 o 3 min, an mean value uing an expeiment wa ue. We imultaneouly meaue goun tempeatue an ola aiation, an ue fo calculating the long-wave aiation coefficient λ. Atmopheic aiation wa calculate fom empiical fomula of ownwa atmopheic aiation efine a function of aily mean ai tempeatue, ou amount, etc.[].

5 Poceeing of Clima 27 WellBeing Inoo Figue how the vaiation of the long-wave aiation atio (T ky +273 /(T g +273 in equation (5 in epone to that of global ola aiation. Rie in the goun tempeatue caue by inceae ola aiation eceae the long-wave aiation atio. Thee i no egional iffeence between Sappoo an Nagoya city. Howeve, the ange of the atio i appoximately. in epone to ame ola aiation. Theefoe, the long-wave aiation atio Ω of atmopheic aiation to the long-wave aiation fom the goun to the human boy epen on the eaon, ola aiation an ky view facto fo the human boy. Figue 5 how the vaiation of the long-wave aiation atio in epone to that of the goun tempeatue afte unet. Becaue the goun uface i exchange fo only the ky afte ak, thee i a popotional elation between the two. Thee i no iffeence in egion o pace which ha iffeent ky view facto fo the human boy. Long-wave aiation atio ange fom.6 to. The elationhip between global ola aiation an long-wave aiation coefficient λ in an open pace of Sappoo city i hown in Figue 6. Inceae ola aiation eceae the longwave aiation coefficient λ, a in Figue. Theefoe, the long-wave aiation atio efine a a function of ola aiation o goun tempeatue make it poible to calculate the longwave aiation coefficient λ uing ola aiation, the goun tempeatue an ky view facto fo the human boy. Long-wave aiation atio (T ky /Tg [N.D.] (T ky /T g = I TH R =.7 May Jul. Aug. Sep. Dec. Sappoo, open pace Sep. Dec. Jan. Jul. Aug. Nagoya, teet pace Sep. Dec. Feb. Sappoo, coutya pace Global ola aiation I TH [W/m 2 ] Figue. Relationhip between global ola aiation an long-wave aiation atio (T ky +273 /(T g +273 in aytime Long-wave aiation atio (T ky /Tg [N.D.] May Aug. Dec. Dec. Jul. Sep. Feb. (T ky /T g =.3T g -.22 R =.7 Jul. Sep. Sappoo, open pace Sep. Jan. Sappoo, coutya pace Aug. Dec. Nagoya, teet pace Goun tempeatue T g [K] Figue 5. Relationhip between goun tempeatue T g an long-wave aiation atio (T ky +273 /(T g +273 at night Long-wave aiation popety λ [N.D.] May Jul. Aug. Sep. Dec. Sappoo, Open Space Global ola aiation I TH [W/m 2 ] Figue 6. Relationhip between global ola aiation an long-wave aiation coefficient λ

6 Poceeing of Clima 27 WellBeing Inoo Equation (9 how an empiical fomula of the long-wave aiation atio bae on global ola aiation eive fom Figue. Equation ( how an empiical fomula of the longwave aiation atio bae on the goun tempeatue eive fom Figue 5. ( Tky At aytime: =.795.2I (9 T Afte unet: TH ( g ( Tky =.35T g ( T g.22 Calculating λ uing equation (9, ( an ky view facto fo the human boy make it poible to calculate the heat exchange by aiation between the human boy an an outoo envionment uing λ, the goun tempeatue an ola aiation. Howeve, thee empiical fomulae can be applie in moeate eaon becaue thee ae eaonal iffeence in Figue. Empiical fomulae coniee eaonal iffeence mut be etemine with etaile ata eaonally. CONCLSIONS In oe to imply calculate a heat exchange by aiation between the human boy an an outoo envionment, we popoe a linea expeion fomula of aiative heat tanfe bae on a long-wave aiation coefficient of the human boy. We qualitatively analyze the longwave aiation coefficient an the aiative heat tanfe coefficient, an eive concete fomulae fo calculating the long-wave aiation coefficient fom ola aiation, the goun tempeatue an the ky view facto fo the human boy uing human expeiment ata in an outoo envionment. The linea expeion fomula can be applie to the moification of the oiginal WBGT fo an outoo envionment [5], bae on a heat balance equation between the human boy an an outoo envionment [6]. REFERENCES. Kuwabaa, K, Mochia, T, Nagano, K, et al. 25. Effective aiant tempeatue inuing ola aiation, Envionmental Egonomic, Elevie, pp Kuwabaa, K, Kono, M, Mochia, T, et al. 2. Effective aiant tempeatue an opeative tempeatue inuing ola aiation, Poceeing of the 3 Intenational Confeence on Col Climate Heating, Ventilating an Ai-Conitioning, pp Kuwabaa, K, Hoikohi, T, an Mochia, T. 25. Evaluation metho fo themal an comfot enation in outoo envionment, The 3 Intenational Confeence on Human-Envionment Sytem, pp Kono, J, Nakamua, T, an Yamazaki, T. 99. Etimation of the ola an ownwa atmopheic aiation (witten in Japanee, Tenki, 38, Yaglou, C P, an Mina, D Contol of heat caualtie at militay taining cente, Ameican Meical Aociation Achive of Inutial Health. Vol.6, pp Kuwabaa, K, Mochia, T, an Sakoi, T. 27. Deivation an analyi of the outoo Wet Bulb Globe Tempeatue inex (WBGT with a human themal engineeing appoach Pat 2. Popetie of the WBGT fomula fo outoo conition with ola aiation. Clima 27. (