Instructions for use Title Thermal Sensation Analysis and

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Thermal Sensation Analysis and its Application to AirConditioning
Ibamoto, Kan-ichiro; Nishi, Yasunobu
北海道大學工學部研究報告 = Bulletin of the Faculty of
Engineering, Hokkaido University, 46: 73-121
1968-01-29
DOI
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http://hdl.handle.net/2115/40854
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46_73-122.pdf
Instructions for use
Hokkaido University Collection of Scholarly and Academic Papers : HUSCAP
Therma亙 Sensation Analysis aitd its Appli’cation
to Air’Cond飯on豆ng
Kan−ichiro IBAMOTO＊
and
Yasu蔽obu NISH三＊＊
（Receivecl September 8， ！9．67）
Abstract
For half a century or more， many attempts have been made to establish therma／
conditions basecl on Nvhich optimal prorn．otjon of menta］ a．nd phy＄｝cal g． tate to a ta＄k
may be producecl． However， adequate scales of warmth． have not yet been proposed
inasmuch as the eomposition of theri：nal environment has been too complex to be
specified simply vvith a t−ew thermal factors．
RevievLiing the earlier workg． on the subject， some of them were conducted from
a niedical point of vievg’ v，Thile others were carried out froin an engin．eering ftc ngle；
the former， being empirical scales based on experiments， may not be appHcable
under tmusual conditions， and the latter， theoretica｝ scales based on thermal． equi−
librium， have its drawback in physical accuracy．
”1’his pat）er is concerned with the development of a rational comfort index and
its application to heating and air−conditioning．
1）art 1 deals with the fundamentals of heat and mass transfer between man and
environment， and a rational shape factor for rad；’ation will be induced．
In Part II， the heat bahc nce equations 1）etween man and environmen，t are estab−
Iished． ln the ca｝culation of the heat exchanges， mi an must be treated as a whoie
and mean values of each heat transfer coefficient ancl of each thermal factor must
be used． ll；’or such sinLplification of tliLe situatioii the physiological properties are
consul．ted． Further， into the experiment each o：” these approximations is verified．
Part III deals with a rational comfort index and its application． ’1”his index
evaluates each compon．ent of the therinal environment， such as ambient temperature，
racliant temperature， humidity， air−movement， heat ancl vapor resistan￠e and emissivity・
of clothing， work rate， and ．p． hysical properties of air．
Content
Part 1， Fundainental．s of IMIeat Tran＄fer
Cha．pter ！． Racliant luleat Transfer ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ．
75
1−！． Surrounding litacliant Temperature ． ． ． ． ． ． ． ． ． ． ． ． ．
75
！−L． Shape Factor between Sphere Eiement and Rectanguiar XIX，’all． ．
76
1−3． Shape Factor between Cylincler Element and Rectangular XVail
77
’［； Professor， 1）epartrnent of Environment Control．
＊’i‘ A＄si＄tant， 1’＞epartment of Environinent Control．
74
2
Kan−ichiro IBA）iiforro ancl Yasunobu ）N4TlsHI
1−4．
Comparison oLF Sha．pe FaL ctors ． ． ． ． ． ， ． ． ． ． ． ． ． ． ． ．
80
1−5，
Summary ．．．．．．．．．．．．．．．．．．．．．，．．．．
81
Chapter 2，
Convective Heat Transfey ． ． ． ． ． ． ． ． ． ， ． ・ a ・ ・ ・ ・ ・
81
2−1．
Physical Properties of Air ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ．
8！
2−2，
Convective Heat Transfer ． ． ． ． ． ． ． ． ・ ・ ・ ・ 一 一 ・ ・ ・ ・
82
LL3，
Convective Heat Transfer Coefficient for Cylinder ancl Sphere ．
82
ttL−4．
Combined Forced and Natural Convection ． ． ． ． ． ・ 」 ・ ・ J
83
2−5，
Eff’ect of Atmospheric Pressure to Convective lsuleat Transfer
Coefflcient ． ． ． ． ． ． ． ． ． ． ， ． ． ． ． ． ． ． ． ． ． ． ． ． ． ．
83
83
L）一（5．
Summary ．．．．．．．．．．．．．．．．．．．．．．．．．．
Chapter 3．
Evaporative Heac t ’1’ransfer ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ．
84
3−1．
Analo．gy between I Iass ancl Heat Transfer ． ． ． ． ． ， ， ． ， ，
84
3−L），
“’lass． Transfer Coe￡ficient ． ． ． ． ． ． ． ． ． ． ． ． ． ． ， ． ． ，
85
3−3．
Ei”iCect of Atmospheric Pressure on Evaporative lmleat Transfer
3−4，
Summary ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ， ． ． ． ． ．
86
Chapter 4．
Experimental Verification of the Analogy ． ， ． ． ． ・ ・ ・ ・ ・ 一
86
4−！．
Procedure ．．．．．．．．．．．，．．．．．．．．．．．．．．
86
4−2，
Results of Measurement ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ．
87
4−3．
Verification of the Analogy ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ．
88
4−4．
Convective Heat and iMass Transfer Coefficient for Short
Coefficient ． ． ． ． ． ． ， ， ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ．
4−5．
85
Cylindey ．．．．．．．．，．．．．．．．．．．．．．．．．．
88
Sulnmary ．．．．．．．．．．．．．．．．．．，．．．，．．．
89
Part II． Heat Equ三1量br三um on H．uman Bo（ly
Chapter 5．
Radiative and Convective 工｛eat Interchange ， ．
89
」一一1．
Racliant lnvleat Transfer Coefficient． ． ． ． ． ． ，
89
5−L，
Surrounding Rad三ant Temperature and Mean Ra（1iant
89
’1’einperature ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ・ ・
Chapter
C・ hapter
5−3．
Convective lmleat Transfer Coefficient ． ． ． ． ．
90
5−4．
E［，mCect of Clothing ． ． ． ・ ・ 一 ・ ・ ・ ・ ・ ・ ・ 一
90
5−5．
Summary ．．．．．．．．．．．．．．．．．．
6．
Evaporative Heat Loss ． ． ． ． ． ． ， ． ． ． ． ．
90
6一工．
．Vapor pressure over Sk三n Surface ．．．，、．
90
6−2．
Simplification of Saturated Vapor Pressuye
91
6−3．
Va．P・r Resistance・f Cloth三ng．＿．．
91
6−il．
Summary ．．．．．．．．．．．．．．
Thermoregulatory Mechanism of Man
9！
7一工．
Body Heat Production ． ． ． ． ・ ・ ・
92
7−2．
Body 1−leat Lo＄s ． ． ． ． ． ， ． ． ， ．
92
7−3．
Insensible Perspiration ． ． ． ． ． ． ．
93
7−4．
Sweat Secretion ． ． ． ． ． ， ， ． ， ．
93
7−5，
Eff’ect of Clothing on Sweat Evaporation
93
7nt6a
Heat Baiance Equation of IN（［an ． ． ． ． ．
7．
c9（）
92
cj5
．
Chapter
7−7．
Summary ，．．．．．．．．．．．．．．
97
8．
Experimentai Verification
97
8−1，
Procedure ． ． ． ． ， ． ． ． ． ． ． ． ， ． ．
97
8−2．
Experiment−A ． ． ． ． ． ． ． ． ． ， ． ． ．
98
8−3，
Experiment−B ． ． ， ． ． ． ． ． ． ． ． ． ．
cf Heat Balance至￡quとし￡ion
4 一 一 − 1
9fs
f 一
3
75
Thermal Sensation Analyg．is and its Application to Air−Conditioning
8−4．
Experiment−C ．．．．．．，．．．．．．．．．．．．．．．．
8−5．
Summary ． ． ． ． ． ． ． ． ， ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ．
9．9．
！oe
Part肌De・elopment・ξWarmth Diagram ancl its
Application to Air−Conditioning
Chapter 9．
Thermal Sensation ancl ｝vtlode｝ Sl〈in Temperature ． ． ． ． ． ．
． 100
9−1，
Definition． of Comfort ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ．
． 100
9−2．
F．xpression of Thermal Sensation ， ． ． ． ． ． ． ． ， ． ． ． ． ．
． 101
9−3．
Relat三〇n between Thermal Vote and Model Skin Temperature
． 101
9． 一4．
Temperature−Humidity Chart ancl Mode｝ Skin Temperature ．
． 10！
9−5．
Model Sl〈in Temi．）erature as a Scale of “Xarmth ． ． ． ． ． ． ．
． 103
9−6．
Sumlnary ． ． ． ． ． ． ， ， ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ．
． 104
Chapter 10．
Warmth I）三agram and三ts A．pplicac tion．．．．．．．．＿＿
． ／04
10−1．
Principle of XVarmth DiatT：．am ． ． ． ． ． ． ． 一 一 ・ J 一 J ・ ・
． 104i
工0−2．
Graphical Soluti・on of Adodel Sl〈in Temperature ． ． ． ， ． ． ．
． ｝05
10−3．
Warmt旧：）iagram ．．．．，．．．．．．．．，．．．．．．．
． 106’
10−4，
Evaluation of Thermal Env，lronnient with Warmth ll）iagram ，
． ！！4
10−5．
Summary ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ・ …
． ！15
Chapter 1！．
Comfort Detector ．．．．．，．．．．．．．．．．．．・・一
． 1！6
1レ1．
Mo（lel Man ． ． ． ． ． ． ． ． ． ． ． ・ ・ 一 J J … 一 … J
． ！！6
！1−2．
Thermal Sensation Coinputer ． ． ． ． ． ． ・ ． ・ i ・ ・ ・ 一 ・ ・
． ！16
Ii一 3． ．
Summary ．．．．．．．，．．．．．．．．，．．．・・…
． 1！7
AP正）end三x
A−1．
Discomfort lndex ． ． ． ． ・ 一 ・ 」 ・ ・ ・ ・ 一 一 ・ ’ ’ ’ ’ ’ ’
． ，！18
A−2．
Corrected Effective Teniperature ． ． ． ． ． ． ． ． 一 一 ・ ・ 一 ・
． ！1｛
A−3．
ITIeat Stress ln（lex ． ． ． ． ． ． ． ． ・ ・ ・ 一 ・ ・ ・ ・ ・ 一 ・ ・ 一
． 120
Part 1． Fundamentals of Heat Transfer
The funclamentals of heat transfer， which form the basis for expressing the
heat balance equation between man and environment， are summarized．
Chapter 1． Radiant Heat Transfer
1−1．
S泌rrounding R哉dia無もTemperat磁re
is enclosecl with several walls 〈！，2，3， i・・，n），
When a body O
the racliant heat，
O ancl absorbecl by wall 1， is given by
emitted from a body
Ω。一ε，パε。・一
I＆ゼ乱…隅÷273ン罫
（1−1）
In an analogous manner we obtain
2， ・＝・…ゼ斎3鰍・（7玉＋273 （！−2）
where ee， s，． ＝＝ emissivity of a bocly or wall
Se， Si ＝＝ surface area of a body or wall
goi ＝＝ shape factor for radiation between ac
To ＝ surface temperature of a body
body and wall
76
1〈an−ichiro IBsxMoTo ancl ’EE’asunebu INIsl−lf
4
Following Nusselti）， it is possible in． the first approximation to neg｝ect the refiection
from either surface． Then， with reciprecity theorem； goi’So＝＝g．io’Si＋
The quantity of heat exchange per unit time between O ancl 1， is given by
（20i．二＝εo・ε，，、・σ・た⑪1．・（7．b−T，）・Se・∼ρOl （！−3）
where ／e．，，． ＝＝ 100 ’i ・ i’（rll”， 一i一 273）2＋（T， 一t一 ：Lt73）L’／i（T， ＋273）＋（Ti ＋273’ ）111
Then， we get
（20ユ．＝αズ、・（s‘．tei’7”e−geoi・ ”Ll’1）・ Se （！−4）
where cv．， ＝一 c一，，，・c−o・o・leoi r一”’ raclia・nt heat transfer ceefficient
feot”一一tA7’＝ 20ec
A7’二10℃
1・4 ∠ユ7需 5℃
L2
1．O
O−8fito 20 30 40 so ec rJ
Fig． 1−1． Factor 1；／oi and soiid body・ t’einperature
From Fig．1−1 we kn．ow that factor々。1 can be treated as a constan．t value in
common use． Thus， the quantity of heat exchange per unit time between． body O
and solid walls may be w．ritten by
ね
Ω01＋（202＋…÷（20。 ＝＝ a’、、・σ．”， 一Σ SOeガ7．1，か30 （レ5）
玉．
where（Y．1≒・α、．、≒…≒・α，。、藻α，，
Here， t1ユe surrounding radiant temperature is de責ned by
マと
7．∵一Σρ。ガ7．’，、 （！…6）
1
Ancl w．e get simply
H，、＝α、．・（7一』一つr．∵） （！−7）
w．here ll，．：quantity of radiant heat fiow between body O and its
enclosure， per unit time per unit area
1−2。Shape Factor between Sphere Element and Rec￡angular Wall
Generally， it is impossible to determine the shape factor betva・een arbitrary
surface elemerLts．
The shape factor for the geometrical arrangement， shown in Fig．レ2， is given
by the equati・n．
嚇……’マf綴瓢あ・．tttt （・一8）
5
’lkermal Sensation Analys． is and its Application to Air−Conclitioning
ち
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HIII
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LX．．
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；24681245βノ0り
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Fig． 1一一z． Shape faetor betxxreen sphere e｝einent and rectangular xvall
1−3． Shape Faetor between Cylind．er Element aRd． ReetaRgle
It is only an， expedient to regarcl man as a sphere eleinen．t． The authors try
to originate a new shape facter， considering man to be a cylincler element．
As shown in Fig． 1−3， turning the siiaall area element 1 around its vertica｝
axis， it may compose the cylinder element． Fig． ！−3 clenote the geometricai
relation．
JZL
争8
2
，
茶ﾀ9！0ρ0
曲／η8η話2
w
θ
θ
o〃
rt
∠
配。
擢gZO〃θ
θ々卯θρ’1
θ
α
θ一ご・が1薯
，
T910η
4
一チ・θ 一チ
Fig． 1−3．
Elevation view o’f area el．ement 1 ancl rectangular area element 2
78
Kan−ichiro IBfuMo’i’O and Yasunobu NlsHI 6
Let element ！ revolve from angular co−ordinate （一r，／2）
（1）
Region A The shape factor may be written by
（φ・2）1一髪［・…七諾τ・・t・ガ1家賃劉
一 tan’i （一一S一一……… sin cr） ＋ sin ex・tan−i・一tl一一一一］ （1−9）
（2）
Region B ln the interval （一一一C／…一…一＋eN一／／一一） all of the radiant energy leaving
element 1 will arrive at the wall 2． The shape factor is given by
（φ12＞引・・…相舞ア・…一1諾ガマZ・畢碗一・一∵諸謝
＋・・…｛…一・昊マZ爺r・・一…∵論ぞ｝1 （且・）
N
乙
io
1
ト 1一一1
1 一1一一｛
1一
1
O， 112
1
1
8
6
8
1
4
［「
→
＼
0．ll
、
1
L
卜 、＿へ ＼
1＼、
、
ト
＼＼ ＼
O，ノ05
＼＼＼
lt
0，io
2
＼＼
h T
mJJ く 1㌃一
O，OPs
、、、
↓lii『
O，09
0．OBs
O．D8
1＼吏4
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0．07
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A
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ae6 ’
．6
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O， 05
＼
0， 04
＼＼ ＼
＼＼
D．D3
一＼
冥
＼
＼＼ ＼
．2
T＼
ao2
＼＼、
＼＼
＿＿上1
、
0．0／5
＼鮎
・1．ノ
1
i
1
＼
0．oi
．2 ．4 ．6 ．B l 2 4 6 6 10
泌
ム
Fig． 1−4．
Shape factor between cyllnder element and verticai rectangle
7
79
Thermal Sensation Analysis and its Application to Air−Conditioning
（3） Region C The shape factor can be written by
（ψ・2）・一［・…嶺鴛・t・・…1諾ア、
＋＿」L＿…。t。n．．阻＿。互＿＿ト＿一斗＿＿t。。田・＿と璽．皇J
v”i”i”’＋””i）’V”’i’ LL’LL’ ，f’i”i”1””lv2”’V’1 ’2”t／”’IZ）’i” “一’A’ v’II’1；”一2＋＋ILi’1
一・・nα・≠翻・n4マ十二亜＋・・ガ1（H ．一一一…一 sm cr五）1（ト・・）
By integrating （￠’i2）i， （￠i2）2 ancl （￠’i3）3 over their defined regions and averaging by
￡he angle at the circumference， we get the new shape factor by the equation
gi2 ＝ ’／’．，．’；’ ［2 Slll！，，；etan’i（Q 一 sin ev）cicr
÷寓よ羊ゴ・1惜趨1鍔1些1暮宰1購葦留ゴ
・洗雛‡1器；職l11需1訓 （レ・2）
wh。，e PJ尼田，Ω一…μ
．乙 ゐ
h
lo
8
6
to
4
z
h
2
ノ
．8
．6
．4
．2
『ノ
，ノ
．2 ．4．6，8／ 2 468／O
z
h
Fig． 1−5ゆ
Shape fac ctor between cylinder eleinent and horizontal rectangle
8e ． Kan−ichiro IBAMo“ro and Yasunol）u NISHI 8
1−4． Comparison of Shape Factgrs
The characteristics of the shape factor for sphere element and cylinder element
may be made clear by． the following example．
Example 1−1． Determine the shape factor between sph“vre or cylinder element
and rectangular wall （1，2，3，・4・）， shown in Fig． 1−6．
2
2
B’
ご
（2）
A■
（11 グ
β
M ．；
日 O
沌
Li
2＼こ
2
2
∠）
o
2
‘
i
（4）
l
I
」
1・
〆
5
戸
5
石
〈3）
2
〃
o
2
2
o’
2
Fig． 1−6． Geoinetrical arrangement betw・een a body and walE
Solzttion： Each of the shape factors is shown in Table 1−1．
The example mal〈es clear the followings．
（1）
The difference between each of the shape factors is apparent．
（2）
If the wall area and the clistance are the same， each of the shape factors
between the cylincler element and the configurations， shown in （3）， （4）， is
different． These relations give a clear basis for racliant heating in practice．
Table 1−1．
shape factor for sphere
9
PiA ＝： O．0！6
1 o，ofs4
（1）
9二二4・望1A
shape factor for cylinder
望圭A二〇．Ol9
0，076
9 ：＝： 4・ 9，1．t
∼ρ1A’二皿0．0！6
vr・ 1 ．・x ， ＝： O．012
1 o．064
（L））
tコ腿4・∼，1A’
0．048
9＝4 ’ 9”1．x． r
∼銭E＝一・ O．｛） ！9， 9，IF二二G．040
SP｝E二〇．01．6， 硲1F二＝0．033
（3）
0．118
O．098
F・ ＝，＝ 2・ 91E十2 ・ 91 1・7
sp’ 一，：： 2・ s・：，111・ 十2 ・ 9’1 lr
91Ei＝O．0／9， “f，IF，＝（），O：34
∼ク｝E’嘉O．（）i6， 撃フ1F・＝0．033
0．098
（4）
亨り＝・ 2・幹1E’十2・Y’TIF’
9
O．10C5
9．；・・ ＝2 ・ L’，’；・1・flJ十2 ・ S／ilI．，t
9
81
Thermal Sensation Analysis and its Application to Air−Conditioning
1−5． Summary
The problems on radiant heat transfer， especially shape factor， have been． sum−
marized and the authors have proposed a new・ shape factor between cyiinder element
and rectangular wall．
Reference
ユ．＞ Gr6ber，王一1．，￡rk， S．
and Grittul］，
I．J， ： Fundanientals of lileat IXransfer， （1961）， p． 454， Mc（）’raNv一一
1−lijJ．
Chapter Z． Convective Heat
Transfer
2−1． Physical Properties of Air
The infiue．nce of temperature， humidity ancl
atmospheric pressure to some
physical properties of air are summarized in Table
2−！．
Table 2−1．
lnfluence of teniperature， huiniclity and atinog．pheric．
pressure to phy・sical． properties of air
atm． pressure
alr telnp．
hurrユid玉ty
density
ev三dent
evident
little
VISCOSItY
little
litt｝e
．1．i．ttle
kinematic viscosity
Fi／．／r． 2−！
Figr． 2−1
little
specific heat．
little
］ittle
little
heat concluctivgty
a lit宅le
little
litt｝e
ther．nial c｛i’ait‘：usivity
llAif，．，・f． 2−2
Fig． 2−2
little
mass diffusivity
Fi，．／r． 2一・／／i
F三9．2−3
nes，lis，ible
Prancltl nttml’）er
nes．］ig．iible
negi三9三ble
negligible
Sehmlclt number
negligible
ne／gligibie
negi三9三ble
‘つ
．一．眠．．γ
級プ励争
，．一e ．．
xt，v m’；’S
．xO
v’
n
2／3 aim
Z．S oim
き
ミ
：5
旨
ミ
誌
ミ3a
．寒
エ
ミ20
り
短
8
’σ如
．窒
ミ
ち
ミ 1♪
聖
20
桑
ノ0
2aim
Sb ！0 20 3び 40 5卿
tt・a 20”’30”’ 4・o so oo
Ofr temperoture
・7’．！ど．8’脚砂ピ．酬．8
Fig． 2−1． Kinematic viscosity ef air
Fig． 2−2． Thermal dif±’usivity of air
82
Kan−ichiro IBAMo’1’o and 1（’asunobu tNlsl−II
IO
’w「％蕗
5グ
磐6伽
ぎ
g；o
建
30
t atm
20
2adcr
io
5グ曽
σ〆、弓岬9．．v加
Fig． Z−3．
1∼4aSS CIittiUSiV三tV Qf Wateτ VaりOr illtQ a｛r
It is known that clensity， kinematie visccsity， thermai diffusivity ancl mass
’diffusivity are affected by atmespheric preew・sure， but little by humidity．
2−2． Convecti’ve Heat Transfer
Natural convecticn is causecl by the density cl’ifference of the air between
heated surfac ces and fiuicl． Otherwise forced cenvection is caused on the air fiow．
The rate of the heat transfer by convection between a soiid boundary and fiuticl
may be evaluated by means of the equation
耳，一αc・（7．1．，一η （2−1）
where ff． ＝＝： quantity of ｝ieat transferecl by convection per unit time
per umt area
cr． ”一 convective heat transfer coefficient
7’1．， ：＝＝ temperature of solicl bounclary
T，， ＝ fiuicl temperature
The above equation is a de丘nition of出e cOnvective heat transfer coe缶cientα、，．
The convective heat transfer coefficient is a complicated function of the fluicl
fiow， the thermal properties of the fluicl medium and the geometry of the system．
2−3． Convec重董ve Heat TTansfe測 CoerHeie睡t fol’Cy旦圭聾（迂er an｛亘SpheTe
Hilpelt summarized the perimeter−mean Table 2−2．
heat transfer coeflicients for the fiow of air value． of “m” and “Cf・1）i“t’”’ 1／or Eq．（2−2）
W㎞箆鎌総｝1愚1。。一騰1億
ll
Thermal Sensation Analysis and its Appiication to Air−Conditioning
83
Cf， m， n w shown in Tab！e 2−2
Ranz ＆ Marshall correlatecl the heat transfer coeflicients of air flow over
a sphere by the equatioR of the form3）
Nu 一一 2．0＋O．6・Prg・Rei 1〈 Re〈7× ！04 （2−3）
2−4． Combined Forced aRd Natural Conveetion
In any heat transfer process density gradients occur and in． the presence of
a forced field natural convectien currents arise． lf the forced convection． effect is
very large， the influence of natural convection currents may be negligible． When
the forcecl convection effect can be neglected the convective heat traRsfer ccefllcients
are given by the equation of the form
Nu＝＝！（Pr Gフう （2−4）
where Gr＝Granshof number
An analysis of the investigation of heat transfer over a small sphere by Yuge
states that if the velocity of air flow exceecls 3 cmfs the effect of natural convec−
tion current over the sphere of 30 cm in cliameter is neglectecl．‘）
2−5． Effect of Atmospheric Pressure on Convective Heat Transfer CeeMcient
As Eq． （2−2＞ involves some physical properties of air， at another atmospheric
pressure region the con．vective heat transfer cce伍cient takes the other value， as
shown in Fig． 2−4．
川竹防r・Deg
25
ぬ
§20
の’〆加露rof30αη4わ〃θどθr
V砂かz勘ビ伽卿ど〃∂；勿℃
違
8
蓮J5
凄
ミ
Totσ
遠
く ∼0
ミ
lo糎
６顔
§
§5
OV．1
i
Zf，？一2 ’bl’3”r一’n’S” ”’b．’i5 ／’ i． s 2 3 m／s
air vefoclty
Fig● z−4ゆ
Effect of atinospheric pressure to convective heat t’ransfer
ceefflcient
2−6． Summary
Estimating the rate of convective heat traBsfer over the human body， the
fol｝owings must be considered．
84 Kan−ichiro IBAMoTo and Yasunobu NISHI 12
The magnitude of the natural convection effects to forced convection may be
neglected．
The fact that the atmospheric pressure affects the convective heat transfey
coeflicient suggests that the design of thermal environment in a pressurized cabin
for medical care or in a low pressure space capsule must be differentiated from
common design．
References
2） ltsyZcAdams， XXi． lrml．： Heat Transmission， 3rd． ed．， p． 260， McGraw−Hill．
3）Gr6ber， H．， Erk， S． an（l Gr三gull，導．：Fundamentals Qf Heat Transfer， p．412， McGraw一田．L
4） Yu，ge， T．： Heat Transfer Experiment over Sphere， Annual Meeting of the Jap． Soc． of
）vlech． Eng． （1956 April）．
Chapter 3． Evaporative Heat Transfer
3−1． Analogy between Mass and Heat TraRsfer
The equation of eonvective mass transfer of an incompressible fluid in steady
flow， with constant fluid properties and in the absence of a pressure graclient and
any external force， can be vv’ritten in a form identical to the Fourier heat transfer
equatlon
・a…a・一S…一一 ＝＝ D・72・C （3“）
where C＝＝concentration
t ＝＝： tlme
D ＝：： mass diffusivity
While， the corresponding equation for convective heat transfer takes the
form
−t−AO・一一 一： a・V2・0 〈3−2）
at
where ct 一一 thermal diffusivitv
v
Further， in steady state mass flux is given by
W’ 一＝ 一D−tl−2g一…… （3−3）
The equivalent expression for heat transfer is written by
・一一礁．一一・4野 （3−4）
Each of the above equations is similar．
The solutions of Eqs． （3−1） and （3−2） describe the fielcl of concentration
and temperature． lt is lmmediately apparent that in the ca＄e where the mass
diffusivity is equal to the thermal diffusivity， the two fields are identicai to one
another as long as the boundary conditions for the two equations are the same．
13
Thermal Sensation Analysis and its Application to Air−Conditioning
85
3−2． Mass Transfer CoeMcient
The rate of mass transfer， as an equivalent expression of Eq． （2−1）， is given
by the equation
IV ut le．・（C，一C，） （3−5）
where k．＝mass transfer coethcient based on gas concentration
In a gaseous system the density of the diffusing substance can be replaced by
c．．．．．．P．．”．．．一 （3−6）
Rv’T
IiV［ass transfer coethcients must be evaluated experimentally， but direct experi−
mental data is lacking． Since the mechanism of mass and heat transfer are closely
relatecl， one might expect data taken for heat transfer to be useful in predictlng
the rate of mass transfer．
Colburn． 」’一factor is defined by the following equations
ノ“＿＿亜。 （3−7）
Re・乃男
ブバ論済 （3−8）
where Sh ＝＝ Sherwood number
Sc ＝ Schmiclt number
The analogy among heat aBcl mass transfer in forced convection systems may
be stated by using Colburn ifactors．
ノ．、t＝ノ．D （3−9）
Fuyther， frem Eqs． （2−2） ancl （3−9）， one obtains for the mass transfer
Sh−C，・Sc’t・Re”e （3−IO）
where the exponent n of the Prandtl or Schmidt number takes the value of 1／3
respectively．
As a result， convective mass transfer ceeflicient can be written as a function
of convective heat transfer coefllcient by
・・一殆δ1・跨1手｝ε7・C8）晋・・c［k・／m2・h・・mmH・1 （・一・・）
where le． ＝convective mass transfer coethcient
C． ＝ specific heat
T＝ absolute temperature
3−3． Effeet of Atrnospheric Pressure on Eyaporative Heat Transfer CoeMcient
Multiplying the latent heat of evaporation L， into the mass transfer coef−
ficient， one obtains the evaporative heat transfer coefllcient by the equa￡ion
86
14
Kan−ichiro IBAiNc［oTo and Yasunobu NTIsHI
β一・Lパle。一κ・α．
rc
4．0
［kcal／m2・hr・mmHg］ （3−12）
3
In the above equation the physical properties，
such as density， thermal diffusivity and mass
20℃，〃％斤．μ
Q2
2．a
〃
diffusivity are affected by atmospheric pressure．
So， the evaporative heat transfer coef−
o
勢
ノ 20ぜ！η
ficient decreases at higher atmospheric pres−
0ど1η岬∼アerio preSS（〃’e
sure regions in contrast with the convective
Fig． 3−1． Effect of atmospheric
heat transfer coeflicient．
pressure to factor ltr
紘σ〃〆・んr・mmHg
養30
山
」
ﾌ〃7伽of 300加ψσ1ηθfθr
ｺ如が睡9んωη1dめ弓60％
霧
ｿη∂勧ぎぎθ卯θ砂加昭」勿『『
登20
葦
ミ
ミノO
Rg．
貼
0
ζ〃 6え203 0．タ O．75 ／ ／5 ．2 air レ’efOC／ty
F呈9。3−2。
3碗
Efr’ect of atmospher三。！〕ressure to evaPorati、・e heat transfer coe拓icient
3−4． Summary
By drawing an analogy between mass ancl heat transfer， evaporative heat
transfer coefllcients can be predicted as the function of convective heat transfer
coel丑cien毛．
Chapter 4． Experimental Verification of the Analogy
4−1． Procedure
IBstead of evaporating liquids， sublimating solids such as naphthalene can be
usecl in mass transfer measurements． The naphthalene was cast in molds that
proclucecl different sizes of cylindrical nap’hthalenes of 2 ancl 3 cm in diarneter and
6 and 9 cm in height respectively． The temperature drop of solicl surfaces with
the latent heat of the sublimation is calculated to be almost O．20C and was neglectecl．
In the test roorn， ambient ancl wall temperatures were maintainecl at 35 tr O．50C
for the cluration of the experiment．
Both ends of the naphthalene cylinders were either coated with a thin film
or exposed．
i5
87
Thermal Sensation Analysis and its Application to Air−Conditioning
4−2． Results of Measurement
Measurecl convective mass transfer coefllcients are ．expressecl in Figs． 4−1 anc1
4−2， ancl by the following dimensionless equations．
4．4
禽
Sh ＝a54s・ReO・5i5
o： both ends coafed
三
x ： both ends exposed
一
！
劉
／
／
Z
一 ／6
／
o ！
）v；」itgg〈ILsh．．Reas
4，2
／／ @美
ノ〆
ノ
Z！
一
bL
e
4．0
x
3，P
6，0 8．2 B．4 8．6
乙〃CRe．）
Fig． 4−1． ）vlass transfer coefficient for naphthalene cylinclers
in cross flow
へ
§46
o
o
5ん諾02・Re o一”li
oX
o： both ends eoated
ミ
x：botん印誌即硲θゴ
／
／
／
−
／
レ／
ノl
s／／
4．4
／
。，．〆一踊2／，融娚
／
／x 洋
／ x
o／ ／x ／
4，2
−
gix／／
e／ ／
／
／
／
／
ン／
4催。
8．2 a4 8，6 B．g
Ln （，？e）
F量9．4−29
1，ltk＄s transfer coefficient for naphthalene cylinders
in paraliel floNxT
（1） ln cross fiow：
both ends coatee
Sh ＝＝＝ Reo・s
（4−1）
88
16
Kan−ichiro IBAMo’ro and Yasunobu iNTIsl｛1
both ends exposed
Sh ＝＝ O．54s ・ Reo・s7s
〈4−L）
（z）In par盆11e田ow：
both ends coateci
（4−3）
Sh． ＝ O．20 ． Ree・706
both ends exposecl
（4−4）
Sh ＝＝］ O．213 ・ Ree・6tj3
where 2700〈．1〈e〈7000
喋一3。．翫Ver澁cation ofもhe An＆logy
If｛’the analogy can be applied， experimental clata
may correspond to the
fo！lowing equations， derived from Eq． （3−10）．
Sh ＝ 1．052・ReO”i66 40〈Re〈4000
（4−5）
．Sh ＝ O．298 ・ ．lxltee’6i8 4000〈1i〈e〈40000
（4−6）
The above relation closely parallels the analogy between mass and heat transfer．
200
／f
俸㌧／／ラ
ミ
8
ミ
（4−4）
ミ
ミ
も
甫
100
’
80
／
／／
^／
60
ti
（4 一2）
／
x
40
30
77
／／Z
7
（4一か
ク
‘4−5ろ64−6）
20
700a 20a〃 4000 uaoO 脚 200zaク
Re／nolds number
Fig． 4−3． Comparison between experimental data ancl analogous
equatlons
4−4． Convective Heat and Mass Transfer CoeMcient for Short Cylinder
Eq． （2−2） is for long cylinders in cross fiow， but the relation for short cylinders
in multiple flow is required． As shown in Fig． 4−2， mass transfer coefllcients
for short cylinders， both ends exposed in parallel flow， closely corresponds to the
ancalogous equations from Eq． （2−2）．
As a result， convective heat and mass transfer coeflicients for short cylinder
ユ7
Thermal Sensation Analysis and its Application to Air−Condltioning
89
can be obtained based on Eq． （2−2）．
4−5． Summary
Mass transfer experiments using naphthalene sublimation laave verified the
・aRalogy among mass and heat transfer， and suggest that convective heat and mass
transfer coefficients for short cylinders may be given by Hilpert’s equation．
Part H・Heat Eq磁ibriu燃on Huma獄Body
The characteris￡ics of racl iative， convective and evaporative heat interchange
．over the human body are investigatecl and steady state heat balance equations are
produced． ・
Sudden changes of environmental condition cause heat shock or heat storage
in． the body， nameユy， it三s a transient problem， and 三n such a case the heat balance
equations can．1／0t be apPlied．
x〃5紛σ伽’・カr
Chapter 5． Radiative aぬd Convective
373ツf
8
Heat l雌erchange
ヤ
5−1． Radiant NeaもTransfer CoeMcien｛； G？
ご ＿ α」6一λ5｛θλPぐ＆μη一1｝
The distribution of black body radiation 6
in a relatively low毛emperature range is shown
in Fig．5−1 and in an average room situation
the radian．t intensity shows its maximum value
i卿
4
at a wa▽e le．ngth of about 10 micron．
It is said that玉n the long wave length
3α7
range the absorption of either the nude or
2
clo宅hed body may be taken as complete and
2Z9
電he radiation of water vapor or carbon dioxide
三n the ro・m can be negleced．
Substituting the numerical value at the oo ／ク 20 ヲoA
・ub・t・・ti・1・・vi・…・・ti・t・Eq・（1−4）・w・g・t F、9．5一、． Vari。、i。。。f、h。i。、ens・、y
the radiant heat tran．sfer coef丘cient as of radiat三〇n with wave！．ength
α、．：： 5 ［kcal／m2・hr・Deg］ （5−1）
where le 一！．1，ε。・ε，。一〇．93
0n the other hand， if the emissivities of walls are difだerent，‘‘αノ’can not be
expressed as simply as the ab・ve．
5−2． Surrounding Radiant「℃emperature and Mean Radiant【滑emperature
In estimating the surrounding radiant te盤perature， the problem changes to the
question as to what k：ind of simpllfied shape factor can be used in place of the
cornpllcated shape factor between the human body and玉￡s enclGsures． In this
．paper， the authors propose to use the shape factor for the cylinder element as an
approximate shape factor for the human body．
90
．Kan−ichiro IBAMoTo and Yasunobu NISHI
i8
NVhile the mean racliant ternperature in a wide sense corresponQis to the
surrouncling radiant temperature， its inaccuracy is evident． iLVforeover the mean
radiant temperature clerived from the arithmetical average of the boundary surface
temperatures or from weightecl averaging ornit even． the shape factor．
5−3． Convective Heat Transfer CoeMcient
The geometrical shape of the human body is too complicated to cletermine the
exact convective heat transfer coethcient， so the human form must be treatecl as
some simplifiecl object ； namely a sphere or cylinder．
The authors propose to treat a cyliRcler of 30 cm in diameter in lieu of the
human form．
5−4． Effeet of Clothimg
（1） 0無rad量atio難
By decreasing the emissivity of clothing， the rate of radiative heat transfer
can be reduced to the ultimate value of zero． This is very effective for protecting／
against the heat or the colcl．
Table 5−1．
（2） en conduction Clo． vague of clothings
“Clo．” is one of the 1）ractical un．its ef tine heat clothing 11／ ao， value
resistance of clothing． ””””1”／””””’…””””’”””i””””／／／”””””
5．5．、論α！8［ 9／㎞11（5’2）灘聖一：1
器1∴鷹野慧四四t瀦計1黙総蜜
Determining the cenvective and evaporative heat
transfer coeflicients for men， the authors have proposecl to regarcl man as a cylincler
of 30 cm in diameter．
Chapter 6． Evaporative Heat Loss
6−1． Vapor Pressure over Skin Surfaces
In an ordinary situatioB skin surfaces are nearly dry， ancl with the secretion
of the perspiration wettecl， parts gradually appear．
In estimating the vapor pressure over such an indefinite surface the following．
methc・ds may be appliecl．
（1） Average vapor pressure
The skin surface is maintained at avercage vapor pressure ancl sweat evaporation
depencls on the graclient between average vcfi．por pressure and ambient vapor pressure，
as expressecl by the equation
W＝＝： kp（9s’“iils−Pa） （6−1）
where y，，， pm一 factor for average vapor pressure
R， ＝ saturated vapor pressure at mean skin temperatuye
19
Thermal Sensation Analysis ancl its Application to Air−Conditioning
91
／）． ＝ ambient vapor pressure
The actual value of g， can not be cleterminecl， but in the case of the skin surface
beiRg completely wet it takes the ultimate value of 1．0 ancl in the case of zero
moisture， gs＝P．／ll，・
（2） Wetted area ratio
Sweat evaporation may occurs over specifiecl wet sl〈in surfaees， which have
been saturated at mean sl〈in temperature，
Imlere，
W皿＝たP（瓦一君‘）・ε （6−2）
Wh・・……器畿濃1§鍔一一W・…d−a…
The proportion of wettecl area to the total surface area are to be called “wettecl
area ratio”． The actual value of “E” is also uncletermined， but when fully wetted it
tal〈es the ultirnate value of ！．0 and in the case of zero moisture， E ＝O．
The idea of wettecl area ratio becomes more effective for cletermining the
comfort index．
6−2。 S量磁P墜i負cation of Sa加rated Vap◎r Perssure
Over a reasonable range of skin． ancl ambient temperature， the vapor pressure
may be approximatecl by the equatioBs
2， 一一 2．15・T，一31．91 ［mmHg］ （6−3）
1）a．．，鑑0．031・7” 一〇．031・7．∴、＋5．69 ［lnln正一｛g］ （6−4）
6−3． Vapor Resistanee of Clothing
Heat resistance of clothing can be evaluated cluantitatively ag． shown in Table
o”
D一
I， but the vapor resistance of clothing， being． cllstinguishecl fi”om that of fabric，
has not been cletermined．
The authors try to sim−plify t｝）一is complicatecit relaL tion by the following form
to， t＝ ｛； ． p （6−5）
where 4 ＝：＝ permeance ratio
The actuac l value of permeance ratio may vary accorcling to clothing type， but
in the case of nuclity it takes the ultimate value of 1．0， as in the case of perfect
clamp−proof clothing， C＝O． Fureher， in Chapter 7 the substantial value of perme−
ance ratio may be approximately obtainecl by the clata of some experiments．
6−4． Summary
Estimating the rate of sweat evaporation， the authers hac ve proposecl a simpli−
fiecl equation ； the wetted area ratio， the approximation of saturatecl vac por pressure
ancl the permeanee ratie of clothing．
92
20
Kan−ichiro IBi，x）L（oTO and ”E（”asunobu NISI−II
Chapter 7． Thermoregulatory Mechanism of Man
”i−1． Body Heat Production
Under the basal metabolic condition it is said that normal man produces，at least
40 kilogram calories per unit of skin surface area per hour， and in viole，nt exercise
the metabolic rate can be as much as 10 to 16
κ0σ／／，m2・かノ『
times that of the basal rate． There is a re．crion
Joa
蓑，“
of temperature， 25 N290C， over which the
metabolic rate is almost constant． ’When the
；｝ 60
x×
Xux
＼勉
ambient temperature falls， the beclily heat
ミ
procluction rises to maintain a constant tem−
ミ40
pe，rature， ancl when the ainbien．t temperature
＼遮こ＼こづグ
h−O’
rises the be（My heat precluction rises alse，
2グ
ジ ノρ 2P ヲβ ijO ev
due to the increasecl rates of chemical reaction．
ot7 temperature
／Met． an（1 R．M．R． （relative metaboiic rate）
Fig． 7−1． Variation oi bodi｝y heat
production 〈Houssay・， Human
care the stanc！ard expressions of metabolism．
PhysioL， p．518， McGraw一田1）
Here，
・M・・一・・［kcal醐・nd R・MR・一二9器器1譜。壷
Comparing the two indexes， R．M．R． is used as aR index of intensity of manua！
work， but it cloes not indicate the metabolic rate clirectly．
The Met． value for typical work categories is shown in Tac ble 7−1．
Table 7−1．
rvlet． vaiue t’or typical xvorl〈 categories
Met．
kcal！m2’・hr
t
sleel）．ing，
O，8
40
Slttln⊆ア
1．C）
50
／．6’
80
ttt．e
100
−Tall〈ing 4・ knYhr
3．0
150，
5．C’ km！hr
4．0
200
6．C
300
e
seclentary wo．rk
Iight “Tork in a standiRg
1）OSture
5，6． kni！hr
（“Tith 2 kg． “reight）
7−2． Body Heat Loss
The heat generatec／ within the body is baianced by losses to the atmosphere
as radiation， convection， evaporation and in xvarming food ancl inspired air， but
the proportion of heat losses by the three principal ways to the total heat loss is
large ellongh to neglect the others． The rate of heat losses by radiation， convection
and evaporation depends on the condition of the environment and the amount of
work． Fig． 7−2 is an example， clerivecl from Fahnestock’s report．5）
21
93
Thermai Sensaticn Analysis and its Application to Air−Conditioning
7−3． lnsensible Perspiration
Kcal／m2・hr
olo
15a
Insensible perspiration is an imperceptible
lefi
貼
き
loss of water through the skin ancl is clis−
tinguished from sweat secretion．
At the rate of approximately 23 grams
per unit of skin surface area per hour， bet−
ween 800tv！LtOO grams of water are evapo−
E
達
15誌
讃が
ミノoo
鳶
ミ
g
鳶
艶
50ミ
ミ
tii
rated by insensible evaporation every 24 hours，
登
5V
25 ￥
and this evaporation accounts for one−quarter
of the heat loss in a resting subject． This
x／
fact is very important for the analysis．
Insensible perspiratien is greatest on the
palms of the hands， and the soles of the feet；
next on the bacl〈 of the hand， the neck ancl
戟
／
0 ／ 2 ヲ帽，0
個θご。か。億〃
F三9．7−29
Variation of the rate of each heat loss
the face： and least on the remainder of the
龍σ伽2・ゐノ
，
60
bo（ly surface． Thus， even with clothing， the
．
rate of insensible perspiratien is niaintainecl
婁・・
at a constant value．
至
一 一
x 〉・ 7e’ e／”
．
．
0 5ノー一75哩己島
も。
7−4． Sweat Secretion
肋儒htimidi4・
・
●
●
． 50s・s＞
■
ミ
、事●
老
When． the ambient tempercature rises the
・
妻・・
e
o ●x
e
sweat secretion begins over all the skin sur−
o
face， especia11y at the exposed parts， with the
o
計
？o
exception of the palms of the hands and soles
㌔。’
㌃ 葦。
／0
of the feet．
Fig． 7−3 shovkrs the relation between
ス コ
e
」 。 ・
evap・rative hea貝oss of man at rest and
OJtmut 30 40V
ambiellt tempera加re， derived from Winslow’s
Fig． 7−3． Variation of evaporative heat
report6）， and we know that when the ambient
loss with ambient temperature
ambient fempetature
temperature rises above 280C there is an imcrease
m persplratlon secretlon．
rvi−5．
Effects of Clothing on Sweat Evaporation
experimental data， the magnitude
Analyzing Gagge and Nagata’s
of permeance
become eviclent．
ratio of clothing， defined in Chapter 6，
（1） Gagge’s experiment’）
on sweat evaportion． The experlment
Gagge and his associates presented data
subjects in a semi−reclining position．
was made with two clothed and four nude
of a two plece suit of cotton underwear，
The standard cloth1ng employed consisted
a cotton shirt， socks， shoes ancl a darl〈 gray single−ply suit with three−quarter lined
coat and a fu11y ｝ined vest．
Fig． 7−4 shows that in an average
room sltuatlon
clothing upon sweat evaporation was almost negligible．
the blocking effect of
94
22
Kan−ichiro iBAMOTQ and Yasunobu NIsH工
Kba伽7・hr
き
o
o ：・ nude
一g“
F．80
ミ
o
X；0／bあθ4
C〉“
．R
x
rθ／7tlve hu〃／Zガピン」40∼50％
ce．）s 60
o x
afr ifefocity ； ／0em／sec
ts“
x
｝t
as
@40
粟
啄
x
x o
20
ゆ
o
。。5ゆ蝦粟細安
x×× xx x××
f5 20 25一 30 35 40 eC
卯θ如ぎ惚temperature
Fig． 7−4． Effect of clothing on sxveat evaporation−a
（2） Nagata’s experiment8＞
The sweat evaporation of four subjects in the nuc！e and with various types of
underwear was observecl．
The test room was maintainecl at approximately ・10eC clbt ancl 50％ rh respec−
tively， and both radiant heat and air motion． were not sensible．
In that experiment the amount of secretecl sweat vLras 200N250 grams per
unlt tlme per person．
Table 7−2 shows that when the rate of sweat secietion reaches several times
as much as the normal condition， only 10・一v！5％ of secretecl sweat remains in・ the
clothlng or drips off．
Table 7−Z． Effect of Clothing on Sweat Evaporation−b
inudity ’1 iinen
heinp
hemp ＆ rayon i cotton 1 nylon
．．．ρ塑9璽g“．．景．寮賦．．．．
（％〉
9． ，O．：1
secreted sweat
81，8
84．L）
87．6
86．2
88，：）
84
89
88
89
9．！
e．．．．M．．，｛，．．．p．ro一；．a．．，1．e−d一．．．g．．w．．．e，．．Fl，｝．1ww．．一．一．．
（90） li loo
secreted sw．一dripped sw．
Further， Nagata observed the sweat evaporation on the subjects with underwear
and outer garment．
The test room was maintained at 30eC dbt ancl 75・一v85％ rh respectively．
Two subjects were clothed in various ty−k es of clothing ancl were made to walk
around at a rate of thirty steps per minute for two hours． ln this test the amount
of perspiration secretion was about 150 grams per unit time per person．
Table 7−3 shows that when the subjects put on damp−proof clothing， they
23
95
Thermal Sensation Analysis and its Application te Air−CQnditioning
on1y blcck about 2090 of the secreted perspiratien．
Gagge and Nagata’s observations suggest that the vapor resistance of light
clothing ’may be neglected ancl its permeance ratio seems to take the value of
nearly 1．0．
Table 7−3．
evaporatecl sweat
（％＞
secreted sweat
Effect of Clothing on Sweat E・vaporation−c
Cl
C2
C3
76．4
78．0
78．0
L
C4
C5
86．0
81．4
E
The five types o’f outer gfarmients used were as follows：
Cl： a knee−length vinyl raincoat
C2： a knee−length v・inyl raincoat vvrith very fine holes
C3： a waist−length viny・1 raincoat
C4：awaist−length v三nyl ra三ncoat wlth a spedal rift in the｝）ack
C5： a knee−length cotton coat
7−6． Heat Balance EquatioR ef Man
The expression of the ecluati6n is slightly different in each case of nudity and
c｝othing， because of the existence of heat and vapor resistance．
（1）
In
Heat balance equatien of the nude man
a steacly state， t’i e heat produced within the body is balanced by cooiing
powers of the envirenment as radiation H． convection H． and evaporation H，
．五τ罵1＝乙，＋五乙，＋瓦 （7−1）
J・＝αヂ（7．ls−T，．）＋αバ（T，・一7う、）＋β・（疏一．ε、）・ε （7−2）
where H＝＝ prcclucecl heat per u．nit of skin surface area per unit time
T， ＝ mean skin temperature
P， 一一 saturated vapor pressure at T．，
P，， ＝：pac rtial vapor pressure in the air
e ＝＝ wetted area ratio
the term of heat storage is joined to the right−hand side of Eq．
Generally，
（7−2）．
The authors clo not deny the existence of heat storage， but it appears as
an unsteady state heat exchange．
As mentioned in Chapter 6， the vapoy pressure over skin surface and in the
air can be expressecl simply by
瓦一α・鶴＋b
（7−3）
and
瓦一（A・T，1＋B7隔＋C）・ρ．
（7−4）
where y，， ．＝＝ relative humiclity
Substituting the above relations lnto Eq． （7−2） we get
H一α，．・仏一：τD＋a，，・（［Z”’s rm Ta）
where
（7−5）
96
24
Kan−ichiro王BAMOTO alld Yasunobu NエsHI
ど1．
（7−6）
痺ｿ＋α・ε・κ）・α。
ノ，、」些焦狸・‘14二τ妊B．T・・土9一々楓
（7−7）
1十aiE＋ rc
（7−8）
P ＝＝： rc ’ cr．
嚢
薯
th
ar
Hlll・舳伽
1
ac
Hbi伽・伽
1
a・E＋K・ac
Pa 一b
0
HIlt’ Eyaporotfon
Fig． 7−5． Tiiermal netxv・ork ’for Ec／，． 〈7−5）
（2） Heat balance equation ef the clothed man
When clothed， the following equations may be obtained．
H＝ crr’（Tc ww Tn）＋crc’（Te−Ta）＋g” ’P’（Rs−Prt）’E （7−9）
and
crr’〈Tc−Tr）＋crc’（Te−Ta） mm ”1””’〈Ts−Tc） 〈7−10）
Rc
where T． ：＝＝ surface temperature of clothing
R． ＝ heat resistance of clothing
and therefere，
仏取∴墜碗ゲαい7し）＋葺πf㍍；凝7、一勾 （7一”）
where
御斗＋・一ζ・｛蜘・・’＋州・・tT （7一・2）
f酒孔±蟹ゑ溢泌盈（璽・±磁巳蝶土B二・．辺型塑臼3）
｛1÷R，，（α、．＋α，，）｝
1＋ cz ・e・ ig ・4・
The above heat balance equations can quantitatively evaluate each component of
the thermal environment， and will be applied in determining the comfort inclex．
25
97
Thermai Sensation Analysis and its Application to Air−Conditioning
亀
震
．ミ，
薙
lii Radiatiqn
ト樋・繍〃
Hli・i E・ap・伽
Fig． 7−6． Thermal network ’for Eqs． （7−9） and （7−10）
7−7． Summary
In expressing the heat equilibyium between nian ancl thermal environment with．
the engineering methGd， the physioiegical characteristics of the human were taken
into consideration． Then， on the basis of the above the heat balance equations
were proposed．
References
5） Fahnestock， ）ivl． 1〈， et al． ： Comfort and Physiological Response to Worl〈 in an Environment
of 75 F ac nd 4590 R．H．， ASHRA｝“一’． Journal （！963 March）， p． 25．
6） Vgi．inslow， C． E． A． et al．： Physiological． Reaetion of the Elumftc n Body to Variou＄ Atmos−
pheric Humidities， Arn． J． of Physiol． Vol． 120 〈1937） ．p， 290．
7）Gagge， A． P． et al．；The In伽ence of Clotl翻g on亡h．e Physiological Reaction of the Human
Bocly to Varying， Environmental Temperature， Am． J． e’f Physiol． Voi． 1．24 （！938） p． 30．．
8＞ Nagata， H．： Evaporation of Sweac t on Clothecl Subject， Jap． J’． of 1’一lyg． XJol． 17（3） （1962＞
p． ！55．
Chapter 8． Experimental Verification of Heat Balance Equati，on
8−1． Precedure
The skin temperatures and thermal sensations of two ma｝e subjects， ages 22，
were observed． The （letac ilecl physical clata en the subjects are summarizecl ln．
Table 8−！．
The clothing employecl was as follows： a） nucle with bathing trunks， b）
Table 8−1． Physical data of the subjects
subject
height
，．（，．n．1．」，．．
weight i surface area
physique
鰯、…．L．．．（熱・）
inetaboki￠ rate
（3 measurements）
Clsf．．．g！．（in−2，．，r．！．，．，x．．L．．．．．．．．．．．．．．．．
1
1）
1，67
54
王、．66
s
！．60
58
1．61
t slender
50．3
［ sliglitly fat
60．7
98 Kan−ichiro IBAMoTO and Yasunobu Nlspa 26
cotton underwear and underdrawers， c） cotton underwear and underdrawers fully
saturated with water．
Skin temperatures were measured with a copper−constantan thermocouple and
the mean skin temperatures were calculated by the equations
mean skin temp． ＝＝： O．1 × forehead ＋O．05 × forearm＋O．05
＞〈 back of the haRd“O．4×chest＋O．2’
xthigh十〇．2×leg 〈8−1）
and
m，an ski。、。即。、 w。，t。d p。，、一．触興吐gh釜㌻．±晦的±．！皇銭田（8．2）
4
AIlalyzing the exper玉mental data， some therma．1 factors were assumed as foi．工ows：
1 ） convective and evaporative heat transfer coefficients are calculatecl！ based
on llqs． （2−2） and （3−！2） for the cylincler of 3〈） cm in diameter．
2） racliant heat transfer coeflicient is the va｝vte of 5 ［kcal／m2・hr・Deg］．
3） heat resistance and wetted area ratio of the subject with fully wette（1
clothing are the value of R．＝＝O ［m2・hr・Degfkeall and g”一一1．O respectively．
4） metabolic rate of the subject in． a seated position is the value of H＝＝’50
［1〈calfm2・hr］ 〈1 Met．）．
5） permeance ratio is the value of （；＝！．0．
8−2． Experiment A
The heat balance equation suggests that， u．nder very hot circumstances where・
even radiative and convective heat fiow is allowed into the body， maB would feel
cold so／ong as capacity of the env玉ronment to accept￡he evaporation is sufHcien亡ly
large．
The test room was maintainecl at 47．40C dbt， 2090 rh and O．7NO／／．8 m／sec air−
movement respectively， and the subjects were in a seated pesition．
From Table 8−2 we know that in v・ery hot environments， the irnpssecl heat
load cannot be compensated for by man’s thermoregulatory ability， burt the cooliRg
Tab！e’ 8−2． 1）ata of Experiment A
condition of clothing
dry， O．3 Clo．
fully saturated， O C］e．
watted area ratio
E ＝＝ O．35
E＝1．0
sweat secretlon
much， but surfaces are clrying
none
33．00C （forehead； 39． ．40C， back
mean skin temp．
36．50C 〈foreheacl ； 35．4CC・， back
of hand ； 40．2LC）
af hftt nd ； 37．4“C）
3！．30C （average of wetted parts）’
Skin tel丁」P． frQln 難eat
balance equation
thermal vote
36．5eC （where c一 ’L：O．3’5）
very hot
：’51，60C （where E ＝＝ 1．0）
cold
27
Thermal Sensation Analysis and its Application to Air−Conditioning
99
effect of the evaporation of supplied water is large enough to maintain a heat
equilibrium． This fact may be of some value for improvlng sports conditions or
industrial environments．
8−3． Experiment B
The higher the velocity of the air flow， the more the evaporative heat loss
increases， but in the case when ambient temperature exceeds the skin temperature，
the convective heat gain increases also． When the heat loss ancl gain offset each
other， the mean skin temperature is scarcely concerned with the air movement．
The test room was maintained at 34．40C dbt and the surrounding radiant
temperature， 8590 rh and ！．5， 2， 3， 4 m／sec air−movement respectively．
The subjects were in a seated position and were clothecl with underwear and
underdrawers fully sa加rated with water．
In spite of changing the air−movemens from 1．5 m／sec to 4 m／sec， the clrop
in mean sl〈in temperature was only O．40C． Furthermore， the differeBce between
experimenta｝ data and calcu！atecl values was sufficiently small． At that time the
thermal vote of the subjects gradually changed from ceol to slightly cold．
薪
蓬
N．S
ooκ〃／∂ねゴ
蓑・3
s
ミ
！ηθ（泌rθσ
32
3i
肥 加ノδ
2
1・5
でθ！η．
3 4m／s
Oノ1’ 1／θ／001≠ン
Fig． 8−1．
Variation of skin temperature
8−4． Experimaent C
The relatien between measured skin temperatures and calculated values was
examined． 26．4N38．40C clbt， ！7N39 mmHg humidity， and O．7tN・4．O m／sec air−
movement， constituted 46 test conditions， and the surrounding radiant temperatures
approximately coincicled with the ambient temperature．
The subjects were remained seated and put on underwear and underclrawers
fully saturatecl with water．
In Fig． 8−2， if the heat ba！ance equation ls idealistically precise， each dotted
point must be superposed on the sdlid line， and should approximate its location．
lee
28
Kan−ichiro IB．tu，forro ancl Yasunobu INISI−II
36
1
oOOo
ミ
ﾓ偽
ミ
駐
聡34
t−ny
二
o o
Oc◎
刀
@ 80
｛ 32
o O
℃t
o
o
潤@ o
@oOo
B・ts
30
OD
2B
26
o
242ftt6 2s 30 32 34 360C
α伽后加．〃θση轟ηte！npe！uture
Fig． S−Z． Comparison between experimental data and calculated values
8−5． Summary
The experiments have verified that calculated skin temperatures were approxi−
mate to measure6． values． ’￡hus， it may be saicl that the heat balance eqnations
are rational．
Part III． Development of Warmtk Diagram axxd its
Application to Air・Conditioning
On the basis of the heat balance equation “the model skin temperature”， that
expresses the therm／／一t，1 sensation， i／nay be clecluced， ancl to simplify the calculatin．a
process of mQdel skin temperature“the War胆th Diagram”and“Comfor由etector”
may be propvsed．
Chapter 9． Thermal Sensati．on and Model Skin Temperature
9−1． Definition of Comfort
From a engineering Po三nt Gf view the authors de飴e‘‘comforゼ’as follows；‘‘the
condition in which man is emitting the entire produced heat steadily at the
optimum ancl constant body temperature without any additional aid of a thermo−
regulatory mechanism”．
The following condition may be assumed to be a comfortable condition．
29
Thermal Sensation Analysis and its Application to Air−Conditioning
IGI
Envirenmental side ：
ambient temperatare （surrounding radiant temp．）： 27．50C
relative humidity ： 50％
air paovement ： IO cm／sec
Physical side ：
clothing ： OCIo．
work rate ：IMet．
mean skin temperature ： 33．00C
percentage of evaporative heat loss ： 259（o
（by insensible perspiration）
If the wetted area ratio takes the value of O．16， the above physical conclition
is realizecl at the above thermal environrnent． This relation suggests that in
a comfortable condition without perspiration secretion， the wetted area ratio of
the human body may be maintained at the value of O．16．
In other worcls， any environment， at which mean skin temperature is 33．00C
with E＝O．16， may be assumed to be a comfortable condition．
9−2． Expression of Thermal Sensation
In hot or cold circumstances men are obliged to set the thermoregulatory
mechanism to work in order to maintain a constant bocly temperature． Then， the
quac ntity of the expended effort is concemed with the thermal sensation．
To extract the quantity of the expencled effort we consicler “the moclel man”
having the same thermal characteristic as that of the man in the comfortable con−
clition．
In aBy environment， the difference between the skin teinperature of moclel
man and the comfortable skin temperature of 33．00C seems to be clirectly related
with the quantity of the expendecl effort．
The authors propose to express the thermal sensation by the following defini−
tion； “the difference between the moclel man’s skin temperature， in． short， the
model skin temperature and the cemfortable skin temperatuye of 33．00C expresses
the deviation of the sensation from the comfortable condition．”
9−3． Relation between Thermal Vote and Model Skin Temperature
The relation be￡ween the thermal sensation and the model skin temperature
can be examined by the subjects’ thermal votes．
The test conditions were as follows ； room temperature ： 20・一一・490C， humiclity ：
10・一v18 mmHg， air−movement： O．！tv l m／sec， work： in a seated position （1 Met．），
clothing： in the nucle or with underwear and uBderclrawers （O．3 Clo．）， subjects： D
and S．
The results were summarized in Fig． 9−1．
9−4． Teinperature−Humidity Chart and Model Skin ’remperature
OR the basis of ｝arge scale experlments， Nevins and his associates proposed
“the Temperature−Humidity Chart”．9）
Test conditions were as follows； room temp．： 19N280C （9 dbt）， humidity：
102
Kan−ichiro IBAMOTo and Yasunobu ：K4TlsHf
30
ゆ
c
45
薯
o
43
◎
這
g
N
叢
41
◎
’
39
’
悪
37一
R
35
ノ
o
33
’
o
o
31
’
曾。
o
29
o
o
⑳
21
わ
o
25
， o o
23
：ミ ：ミ
9 b
fo s
、
へ
q
o
x
D
x
Q
一一一
ミ さ
x
電
く） q）
鳶 〉
く
．偽
ミ
“
ミ
ミ
ミ
婁
ミ
k
額
v
ミ
ぬ
ミ
）
も
さ
違
聖
8
ミ
孕
り
Fig． 9−1．
’1“hermal vote and model skin temperature
（（29 marks were derivediT，from Nevins’ reDort
i・一．irom Nevins’ report）
15tv85 cr／o （8 rh at each of 9 dbt）， air−move−
Table 9−1． Comfort vote ＄eate
ment： assumed to be 15 cm／sec， work： in
a seated po＄ition （1 Met．）， clothing ： standard−
value of Yc
thermal s．ensation
ized clothing 〈O．52 Clo．）， subjects： 360 male
1
coEcl
and 360 female students raRging from ！8 to
2
coo｝
23 玉n age．
3
slightly ￠ool
From the thermal votes of the subjects，
4
comfortable
5
s難9htiy xxrar工n
the following equation has been propos6cl．
6
7
’warm
hot
31
Thermal Sensation Anftc lysis and its Application to Air−Conclitioning
103
Y，，一一！0．749＋O．183・T＋OOOO17・T・U （9−1）
where Y．＝estimated population mean vote for males and females
combined in equal numbers． Comfort vote scale is
shown in Table 9−1
T ＝ dry bulb temperature OF
H＝：： relative humidity in percentage
Nevins’ comfort lines and authors’ equal model skin temperature lines are
given in Fig． 9−Lt．
oC
30
cet
tsb 26
g
茎
ミ
奎22
／8
ノ4
fO
20 22 24 26 28 30 eC
amblent temperafure
Fig． g−2． Comfort line and modei slcin temperature line
9−5． Model Sl〈in Temperature as a Scale of Warmth
From Figs． 9−1 and 9−2， we can recognize that model skin temperature is
closely relatecl with thermal sensatien．
The model skin temperature dees sy．nthetically evaluate many thermal factors，
such as ambient temperature， surrouncling radiant temperature， humidity， air−move−
ment， heat ancl vapor resistance ancl emissivity of clothing， work rate and physical
properties of air． So， the model skin temperature may be used as a ratienal
comfort index．
le4 Kan−ichiro IBAMoTo and Yasunobu NlsHI 32
9−6． Summary
By means of a engineering method， the human thermal sensation has been
expressecl with the model skin temperature that defined by the authors．
Reference
9．） Nevins， R． G， et al，： A Temperature Humidity・ Chart for Thermal Comfort of Seatecl
Person， ASHRAE J． 〈1966， April） p． 55．
Chapter 10． Warmth Diagram and its Application
le−1． Principle of the Warmth Piagram
K． lbamota， one of the authors， first proposed the principle of NVarmth
Diagram．
Radiative and convective heat interchange Hn are expressed by
ffD ＝＝： crr’（Tc−Tr）＋a’c’〈Tc’Ta） （！0−！）
；（α，，＋α、．，）・（ア1，一丁，｝） （10−2）
where ［zr， ＝＝ 一9一（一！：一1一一Zl，’一L一等一一q・i；・一：一一7…［lfi，一 ＝＝ operative temperature
αブ十αc
And transformed to
T・・ ：＝＝ ”cr”t7”’（Tc−Tft）＋Tc一”ll’ 1””｛？”’ （10’3）
α，・ αノ・
Then， Eq． （10−3） can be expressecl in Fig． 10−1．
lr
ぺ
認る％）
w
砺μ’
V
レ
@ ク
@ 石一佑仰
ﾆ
S5σ @ 4プ
eHD／a．一 Ta fo fc
Fig・10−1。 Schematic expression of Eq．ほ0−3）
In Fig． 10−1， the line V， expressing the air−movement， is characterized by
the angle of e＝＝tan’icr，，／cr． The point M expresses the operative temperature， but in
the case of the heat production being zero it gives the surface temperatgre of the
le5
33 Thermal Sensation Ana｝Ysis and its Al）plication to Air−Conditioning
body．
From the above relation we get the following concrete scheme．
alrフηotremθnl／加θ
説試
虞
ミ
ー一
詑
¥．
噛
げ
も
ミ
s
9
麸
0
CL FL
ミ ミ
as q
一＋・J 「り
st．） M
Cこ Q
碧 曼．
ミ こ｝
b （つ
Fig． 10−2． Principle of warmth diagram
le−2．” Graphical Solution of Mede！ Skin Temperature
（1） For the nude model
In a similar way as Eq． （！0−3）， from Eq． （7−5） we get
T、．一．鉱朋。（Ts−Tf、）＋Tr．旦
（10−4）
α，・ αノ・
wet and dry
While， substituting the following Sprupg’s formula， with respect to
bulb temperature， lnto Eq． （7−7） we get Eq． （！0−6）．
瓦峨・一三瓦・・（7’”，， 一 T，，，）
（10−5）
o io 20 po 40 Ta
50 ZC
o
ミ
4葦
，量
i2 h“
早f
g
16毫
20壽
t Deg．
Fig． 10−3．
Graphical solution of rf’a
106
Kan−ichiro IBixMoTo and Yasunobu NISI−II
34
T・《百振）・｛A‡瓢・嘘：麓繊蒲一、．。．（c一∂）｝
（！0−6）
￡q．（！0−6）inv・1ves s・m・v・・i・bl￠s，・u・h・・T。， t・T，、一丁，の君、、，・and・・王f
，・m。v。，i。bles a，e丘xed， as・P，、、一！・tm，’c・一一 2．2・nd・＝＝O．16， the va・i・bl・T”，， can b・
graphically solved with Fig．10−3．
（2）For the do重hed modeI
The Eq．（7−！！）can be transformed to
z．．＝．．生（T，s・ 一 fra）孤＿．．．理 （・o−7）
α．！． α．，・
where
U’・…｛・＋R、，（・，・＋・，，）｝・H （・0−8）
The algebraical symbols；「1’，、，9i，。 and．1，，1，t involve the heat resistance of clothing
R，respectively。 Hence， diagrams should be constructed， treating the variable R，，
as a parameter．
Further，7■。 and H’｛n．v・1ve the variableα、，． In an average ind・・r situati・n，
the var1ation ofα、， a狂ects H’in several areas， but has little effect on 7■，、．
．．． 10−3．War瓢th Diagram
ドぞ ヨ ご フごド ワ ぴダこしマリも リピ
、．∫ The com・le亡ed Wa「mth Diag「ams a「e
shown in Figs． 10−5・一v！O−11．
い 譜
、㌦こ：摯
f群
（1） Select the proper diagram， acc，ording to
O atmospheric pressure， ＠ Clo． value and ＠ emis−
siv三ty of dothing．
｛2） Draw vertical iine from inter＄ection ．／’1， of
＠ ambient temperature and ＠ relative humidity （or
（S）” clifference bet“reen T（t and T？t・）．
（3） At ＠ surrouncling radiant temperature
clraw horizontal line； thus get intersection ／’i
（4） Passing through intersection B． draw the
’ltt．1・ fnodei skir］ ft”，np．
庵
｝’lf 1 ； therrvai str’fisoitbn
e air−movenient ｝ine Y of slope 0＝’ tan’i cv，Vcv，・，
t’：
（5） From the intersection C of line V and （g）
f
A
一一
ｩ一《蓼南一．r。
G），
燭婦
鰯吻．．
ee．difo4gCtl’
一g〈’zl woyk rate ＆ air−movement 11ne of slope 450，
draw vertical line clown“，ac rd and deterniine niocle｝
skin temperature or thermal sensation．
／etpp
Fig◆10−4。 Procedure for（1eterm三ning
model skin temperature or thermal
sensatlon
If one adheres to the above regulations
the Diagram can be used in many ways
to obtain other thermal factors．
107
Thermal Sensation Analysis ancl its App］ication to Air−ConcHtioning
35
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36
Kan−lchiro IBAMo’ro andi Yasunobu Nls！一II
IG8
ノatm．，05G／0．
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Fig． 10−6． X）Varmth Diagram； l atm．， O，5 Clo．
20
Peg
le9
Thermal Sensation Ana｝ysisland its Application to Air−Conditioning
37
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Fig． 10−7． Warmth Diagram；latm．， I CIo．
2a
peg
11e
38
Kan−ichiro IBAMo’ro and Yasunobu NlsHI
10ど〃ワ20’o．
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Warmth Diagram； ！atm．， 2 Cio．
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Fig． 10−S．
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39
111
Thermal Sensation Analysis and its Application to Air−Conditioning
／・畝a5αα，動ノ∬励顔
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16
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Fig． 10−9． Warmth Diagram； ！atm，， O．5 Clo．， emissivity O．5
s
導
軍
％％診
12
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112
40
Kan−ic｝．iiro IBi，xMOTO and Yasunobu LN］sl…II
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Fig． 10−10． Warmth Diac ．crram； L，・”3 atm．， I CIo．
41
Thermal Sensation tX， nalysis and its ．gXpplication to Air−Conditioning
113’
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Fig． 10−11． NVarinth Diac gram； 2 atm．， I CIo．
Oeg
114 Kan−ichiro IBAMoTo ancl Yasunobu NlsHI 42
10−4． Evaluation of Therrnal Environment with Warmth Diagram
By the use of Warmth Diagram one can easily evaluate the condition of the
thermal environment．
Exa皿p正e 10−1
1n a room at ambient temperature： 250C， surrouncling racliant temperature：
200C， air movement ： ！0 cm／sec， a man is in a seated position （！ Met．） with 1 Clo．
cloth三ng． If the relative humidity takes the value of 20， 40， 60 and 90％
respective｝y， the comfort sensation in each case may be estimated．
Solutioiz
Using Fig． 10−7， the following relatien is derivecl．
Isi’c
s／igh t／y vearm 35
ヲ4
comfortabfe 33
’” 32
s／ight／y coo／ 3i
20 40 tiO 90 ”／o
re／atlve h〃〃彫か
Fig． 10−IZ． lnfluence of humidity in the substantial
room sltuatlon
As show．n above， in a substantial room situation the effect of the humidity to
comfort sensation is almest negligible．
Example 10−2
1n a rocm at ambient temperature：35℃， surrounding radiant temperature二
300C， air movement： 10 cm／sec， a man is in a seated position （1 Met．） with O．5
fs ec
yer／ hot 41
1
40
hot 39
吻7〃η37
ヲ6
20 40 tiO 90％
畑／0加功σ！η！（塘
Fig． 10一一13． lnfluence of humidity in the hot environment
43 Thermal Sensation Analy・si＄ ancl its Appiication to Air−Conclitioning 115，
Clo． clothing． lf the relative humiclity takes the value of 20， 40， 60 ancl 90e／o
respectively， the comfort sensation in each case can． be estiinated．
Solt（．tio7t
Frorri Fig． ！0−6， the result is given in Fig． 10−！3．
1，n the hot environment， the humiclity advances to one of the esscntial thcrmal
factors．
Example 10−3
A man is in a seatecl position （I Met．）， with I CIo． clothing， uncler the
atniospheric pressu；“e of 2／3， 1 and 2 atin． respectively． The other therinal factors
for tlrie comfortabie condition． n／iay be clecicled， wiLere air movement is flxecl at
20 cm／sec
．S’fo／ution
From Figs． 10−10， ！0−7 and ！0−！！， we get the following iliustration．
oC
28
ミ
ミ
ミ
dj 27
気
ミ
禽
起26
．ミ
b
ミ
書25
3／
自24
ご
gt 23
g
2／3 atm
22
／ otm
2 atm
2」2dito bo so loo o／e
re／atルθhumidity
Fig． 10−14． Coiniortable condit’on and atmospheric pressure
As shown in 1一”ig． 10−14 uncler the higher atmospheric pressure region， inan．
feels slightly warmer， due to the reduction of the evaporative heat transfer coeflicient．
le−5． Summary
The authors have proposed the Warmth Diagrain for eva｝uating the condition．
of thermal environment or estimating the thermal sensation．， and have shown its
effectiveness by solvi．ng． some examples．
116
’1〈an−iel“ro 1．BAr ・lo’1’o anc！ ’Yasunol）u NI＄1・11
44
Chapter 11． Comfort Detector
11−i． Model Man
In the existing methods of heating ancl air−conditioning control， the conditions
of the thermal environments have been specifiecl in terms of ambient temperature
only， or of the temperature and humidity． However， considering the complexities
of the thermai sensation the defects of the usual methocls are apparent． For
cletecting the comfort sensation． directly the authors propose the rationai metheds．
The heat balance equation， that induces tlte model skin temperature， can be
realized on the folloxxTing “moclel man”．
！ユ．） The model man is the circular cylin．der of 30 c加in diameter an．d 90 cm
i．n height， emitting the same rate of heat as man does， per unit time per unit
surface area．
（2 〉’ ！6 percent of the entire surface is completely saturated with water．
〈3） The surface is covered with some mac terial having the same heat and
vapor resistance ancl emissivity as that of clothing．
The inner temperature of the model man indicates the model skin temperature
directly．
Further， in an attempt to make a smal｝er scale model， the sensitivities to each
of the thermal factors were found to vary inclependently， so scaling clown may
have causecl the clistortion．
ll−2． Therma！ Sensatien Computer
By cletecting． each of the thermai factors as an electrical． signal， the model
ski．n temperature can be co．mputecl automcatically．
Fro．m Eq．（7−5）the model skin temperature 7いs given by
7ド佑∴7∴・廿．．田τ・・ナ．…耳．田 （1且）
cv，， ＋ tl’．
an．cl t’roni Eq． 〈2−2） we get
（／t． r一 in！・V” （！！−2）’
where V＝：：air−movement
’xVhi｝e， if the temperature of the black cylinder thermometer （a sort of globe
thermometer） is known， the surrouncling racliant temperature may be given by the
e’
曹浮≠狽撃盾
T，．一7∵。＋．儀・・．．．α隔．，，一7悔） （11−3）
cu．，．，”
where TB．，， 一＝ temperature of the black cylinder thermometer
The above relations can be expressecl by the following computing n．etwork．
4r）
117
’S．’1・itrmal Sensation t’iLnalysls ttnd its i‘iLpplicat／ion to iXir−ConditiQnlng
P，
MULT．
x
TB ・e
乏）／σck cア〃ηdθr ビθmρ．
一αン弄
X・Y
Pt ＝ ar
Y
9柵”
4c・c
Ps ＝” m’
R＝E・lt・A
F・G
air−moyement
Xm
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ac
Ps
一ac’ Ta
X
MULZ
0ノ区
X
X・Y
Y
F・G
X2
兀シ
u：iet butb temp．
Y
P．
凶
Y
ノ宅二1−a5・ε・κ
al c＋atr
P， 一M E・re一（C−b）
Ps
！言扁1＋ε・κ・a
Pp ＝： ar
dc
ambient temp，
瑠
ar
H
島一〃
P，e
UNIT
Fig． 11−1． Computing network for thermal sensatiui’i
11−3． Sununary
LMoclel skin temperature can be obtained by inoclel man or by thermal sen−
sation computer， airicl these devices may becoine the funclamentals for rational
autoniatic control of heating ancl air−conditioni．ng．
46
1〈an．ichiro iBAMQTo and． Y．aSUnobu LNTiS正．．1工
118
Appe捻．d圭x
respect to comfort indexe＄．
The attthors had presented． soine reports with
These are summarized below．
A−1． Discon！fort lndex
The discomfort ir］．dex （o，r U． S． ’X’Veather Bureau Temperature−Humiclity lndex）
is one of the simple and comprehensib｝e comfort indexes， and is given by the
combination of ambient temperatux”e and wet bulb temperature as
D．1＝＝］ O．72（7’i，， 一一 tl’」，．，） 一im 40・6 （a−！）
む 0．1
艶
50
1ts @ 一一一一・一一 E．τ （baS10 0んort♪
ミ
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巴
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40
、、 @ 、、、、 E・ z（OF？ o， f
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こ一一 こミ≡≡s’≡一嘉こ
s−
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ミ
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30
へ ヘ
20
40 bO 80 ／00．％
rθノ。加θ加〃グ！か
Fig． a−1． Relation between 1）isconxt’ort／ lndex and Effeetive ’lteniperature’
’XVhile， Fig． a−1 shows the re’la一 3？1
tioii between． Discoinfort lnclex ancl
＼ ＼
1！準！5翻／∫
Effective Temperature， where the
solicl and broken lines nearly coincide
uncler vLTindless circutmstances． Froin
the above， we can perceive that the
Discomfort lnclex is a siinplified
methocl to obtain the E’｛1’ective Te．m−
〃醜5々〃ノどゆ
ミ
ミ
、
ミ
ミ
亀
Setting aside its non−allowance
for radiation， ac s Yaglou has pointe（1
0utiO） the Effective Temperature over−
estiinates the influence of humidity，
一 『
＼
＼ ＼
∠）．∫
鞠幡撚の
一 卿 一
＼
ミ L’6
＼ ＼
ミ
＼
ミ
② 噂
今
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きレ
perature under restrictecl conditioi／is．
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一 一 一
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∼
＼i
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、
坐慢 な卦 ＼
翻こ＼
謁
ミ
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＼
g
＼
ミ
＼
＼
as shown in Fig． a−2．
As a resu｝t it may be conc｝udecl
2態
that in the presence of contro｝c’d air
inotion， coolecl or heated panel， sig一一
n．i丘can．t error wil／be in．troducecl， if
＼
＼
40 cto θ0 ノ（70％
．・∼∼．ott ve humtゴ”自・
Fig＋ a…Z．
C・ornparison bet’“，een 1）is．cotn／fort lndex
ancl the other lnde’xes．
47 Therinal Senstation ．Anal＞’sis and its ，tXppllcation ’to ．Air−Conditioning
119
the Discomfort lnclex is usecl for evaluating． the thermal environ．ment．
A−2． Correeted Eff’eetive Temaperature lndex
Vernon and his associate app｝ied a radiation． correction to Effective Tempera−
ture by using the globe thermometer in． place of the dry−bulb temperaturei’U．
Further， in the URited States the equivalent wet−bulb temperature，， as shown in Fig，．
a・一3， was proposed to replace the wet−bulb temperatureiL｝．
The problem in the subject is whether a globe thermometer of 15 cni in
diameter can evaluate the same radiatio．n ef．fect as that imposed on man． Fig． a−4
shows that the reading of eac’n globe thermometer depends on its cliameter．
む
RC’t
μ卿加ノη認廊charf
℃繊も
20
3
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φC印
ミ
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や
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t“一
Q
V ＝： 50 CM／S
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1
Ta ＝＝ l s Oc
書
／0
Tr＝： s Oc
xss
ar＝＝ 5 Kca／／m2・hr・Deg
碗
窪
佃
一一一
oa
06
乃 奄
la 20 Oe
amblent temp・
F三9・a−3・
Elquivalent ivet bui．1） tein．perature
Fig． a． 一…4・
1〈eading， of each gJlobe t／herinoniet／er
b w一・ vuv一．L to
As mentioned in Chapter 5， the equivalent body of the human may be assumed
to be a circular cylinder of 30 cm in cliameter， and in the low air−velocity range，
from Eqs． （2−2） ancl （2−3） we know the correspondintt． sphere of this cylinder
being of 40 cm in diameter．
In other words the reading of a g． Iobe thermometer of 40 cm in diameter
must be usecl for the proper racliation correction．． The following example shows
that the Corrected Effeetive Temperatures is improved by this inodification．
Example A−1 A room is maintained at dbt：250C， wbt： 200C， air一一moveme，nt：
1m／sec and the reading of the globe thermometer： 300C．
Estimate E．T， C．E．T （15， Y”） and C．E．T （4（）’‘） respectively．
βoZZ’廊0〃
We fincl 7L， ＝：：38．20C ancl T，（40S”）＝＝3！．70C by the similar manner on IEq． （11−3）．
The equivalent wet bulb temperatures are T侭15｛ラ）＝2ユ．5QC and 7．ll，，（40φ）＝22．OQC，
and the followin，cr．． result is obtaine（1．
120
48
Kan−ichiro ．1．B． ixpt4．orl”o an．（1 ｝t”asunobu Nls｝tl．
lin spite of a radiation correction，． it
Table a”1．
Coinparis， on between itl．’1’，
C．li’；．’1“ （15f”） and C．1’，．．T （，40； ），
seems that the usual． Correctecl Effective Tem−
perature can not evaluate the ra（liation effect
basic chart
normal ehart
properly． Besides， xKre must notice that the
modification of this stucly is useless for cor−
recting the deviation of Effective Temperature
itsel．f．
18．8
2ユ．2
c． ｝i，”r （lsti ）
L72．7
L4．5
C．E．T ［40f’・）
23．8
25，6
．正t）．戸．1．、
A−3． Heat Stress lndex
Belding． and Hatch proposecl the Heat Stress lndex which measured the magni−
tucle of heat stress imposed on indiviclua！s exposecl to different combinations of the
four components of the thermal． environment，（radia撹and air te・nperature、 air−
motion an．d humidity）an．cl operating at different levels of activitジ：s）
Apart from the question of approximations ancl assumptions in this index， the
authors have a few poin．ts i．n question on the physical accuracy of each heat
transfer coefllcient．
The convective and evaporative heat transfer coefllcients for human bod［y are
expresg． ed by
（a，，）”，．s・．，一 ＝T一 6．9． 5・VO’”’ ［kcal／in2・hr・Degl （．a−21
（P＞．，，，．，＝！1．7・VO”i lkcal／mL・hr・mmHg］ （a−3）
where 1，」＝：air一一velocity ［m／sec］
Further， in．ユ．963， ．Hatch correctecl these heat transfer coef丑cients by reex−
ainining the original datai’i・i5）
〈（u．），，，，＝（3 ．35 VO’6 （aHtcl，）
（β）．〃∼，一ユ．3ユ「［／o’6 （a−5）
Kco／／，刀2・hr・Deg
ノ5
装
・ミ
＄v
．b“
禽・・
S’L
糞
Xk
8s 5
E
O i− 狽?．i
a2 a．ヲ 〃5 0．75 ／ ／．5 2 3嬬
o／？’ ye／oGftit
Fig． aL5． Reiation bet／“’een conve’ c．t／ive hea！’ transfer coef”ficients
49
TiLernrLal S． ensation t’一Xnal＞．Tsis and its tis．pplicat．i．c）n to Air一（ll・oiTiditloirLiirLg，．
IL）1
Kca／／m”hr・mm”g
タ〃
z，
ヲ0物 の伽詑γ
tt
’
R
〃∂ど6カ
馨20
1％3〃ス1・
轡 ノ ノ
シ伽
ミ
F
t
7ノ
〆
ミ
ミ10
θ，∫乏．
動4θ石μ7・〆4
量
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！
11
4
ノ
〆！
〆
’
Y
@〆 〆
f
@ ノ
@ノ
m
！！
O，2 a．3 as a7s ／ ／．5 2 3 m！s
oir ve／ocfty
Fig． a−6． Relation bet’ween evaporat／ive heat transfer coeflicients
Figs． a−5 and a−6 show the relation between the above equatio．ns and each
heat transfer coeflflcient of circular cylinders．
From the above we 1〈now that on Heat Stress lnclex the equivalent body to
the human with respect to convective heat transfer is a cyliBder of ！5N25 cm
in diameter and that with respect to evaporative heat transfer is a fairly large
cylinder in higher air−velocity range． This may be the very cause for overestimating
the e｛モect of the air temperature and underestlmating the e脆ct of the hulnidity．
References
／0）
Yag， lou， C． 1？，： A ｝vlethocl for lmproving the lt）ffect／ive ”l／”emperat／ure ’rnclex， tA．S． HVE Trang．．
Vol． 53 （1947） p． 307．
／1．1 ）
X，’ernon， 1−1． iN，1． et al．： IFhe lnf／luence o．f the lmlunitidity of the IXir on Capacity ／for XN」ork at
I−ligh ’1“eniperature， IL of ILIyg． London， XJol． 32 （19．3Lt） p， 431．
12）
13）
A．ni． J． of Public ltlealth and Nation’s lileait；i Yearbook， XJol． tl（） （1950） p． ！4：，i
Beldlng， 1−1． S． and 1−latch， T． F， ： Ilndex for llt．．valuat5ng ’Heat Stres＄ in Terin＄ of Resui．ting．，
Physiologi・cal Strains， ILIeatin．g， Piping ＆ Air−Conclitioning， （1955， fiLu．gust） p． 129．
／l4＞
Irla， tch， ’1）． IF．： Assessnient of 1±leat Stress， ”1”einperature， lts Measureinent and Control in
Science and Iln（luf）’try． Reinhold， Ne“’ Y（）rl〈 （1963） p． 3（）7．
IL 5）
Nielson， N， et al，： ’！l’hernial F．xchange of ’t｝V［an at ’ILIigh ’1）eniperature， A．ni． J． ｛／）f Physio］．，
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