ArticlePDF Available

The P.E.T. comfort index: Questioning the model

Authors:
  • Institut National des Sciences Appliquées de Strasbourg

Abstract and Figures

[link to full text download on Elsevier https://authors.elsevier.com/a/1Wq~-1HudMvux8 (valid until May 25th 2018)] This work is a first thorough presentation of the widely used PET (Physiological Equivalent Temperature) comfort index. It underlines the simplifications made in solving the equation system for the PET and proposes a correction of the errors in the widespread version of the PET calculation routine. A comparison of the corrected model with a stringent solving of the equation system is made: as a result, the PET calculated after the original method introduces a bias of − 0.5 to + 2.3 [K] in the studied conditions (operative temperature, high mean radiant temperature and windy environments). The original vapour diffusion model is also examined and shows no dependency to the clothing level. The comparison with a state-of-the-art vapour transfer model exhibits a significant − 7 to + 2.6 [K] discrepancy with the corrected PET model in the aforementioned studied conditions. Links to the two versions of the code are provided in the appendix.
Content may be subject to copyright.
UNCORRECTED PROOF
J>A9>C<6C9CK>GDCB:CI MMM  MMMMMM
DCI:CIHA>HIH6K6>A67A:6I,8>:C8:>G:8I
J>A9>C<6C9CK>GDCB:CI
?DJGC6A=DB:E6<:LLL:AH:K>:G8DB
-=: )- 8DB;DGI >C9:M *J:HI>DC>C< I=: BD9:A
 06AI=:GY6 * D:HI8=:AY7Y Y
6AREP, 16 Avenue dIvry, 75013 Paris, France
7LMT-Cachan / ENS Paris-Saclay, 61 Avenue du Président Wilson 94230 Cachan, France
+-"% "'(
Keywords:
DB;DGI >C9:M
)-
>;;JH>DC K6EDJG IG6CH;:G
,-+-
-=>H LDG@ >H 6 RGHI I=DGDJ<= EG:H:CI6I>DC D; I=: L>9:AN JH:9 )- Physiological Equivalent Temperature 8DB;DGI
>C9:M "I JC9:GA>C:H I=: H>BEA>R86I>DCH B69: >C HDAK>C< I=: :FJ6I>DC HNHI:B ;DG I=: )- 6C9 EGDEDH:H 6 8DGG:8
I>DC D; I=: :GGDGH >C I=: L>9:HEG:69 K:GH>DC D; I=: )- 86A8JA6I>DC GDJI>C:  8DBE6G>HDC D; I=: 8DGG:8I:9 BD9:A
L>I= 6 HIG>C<:CI HDAK>C< D; I=: :FJ6I>DC HNHI:B >H B69: 6H 6 G:HJAI I=: )- 86A8JA6I:9 6;I:G I=: DG><>C6A B:I=D9
>CIGD9J8:H 6 7>6H D; V  ID   3$4 >C I=: HIJ9>:9 8DC9>I>DCH DE:G6I>K: I:BE:G6IJG: =><= B:6C G69>6CI
I:BE:G6IJG: 6C9 L>C9N :CK>GDCB:CIH
-=: DG><>C6A K6EDJG 9>;;JH>DC BD9:A >H 6AHD :M6B>C:9 6C9 H=DLH CD 9:E:C9:C8N ID I=: 8ADI=>C< A:K:A -=:
8DBE6G>HDC L>I= 6 HI6I:D;I=:6GI K6EDJG IG6CH;:G BD9:A :M=>7>IH 6 H><C>;>86CI V  ID   3$4 9>H8G:E6C8N
L>I= I=: 8DGG:8I:9 )- BD9:A >C I=: 6;DG:B:CI>DC:9 HIJ9>:9 8DC9>I>DCH %>C@H ID I=: ILD K:GH>DCH D; I=: 8D9:
6G: EGDK>9:9 >C I=: 6EE:C9>M
1. Introduction
-=: )- 8DB;DGI >C9:M >H 76H:9 DC I=: DG><>C6A LDG@ 7N +:;H 34
6C9 JH:9 6H 6 G:;:G:C8: >C I=: :GB6C CDGB /" 34 L=>8= EGDK>9:H 6
76H: ;DG I=: HDJG8: 8D9: D; I=: G6HH!DEE:G%69NJ< IDDA 34 (K:G I=:
E6HI 9:869: >I =6H 7::C JH:9 >C CJB:GDJH 86H: HIJ9>:H 34
-=>H 8DB;DGI >C9:M >H 76H:9 DC 6 ILDCD9: BD9:AD; I=: =JB6C
I=:GBDG:<JA6I>DC HNHI:B 6;I:G 34 ;GDB L=>8= I=: Standard Effec-
tive Temperature ,- L6H 9:G>K:9 ,J8= BD9:AH N>:A9 I=: @:N E6G6
B:I:GH >C I=: :HI>B6I>DC D; 8DB;DGI 8DG: I:BE:G6IJG: H@>C I:BE:G6IJG:
6C9 H@>C L:II:9C:HH G:HJAI>C< ;GDB I=: :MEDH>I>DC ID I=: :CK>GDCB:CI
8DCH>9:G:9
-=: EG>C8>EA: D; I=:H: >H ID G:IG>:K: I=: I:BE:G6IJG: D; 6 G:;:G:C8:
:CK>GDCB:CI I=6I LDJA9 EGDKD@: I=: H6B: E=NH>DAD<>86A G:HEDCH: 6H
I=: HIJ9>:9 :CK>GDCB:CI DG 7DI= I=: )- 6C9 ,- I=: G:;:G:C8: :C
K>GDCB:CI >H K:GN H>B>A6G ID 6C D;R8: ADL 6>G K:AD8>I>:H G:HE:8I>K:AN
 3BHYV4 6C9  3BHYV4  G:A6I>K: =JB>9>IN DG  3)64 ;DG
)- -=: B:I67DA>8 A:K:A ;DG )- >H 8DBEDH:9 D;  304 68I>K>IN EAJH
I=: 76H6A B:I67DA>HB L=>8= 9:E:C9H DC I=: 6<: <:C9:G 6C9 BDGE=DA
D<N D; I=: HJ7?:8I
-=: B6>C 9>;;:G:C8: 7:IL::C I=: ,- 6C9 )- 8DB;DGI >C9:M:H 6G:
;DAADL>C<
-=: ,- >H I=: 6>G I:BE:G6IJG: >C I=: G:;:G:C8: :CK>GDCB:CI N>:A9>C<
I=: H6B: H@>C I:BE:G6IJG: 6C9 H@>C L:II:9C:HH 6H I=: 68IJ6A :CK>GDC
B:CI L=:G:6H I=: )- >H I=: 6>G I:BE:G6IJG: >C I=: G:;:G:C8: :CK>
GDCB:CI N>:A9>C< I=: H6B: H@>C 6C9 8DG: I:BE:G6IJG:H 6H I=: 68IJ6A
:CK>GDCB:CI
-=: )- 8ADI=>C< A:K:A >H H:I 6I  38AD4 ;DG I=: HI6C96G9 :CK>GDCB:CI
L=:G:6H I=: ,- 8ADI=>C< A:K:A >H 86A8JA6I:9 ID B6I8= I=: 68I>K>IN
A:K:A
-=: ,- >H 86A8JA6I:9 6;I:G 6 IG6CH>:CI 86A8JA6I>DC L=:G: I=:
ILDCD9: BD9:A D; B:I67DA>HB >H :MEDH:9 ID I=: 8DC9>I>DCH ;DG L=>8=
8DB;DGI =6H ID 7: :K6AJ6I:9 -=: )- B6N 7: 86A8JA6I:9 >C 7DI= HI:69N
6C9 JCHI:69N 8DC9>I>DCH D; I=: B:I67DA>HB >I I=: A6II:G 86H: >I >H JH:9
L>I= I=: "&& Instationary Munich Energy balance Model34 "C
I=>H LDG@ L: :M6B>C6I: I=: HI:69NHI6I: 86A8JA6I>DC
"C 8DBE6G>HDC L>I= I=: L:AA@CDLC )&/ >C9:M 34 I=6I JH:H 6 I=:G
B6A H:CH6I>DC H86A: I=: G:HJAIH D; I=: )- 6C9 ,- 6G: :6H>:G ID JC
9:GHI6C9 6H I=:N G:EG:H:CI 6 I:BE:G6IJG: -=: )- >H 6AHD 696EI:9 ID
:K6AJ6I>C< DJI9DDG :CK>GDCB:CI L=:G: I=:GB6A 9>H8DB;DGI 86C 7: =><=
L=:G:6H I=: )&/ L6H 8DCHIGJ8I:9 ;DG I=: >C9DDG HE68: &DG:DK:G G:
HJAIH EGDK>9:9 7N I=: )&/ 6G: ID 7: I6@:C L>I= 86G: L=:C DJI D; I=:
I:BE:G6IJG: G6C<: ;DG L=>8= >I =6H 7::C :HI67A>H=:9 id est  ID 3Y°4
D; G69>6CI I:BE:G6IJG: 34
DGG:HEDC9>C< 6JI=DG
Email addresses: :9DJ6G9L6AI=:G6G:E;G  06AI=:G FJ:CI>C<D:HI8=:A:CH868=6C;G * D:HI8=:A
=IIEH9D>DG<?7J>A9:CK
+:8:>K:9 :7GJ6GN+:8:>K:9>CG:K>H:9;DGB &6G8=88:EI:9 &6G8=
K6>A67A:DCA>C: MMM
 P 
UNCORRECTED PROOF
E. Walther, Q. Goestchel Building and Environment xxx (2018) xxx-xxx
-D I=: 7:HI D; I=: 6JI=DGH @CDLA:9<: I=: DG><>C6A 9:K:ADEB:CI D;
I=: )- 34 86C DCAN 7: ;DJC9 6H =6G9 8DEN :I6>AH D; I=: BD9:A 86C
DI=:GL>H: DCAN 7: G:69 E6GI>6AAN >C +:;H 34 DG 9:8GNEI:9 ;GDB I=:
8D9: >C I=: 6EE:C9>M D; 34Y -=:G:;DG: >I >H ?JHI>R:9 ID :MEDH: I=:
BD9:A I=DGDJ<=AN RGHI H=DL>C< I=: 6HHJBEI>DCH B69: L=:C HDAK>C< ;DG
I=: )- >H8G:E6C8>:H I=6I G:HJAI ;GDB I=: H>BEA>;N>C< 6HHJBEI>DCH 6C9
H=DGI8DB>C<H D; I=: BD9:A 6G: :MEDH:9 >C I=: H:8DC9 E6GI D; I=: 6GI>8A:
-=: EJGEDH: 6C9 D7?:8I>K:H D; I=>H E6E:G 6G: =:C8: I=: ;DAADL>C<
)GDK>9: 6C :M=6JHI>K: 9:H8G>EI>DC D; I=: BD9:A 6C9 >IH DG><>C6A G:HDAJ
I>DC G:HE:8I>K:AN >C H:8I>DCH  6C9 
.C9:GA>C: I=: :GGDGH D; I=: L>9:HEG:69 )- GDJI>C: JH:9 >C +:;H
34 >C H:8I>DC  6C9 EGDK>9: 6 8DGG:8I:9 K:GH>DC >C I=:
EE:C9>M 
DBE6G: I=: H>BEA>R:9 G:HDAJI>DC JH:9 >C I=: DG><>C6A BD9:A L>I= 6
HIG>C<:CI G:HDAJI>DC D; I=: :FJ6I>DC HNHI:B ;DG I=: )- >C H:8I>DC 
DBE6G: I=: :;;:8I D; I=: DG><>C6A K6EDJG 9>;;JH>DC BD9:A L>I= 6
HI6I:D;I=:6GI DC: >C H:8I>DC  6C9 EGDK>9: I=: 8DGG:HEDC9>C<
GDJI>C: >C I=: EE:C9>M 
2. Description of the two-node model
 8DBBDC 6EEGD68= ;DG I=: :K6AJ6I>DC D; 8DB;DGI >C H:B>DJI9DDG
HE68:H >H ID JH: 6 BD9:A D; I=: =JB6C B:I67DA>HB G:EG:H:CI:9 6H ILD
8DC8:CIG>88NA>C9:GH ;DG 8DG: 6C9 H@>C 8DBE6GIB:CIH 6H 9:H8G>7:9 >C I=:
LDG@ D; 34 C JE96I:9 K:GH>DC 86C 6AHD 7: ;DJC9 >C +:; 34 AA
:FJ6I>DCH >C I=>H H:8I>DC DG><>C6I: ;GDB I=: 8D9: >C I=: 6EE:C9>M D; 34
JCA:HH HE:8>R:9 DI=:GL>H:
2.1. Heat transfer with the environment
-=: B:I67DA>8 >CI:GC6A :C:G<N >H 86A8JA6I:9 6;I:G I=: 76H6A B:I67D
A>HB 6C9 I=: 68I>K>IN D; I=: HJ7?:8I -=: 76H6A B:I67DA>HB M9:E:C9H DC
I=: B6HH m =:><=I H6C9 6<: ;DG B6A: FJ6I>DC  6C9 ;:B6A: >C9>
K>9J6AH FJ6I>DC 


-=: =:6I :M8=6C<: D88JGG>C< L=:C I=: 6>G >H =:6I:9 DG 8DDA:9 7N I=:
AJC<H 6I 8DG: I:BE:G6IJG: 6H L:AA 6H I=: B6HH :M8=6C<: L>I= I=: 6B7>
:CI 6>G 6G: 6AHD I6@:C >CID 688DJCI -=: 7G:6I=>C< SDL G6I: >H 9:
E:C9:CI DC I=: 68I>K>IN A:K:A M30BYV4

-=: I:BE:G6IJG: D; I=: 6>G :ME>G:9 T:ME >H 8DGG:A6I:9 ID I=: 6B7>:CI
6>G I:BE:G6IJG: Ta

-=: )NI=DC HDJG8: 8D9: ;DG )- 86A8JA6I>DC 86C 6AHD 7: 9DLCAD69:9 DC >I=J7
-=: H:CH>7A: =:6I ADHH CG:HE >H I=:C 86A8JA6I:9 L>I= I=: I:BE:G6IJG:
9>;;:G:C8: 7:IL::C >CHE>G:9 6C9 :ME>G:9 6>G 6C9 I=: 6>G HE:8>R8 =:6I 86
E68>IN c6

H ;DG A6I:CI =:6I IG6CH;:G >I >H 6HHJB:9 I=6I I=: 6>G >H H6IJG6I:9 L>I=
=JB>9>IN L=:C :M>I>C< I=: AJC<H 6I I:BE:G6IJG: T:ME FJ6I>DC  6>G
8ADH: ID H6IJG6I>DC DG H6IJG6I:9 L6H B:6HJG:9 7N +:; 34 -=: K6EDJG
EG:HHJG: D; 6>G :ME>G:9 >H 86A8JA6I:9 6;I:G I=: 8DGG:A6I>DC ;DG H6IJ
G6I:9 K6EDJG EG:HHJG:

-=: A6I:CI =:6I IG6CH;:G EG:HE >H I=:C 86A8JA6I:9 L>I= I=: 9>;;:G:C8:
D; K6EDJG EG:HHJG:H 6H

L=:G: p>H I=: 6IBDHE=:G>8 EG:HHJG: 6C9 LvI=: A6I:CI =:6I D; K6EDG>O6
I>DC
8IJ6AAN I=: =:6I :M8=6C<: 7N 7G:6I=>C< QG:HE >H I=: HJB D; I=: H:C
H>7A: 6C9 A6I:CI =:6I SJM:H QG:HE CG:HE EG:HE FJ6I>DCH  6C9
 6G: H>BEA>R:9 K:GH>DCH D; I=: 68IJ6A 7G:6I=>C< =:6I IG6CH;:G =DL
:K:G L>I= 6 8DGG:8I A:K:A D; 6EEGDM>B6I>DC 6 9:I6>A:9 6C6ANH>H >H <>K:C
>C EE:C9>M 
-=: 7D9N HJG;68: >H 86A8JA6I:9 6;I:G I=: J7D>H HJG;68: A>C HFJ6G:
B:I:GH 9:E:C9>C< DC I=: 7D9N B6HH m6C9 =:><=I H 9:H8G>7:9 >C FJ6
I>DC 

-=: HJG;68:H D; :M8=6C<: L>I= I=: 6B7>:CI 8DC9>I>DCH 6G: HEA>I >CID
76G: 6C9 8ADI=:9 6G:6H -=: ;G68I>DC D; I=: 7D9N 8DK:G:9 7N 8ADI=:H >H
<>K:C 7N ;DAADL>C< 8DGG:A6I>DC 9:E:C9>C< DC I=: 8ADI=>C< A:K:A i8A >C 8AD

-=: 76G: 6G:6 A76G: >H 6 ;G68I>DC D; I=: 8ADI=:9 HJG;68:

I I=: HJG;68: D; I=: 7D9N 8DCK:8I>DC 6C9 G69>6I>DC ADHH:H 6G: EGD
EDGI>DC6A ID I=: 8ADI=>C< HJG;68: A8A L=>8= >H 86A8JA6I:9 7N HJ7IG68I>C<
I=: HJG;68: D; I=: 76G: 8NA>C9:G AX V f68A ID I=: 8ADI=>C< HJG;68: Af8A

"C FJ6I>DC  I=: I:GB f8A >H I=: JGIDC 8D:;R8>:CI I=6I 9:H8G>7:H
I=: A>C:6G >C8G:6H: D; =:6I :M8=6C<: 6G:6 L>I= 8ADI=>C< A:K:A i8A I=: >C
8G:6H: 86C 6AHD 7: 6 E>:8:L>H: A>C:6G ;JC8I>DC 34

-=: =:6I SJM I=GDJ<= I=: 8ADI=>C< >H 86A8JA6I:9 6;I:G DJG>:GH A6L
I=GDJ<= 6 8NA>C9:G -=: >CI:GC6A 6C9 :MI:GC6A G69>JH D; I=: 8NA>C9:G 6G:
G:FJ>G:9 %:I r67: I=: >CH>9: G69>JH D; 8ADI=>C< DG 6C >C9>K>9J6A =:><=I
D; H6C9 6 8ADI=:9 ;G68I>DC D; 7D9N y I=: 8ADI=:9 6G:6 >H I=: DC: D; 6
8NA>C9:G D; =:><=I HXy6C9 >H :FJ6A ID I=: IDI6A HJG;68: D; I=: 7D9N BJA
UNCORRECTED PROOF
E. Walther, Q. Goestchel Building and Environment xxx (2018) xxx-xxx
I>EA>:9 7N I=: ;G68I>DC 8DK:G:9 7N 8ADI=>C< AXf68A

"C I=: DG><>C6A )- BD9:A I=: 8ADI=:9 ;G68I>DC D; 7D9N K6G>:H >C 9:
E:C9:C8N L>I= I=: A:K:A D; 8ADI=>C< i8AD 6;I:G ;DAADL>C< G:A6I>DCH=>EH



-=: :MI:G>DG G69>JH D; I=: 8ADI=>C< 8NA>C9:G D; G69>JH r76C9 =:><=I
HXy>H 86A8JA6I:9 6H ;DAADLH


-=: 76G: 6G:6 >H I=: HJG;68: D; I=: >CI:GC6A 8NA>C9:G D; G69>JH r66C9
=:><=I HI=6I >H CDI 8DK:G:9 L>I= 8ADI=>C<

-=: 8ADI=>C< =:6I IG6CH;:G 8DC9J8I6C8: >H 86A8JA6I:9 6;I:G DJG>:GH
A6L I=GDJ<= 6 8NA>C9:G

-=: :FJ>K6A:CI 8DC9J8I>K>IN D; 8ADI=>C< λ8A >H 86A8JA6I:9 JH>C< I=:
8ADI=>C< I=>8@C:HH r7Vr6

I I=: 8ADI=>C< 6C9 H@>C HJG;68: I=: 8DCK:8I>DC =:6I IG6CH;:G 8D:;R
8>:CI h8>H 86A8JA6I:9 6;I:G 8DGG:A6I>DC

DCK:8I>DC ADHH:H 6G: 86A8JA6I:9 ;DG 7DI= 76G: C76G: 6C9 9G:HH:9 6G
:6H D; I=: 7D9N C8AD 9:E:C9>C< DC 6>G H@>C 6C9 8ADI=:H I:BE:G6IJG:H
HJ8= I=6I


:;DG: 86A8JA6I>C< G69>6I>DC ADHH:H I=: ;G68I>DC D; I=: 7D9N :;;:8
I>K:AN HJ7?:8I ID G69>6I>DC >H 9:RC:9 6H f:U "I >H 6 G:9J8I>DC ;68IDG I=6I
9:E:C9H DC I=: EDH>I>DC D; I=: >C9>K>9J6A -=: :;;:8I>K: G69>6I>K: 6G:6 >H
I=:C AXf:U -=: G69>6I>DC ADHH:H R76G: D; I=: 76G: ;G68I>DC D; I=: 7D9N
I:BE:G6IJG:H 7:>C< :MEG:HH:9 >C $:AK>C >H 6H ;DAADLH

"C :FJ6I>DC  εH@ >H I=: :B>HH>K>IN D; H@>C 6C9 σ>H I=: ,I:;6CDAIO
B6CC 8DCHI6CI
+69>6I>DC ADHH:H D; I=: 8ADI=:9 ;G68I>DC D; I=: 7D9N R8AD L>I= 6 8ADI=
>C< :B>HH>K>IN ε8A 6G: HJ8= I=6I

-=: =:6I IG6CH;:G ;GDB I=: 8DG: ID I=: H@>C A6N:G D88JGH >C E6G6AA:A via
8DC9J8I>DC I=GDJ<= I=: H@>C L>I= 6 =:6I IG6CH;:G 8D:;R8>:CI UH@ 6ADC<
L>I= 7ADD9 SDL q7L=>8= 8G:6I:H 6C 699>I>DC6A SJM I=:H: I:GBH 6G: :M
EA6>C:9 >C ,:8I>DC 
 G:EG:H:CI6I>DC D; =:6I IG6CH;:G I=GDJ<= I=: 7D9N H=:AA >H 9G6LC
L>I= I=: :FJ>K6A:CI :A:8IG>86A H8=:B: DC ><  (C I=: A:;I=6C9 H>9:
D; I=: R<JG: DC: 86C D7H:GK: I=: E6G6AA:A =:6I IG6CH;:G G:H>HI6C8:H 7:
IL::C 8DG: T8 6C9 H@>C TH@ G:A6I:9 ID I>HHJ: 8DC9J8I6C8: 6C9 7ADD9
SDL (C I=: G><=I=6C9 H>9: D; ><  I=: =:6I IG6CH;:G G:H>HI6C8: 7:
IL::C I=: H@>C I:BE:G6IJG: 6C9 I=: :CK>GDCB:CI 6I 6>G I:BE:G6IJG: T6
6C9 G69>6CI I:BE:G6IJG: TBGI >H 9G6LC I=: ADL:G ILD G:H>HI6C8:H G:EG:
H:CI I=: 8DCK:8I>K: 6C9 G69>6I>K: =:6I IG6CH;:G G:H>HI6C8: 7:IL::C H@>C
6C9 :CK>GDCB:CI I=: JEE:G E6GI >C8AJ9:H I=: 8ADI=>C< A6N:G G:H>HI6C8:
R8A >C 7:IL::C H@>C 6C9 :CK>GDCB:CI
2.2. Thermal control of the body
-=: E=NH>DAD<>86A 8DCIGDA BD9:A D; I=: )- >H 76H:9 DC I=: )>:G8:
ILDCD9: BD9:A 34 "I 86C 7: H::C 6H 6 I=:GB6AAN G:<JA6I:9 HNHI:B
:KDAK>C< >C G:HEDCH: ID I=: I:BE:G6IJG: 9>;;:G:C8: L>I= I=: H@>C 8DG:
6C9 7D9N H:I I:BE:G6IJG:H /6HDBDIG>8>IN 6C9 HL:6I>C< 6G: I=: ILD
B6>C E=:CDB:C6 JH:9 ;DG I:BE:G6IJG: 8DCIGDA -=: H=>K:G>C< :;;:8IH
EG:H:CI:9 ;DG >CHI6C8: >C +:;H 34 6G: CDI JH:9 >C I=: DG><>C6A K:G
H>DC D; I=: GDJI>C: 34
Fig. 1. FJ>K6A:CI :A:8IG>86A H8=:B: ;DG I=: HI:69NHI6I: =:6I IG6CH;:G ;GDB 8DG: ID H@>C
UNCORRECTED PROOF
E. Walther, Q. Goestchel Building and Environment xxx (2018) xxx-xxx
-=: 7ADD9 SDL G6I: q7>H GJA:9 7N I=: 9>;;:G:C8: D; 7DI= H@>C 6C9
8DG: I:BE:G6IJG:H L>I= I=:>G H:I K6AJ:H 6H E:G FJ6I>DC 

-=: 8D:;R8>:CIH Cd6C9 CsG:A6I: ID I=: 9>A6I>DC 6C9 8DCHIG>8I>DC E=:
CDB:C6 -=: 8DCIGDA B:8=6C>HB >H HJ8= I=6I I=: I:BE:G6IJG: 9>;;:G
:C8:H 6G: H:I ID O:GD >C FJ6I>DC  L=:C I=:N 6G: C:<6I>K: -=: JEE:G
A>B>I D; 7ADD9 SDL >H H:I 6I  3%BYV=YV4 L=:G: 6H I=: H:I K6AJ: >H
 3%BYV=YV4
-=: 7D9N I:BE:G6IJG: T7>H I=: L:><=I:9 6K:G6<: D; H@>C 6C9 8DG:
I:BE:G6IJG:

"C I=: /" CDGB I=: B6HH ;G68I>DC D; 7D9N 8DBEDH:9 D; H@>C DG 8DG:
>H 8DCHI6CI 6C9 9D:H CDI 9:E:C9 DC 7ADD9 SDL =:C8: >I 9D:H CDI 6;;:8I
I=: 86A8JA6I>DC D; T7 JCA>@: >C I=: IG6CH>:CI ILDCD9: BD9:A >C +:;H
34 FJ6I>DC  =6H 6 B6?DG >CSJ:C8: >CHD;6G 6H >I EGDK>9:H
I=: I:BE:G6IJG: 6I L=>8= I=: HL:6I>C< A6I:CI =:6I SJM 7:<>CH
,L:6I>C< >H 8DCIGDAA:9 7N I=: 7D9N I:BE:G6IJG: IG><<:G>C< I=: EGD
9J8I>DC D; HL:6I 9:E:C9>C< DC I=: 9>H8G:E6C8N L>I= I=: 7D9N H:I I:B
E:G6IJG: 6C9 I=: HL:6I>C< 8D:;R8>:CI CHL  X V 
3@<BYV=YV$YV4 6H E:G

"C I=: DG><>C6A BD9:A 34 6C 699>I>DC6A 8D:;R8>:CI D;  6EEA>:H
ID FJ6I>DC  ;DG ;:B6A: >C9>K>9J6AH
-=: :K6EDG6I>DC EHL 6I H@>C HJG;68: 9:E:C9H DC I=: EGD9J8I>DC D;
HL:6I 6C9 DC I=: A6I:CI =:6I LK

-=: B6M>BJB =:6I SJM EB6M I=6I 8DJA9 :K6EDG6I: ;GDB I=: H@>C 6I
H6IJG6I:9 K6EDJG EG:HHJG: pKHTH@ ID I=: <>K:C :CK>GDCB:CI 6I 6 K6EDJG
EG:HHJG: p6>H 9:E:C9>C< DC I=: K6EDJG IG6CH;:G :;R8>:C8N FE8A 6C9 I=:
A6I:CI =:6I IG6CH;:G 8D:;R8>:CI h:

"C I=: A>I:G6IJG: I=: K6EDJG IG6CH;:G :;R8>:C8N ;68IDG FE8A D; FJ6
I>DC  >H D;I:C :MEG:HH:9 6H ;DAADLH 34 H:: 6AHD I=: 9:I6>A:9 :MEA6
C6I>DC D; 34

-=: A6I:CI =:6I IG6CH;:G 8D:;R8>:CI h:>C 30BYV)6YV4 >H <>K:C 6;I:G
I=: %:L>H G:A6I>DC LR HJ8= I=6I

-=: %:L>H G:A6I>DCH=>E LR >H 86A8JA6I:9 6;I:G I=: 6C6AD<N 7:IL::C
=:6I 6C9 B6HH IG6CH;:G 34

"C <:C:G6A I=: %:L>H G6I>D HI6C9H 7N LRW 3$)6YV4 -=: K;68
IDG >C FJ6I>DC  688DJCIH ;DG BDA:8JA6G 8DJCI:G 9>;;JH>DC D; 9GN 6>G
6<6>CHI I=: SDL D; L6I:G K6EDJG 6C9 >H <:C:G6AAN 8DBEG>H:9 6GDJC9 
D; I=: K6EDJG SDL 34 -=: 86A8JA6I>DC ;DG 6B7>:CI 8DC9>I>DCH D; 
 G:A6I>K: =JB>9>IN 6C9 6 H6IJG6I:9 H@>C 6I  N>:A9H K 
9:I6>A:9 :MEA6C6I>DCH D; I=: 86A8JA6I>DC 86C 7: ;DJC9 >C =6EI:G  D;
34
"C I=: 8D9: EGDK>9:9 6ADC< I=: /" CDGB I=: G:A6I>DCH=>E ;DG I=:
:K6EDG6I>K: =:6I IG6CH;:G 8D:;R8>:CI >H <>K:C 6;I:G FJ6I>DC  ;DG
L=>8= CD G:;:G:C8: 8DJA9 7: ;DJC9

-=>H :MEG:HH>DC N>:A9H 6C DG9:G D; B6<C>IJ9: D; I=: %:L>H G6I>D =DL
:K:G >I >H <:C:G6AAN W 7:ADL I=: K6AJ:H <>K:C 7N FJ6I>DC 
-=: IDI6A A6I:CI SJM EIDI 6I H@>C HJG;68: >H I=:C I=: HJB D; I=: HL:6I
>C< 6C9 9>;;JH>DC E=:CDB:C6

"C DG9:G ID 86A8JA6I: I=: 9>;;JH>DC ADHH:H E9>U I=: H@>C L:II:9C:HH
w>H >CIGD9J8:9 "I G:EG:H:CIH I=: G6I>D D; I=: A6I:CI SJM 9>HH>E6I:9 7N
HL:6I 6I I=: HJG;68: D; H@>C EIDI 6<6>CHI I=: B6M>BJB A6I:CI SJM EB6M

"; I=: H@>C L:II:9C:HH w>H <G:6I:G I=6C DC: >I >H H:I ID JC>IN 6C9 I=:
A6I:CI SJM >H 6I I=: HJG;68: D; H@>C >H HJ8= I=6I EHL EB6M (I=:GL>H:
9>;;JH>DC D88JGH I=GDJ<= I=: HD 86AA:9 CDCL:II:9E6GI D; H@>C  V w
6C9 ;DAADL>C< G:A6I>DC 6EEA>:H >C I=: /" CDGB

-=: G:H>HI6C8: ID K6EDJG 9>;;JH>DC R9D; FJ6I>DC  >H H>BEAN 9:
RC:9 L>I=DJI HJEEDGI>C< ?JHI>R86I>DC 6H 6 8DCHI6CI R9 X
3)6H@<YV4 ;DG L=>8= CD G:;:G:C8: 8DJA9 7: ;DJC9 0: HE:8JA6I: I=6I
I=>H B><=I 7: 6 H@>C I>HHJ: K6EDJG 9>;;JH>DC 8D:;R8>:CI =DL:K:G I=>H ;DG
BJA6I>DC >H HJGEG>H>C< 6H >I LDJA9 I6@: I=: K6EDJG EG:HHJG: 6I H@>C I:B
E:G6IJG: >CHI:69 D; I>HHJ: I:BE:G6IJG: 6C9 C:<A:8IH I=: :;;:8I D; 8ADI=>C<
DC K6EDJG 9>;;JH>DC
 <:C:G>8 ;DGBJA6I>DC ;DG I=: K6EDJG 9>;;JH>DC =:6I ADHH ;GDB I=:
CDCL:II:9 HJG;68: D; H@>C LDJA9 7: ;DAADL>C< 34

FJ6I>DC  G:FJ>G:H I=: 8DBEJI6I>DC D; I=: :K6EDG6I>K: G:H>HI6C8:
D; I=: 6>G 6C9 8ADI=>C< A6N:GH R:;DG :M6BEA: 7N I=: B:I=D9 I=DGDJ<=AN
9:H8G>7:9 >C +:; 34 -=: :K6EDG6I>K: G:H>HI6C8: >H 8DBEJI:9 6;I:G I=:
=:6I IG6CH;:G G:H>HI6C8: D; 6>G R6>G 6C9 8ADI=>C< R8A HJ8= I=6I

L=:G: R6>G >H I=: 8DB7>C:9 8DCK:8I>K: 6C9 A>C:6G>O:9 G69>6I>K: =:6I
IG6CH;:G G:H>HI6C8: 6C9 im>H I=: 0DD98D8@ E:GB:67>A>IN >C9:M <:C:G6AAN
I6@:C 6I  34
UNCORRECTED PROOF
E. Walther, Q. Goestchel Building and Environment xxx (2018) xxx-xxx
3. Original solving of the model
"C I=>H H:8I>DC I=: B:I=D9 ;DG HDAK>C< I=: )- :FJ6I>DC 9:H8G>7:9 >C
I=: /" CDGB >H EG:H:CI:9
3.1. Governing equations
!öEE:H G:EG:H:CI6I>DC D; I=: =JB6C B:I67DA>HB >H 6AHD 76H:9 DC I=:
)>:G8: ILDCD9: BD9:A 6H E:G 34 0G>I>C< I=: =:6I SJM :FJ6A>IN
I=GDJ<= 8ADI=:H I=6I :FJ6AH 8DCK:8I>DC 6C9 G69>6I>DC ADHH:H 6I I=: 8ADI=
>C< HJG;68: 6H E:G ><  DC: D7I6>CH

-=: H:8DC9 :FJ6I>DC D; I=: BD9:A >H 6 76A6C8: DC I=: 8DG: CD9:
-=: 6A<:7G6>8 HJB D; B:I67DA>8 G6I: 6C9 G:HE>G6IDGN ADHH:H :FJ6AH I=:
=:6I SJM :M8=6C<:9 ;GDB 8DG: ID H@>C 7N 8DC9J8I>DC 6C9 7ADD9 SDLG6I:
I=GDJ<= I=: H@>C A6N:G

"C FJ6I>DC  I=: G><=I=6C9 H>9: G:EG:H:CIH I=: =:6I IG6CH;:G
;GDB I=: >CH>9: D; I=: 7D9N IDL6G9H I=: HJG;68: D; I=: H@>C K>6 I=: S:H=
:FJ>K6A:CI 8DC9J8I>DC U6C9 7ADD9 SDL q7 -=: A:;I=6C9 H>9: HI6C9H
;DG I=: B:I67DA>8 =:6I EGD9J8I>DC G6I: M6H L:AA 6H I=: H:CH>7A: 6C9 A6
I:CI ADHH:H 7N 7G:6I=>C<
-=: I=>G9 :FJ6I>DC D; I=: BD9:A >H 6 <AD76A HI:69NHI6I: 76A6C8: DC
I=: 7D9N HJBB>C< B:I67DA>8 68I>K>IN 8DCK:8I>DC G69>6I>DC HL:6I>C<
9>;;JH>DC ADHH:H 6C9 G:HE>G6IDGN ADHH:H

L=:G: C6C9 RHI6C9 ;DG I=: 8DCK:8I>DC 6C9 G69>6I>DC DC 7DI= I=:
8ADI=:9 6C9 76G: ;G68I>DCH D; I=: 7D9N FJ6I>DC  >CIG>CH>86AAN 8DC
I6>CH I=: B:I67DA>8 G:68I>DCH D; I:BE:G6IJG: G:<JA6I>DC D; I=: 7D9N >C
I=: 8DCH>9:G:9
0=:C T86C9 TH@ G:HJAI>C< ;GDB I=: HIJ9>:9 :CK>GDCB:CI 6G: @CDLC
I=: 6>G 6C9 8ADI=>C< I:BE:G6IJG:H 6G: >I:G6I>K:AN 69?JHI:9 HJ8= I=6I
FJ6I>DC  :FJ6AH O:GD I=: 7D9N 7:>C< >C I=: G:;:G:C8: :CK>GDCB:CI
9:H8G>7:9 >C ,:8I>DC  -=: 6>G I:BE:G6IJG: D7I6>C:9 >H I=: )-
.H>C< I=: =NEDI=:H>H I=6I I=: I=G:: JC@CDLC I:BE:G6IJG:H T8TH@T8A
6G: >C9:E:C9:CI HDAK>C< ;DG I=: :68= D; I=:B H:E6G6I:AN >H EDHH>7A: "C
DG9:G ID G:9J8: I=: CJB:G>86A 8DBEA:M>IN D; I=: EGD7A:B I=: DG><>C6A
K:GH>DC D; I=: 8D9: 9:K:ADE:9 7N !öEE: 6C9 EGDK>9:9 6ADC< L>I= 34
C:<A:8IH I=: 9:E:C9:C8N 7:IL::C 8DG: 6C9 H@>C I:BE:G6IJG: L>I= I=:>G
:CK>GDCB:CI -=: >CSJ:C8: D; I=: :CK>GDCB:CI DC I=: 7D9N I:BE:G6
IJG:H 6EE:6GH DCAN I=GDJ<= I=: 86A8JA6I>DC D; TH@
3.2. Second-order polynomials for thermoregulation cases
&6@>C< I=: 6HHJBEI>DC I=6I :FJ6I>DCH 6G: >C9:E:C9:CI G:9J8:H I=:
EGD7A:B ID HDAK>C< I=: H:8DC9 DG9:G EDANCDB>6A  L>I= T87:>C< I=:
JC@CDLC -=: H@>C I:BE:G6IJG: >H HJEEDH:9 8DCHI6CI 9JG>C< I=: >I:G
6I>DC 6C9 I=: EGD8:9JG: G:E:6IH DK:G I=: L=DA: HNHI:B JCI>A 8DCK:G
<:C8: >H G:68=:9 -=: 9>;;:G:CI EDANCDB>6AH I=6I 8DGG:HEDC9 ID I=: I=:G
BDG:<JA6I>DC EDHH>7>A>I>:H 9:E:C9>C< DC K6HDBDIG>8>IN 6G: EG:H:CI:9
>C I=>H E6G6
<G6E=
,:I K6AJ: D; I=: 7ADD9 SDL G6I: "C I=>H H>IJ6I>DC I=: 76A6C8: :FJ6I>DC
H>BEA>R:H ID I=: ;DAADL>C<

&6M>BJB 7ADD9 SDL G6I: ;DAADL>C< :FJ6I>DC G:EG:H:CIH I=: B6M>
BJB 7ADD9 SDL G6I: 8DCR<JG6I>DC >C !öEE:H DG><>C6A 8D9:

,:I K6AJ: D; 7ADD9 SDL 6C9 8DA9 H><C6A ;GDB I=: H@>C "C I=>H 86H: I=:
<:C:G6A :FJ6I>DC G:69H

-=: HIG>8I>DC 8DCHI6CI >H I6@:C 6H Cs  3$YV4
"C I=: 86H: D; EJG: K6HD9>A6I6I>DC FJ6I>DC  G:9J8:H ID 6 H:8DC9
DG9:G EDANCDB>6A HJ8= I=6I

"C FJ6I>DC  I=: 8D:;R8>:CIH abc6G: 6H



0=:C K6HD9>A6I>DC 6C9 8DCHIG>8I>DC D88JG 6 H>B>A6G H:8DC9 DG9:G EDAN
CDB>6A 86C 7: 9:G>K:9 6C9 I=: 8D:;R8>:CIH abcD; FJ6I>DC  I6@:
;DAADL>C< K6AJ:H



-=: G:HJAIH D; I=>H BD9:AA>C< 8=D>8: L>AA 7: EG:H:CI:9 >C ,:8I>DC 
6C9 8DBE6G:9 L>I= I=: HIG>C<:CI HDAK>C< D; I=: :FJ6I>DC HNHI:B
3.3. Errors in the existing procedures for the PET calculation
"C I=: DG><>C6A ;DGBJA6I>DC D; I=: 8D9: H:K:G6A INEDH 86C 7: 8DG
G:8I:9 H:: G:HE:8I>K:AN 6EE:C9>M  6C9  -=: 8D9: EGDK>9:9 6I I=:
:C9 D; 34 DG JH:9 >C I=: )- GDJI>C: D; 34 8DCI6>CH BDG:DK:G I=G::
B6?DG :GGDGH
UNCORRECTED PROOF
E. Walther, Q. Goestchel Building and Environment xxx (2018) xxx-xxx
I=: B:I67DA>8 68I>K>IN A:K:A >H @:EI 6H I=: DC: D; I=: G:6A :CK>GDCB:CI
L=:G:6H >I H=DJA9 7: 9:RC:9 6H  304 I=: I:GB MD; FJ6I>DC 
>H =:C8: >C8DGG:8I
I=: 7G:6I=>C< H:CH>7A: 6C9 A6I:CI ADHH:H 6G: 9:RC:9 6;I:G I=: 68I>K>IN
A:K:A 6G: HJ7H:FJ:CIAN >C8DGG:8I 6H >I 9:E:C9H DC I=: 68I>K>IN A:K:A 6H
E:G FJ6I>DC 
I=: K6EDJG IG6CH;:G EB6M >H 86A8JA6I:9 ;DG I=: 8ADI=>C< A:K:A D; I=: G:6A
:CK>GDCB:CI L=:G:6H >I H=DJA9 7: 86A8JA6I:9 L>I=  3)64 6C9 6
8ADI=>C< A:K:A D;  38AD4 -=: 86A8JA6I>DC D; w6C9 E9>U 6G: HJ7H:
FJ:CIAN 6;;:8I:9
-=: EGD8:9JG: L6H HJ7H:FJ:CIAN 6B:C9:9 ID >C8AJ9: 6 8DGG:8I>DC
D; I=: :GGDGH B:CI>DC:9 67DK: >I 86C 7: ;DJC9 >C I=: 6EE:C9>M 
-=: G:HJAIH D7I6>C:9 L:G: 8DBE6G:9 ID I=: G:;:G:C8: K6AJ:H EJ7A>H=:9 >C
+:; 34 ;DG  304 68I>K>IN 6C9 6 8ADI=>C< A:K:A D;  38AD4 -=:N 6G: EG:
H:CI:9 >C -67A: 6C9 EG:H:CI 6 9>;;:G:C8: AN>C< 7:IL::C V  6C9
  G:HE:8I>K:AN ;DG HJBB:G H=69N 8DC9>I>DCH 6C9 L>CI:G L>C9N
8DC9>I>DCH
-=: DG><>C6A )- G:HDAJI>DC L6H I=:C 8DBE6G:9 ID I=: 8DGG:8I:9 K:G
H>DC ;DG K6G>DJH 6B7>:CI 8DC9>I>DCH 6C9 7DI= B:I=D9H I:C9 ID EGD9J8:
H>B>A6G G:HJAIH !DL:K:G 6B7>:CI 8DC9>I>DCH G:;:GG>C< ID 6 =><= B:6C
G69>6CI I:BE:G6IJG: EG:H:CI 6 BDG: H><C>;>86CI 9>;;:G:C8: DC ><  I=:
)- >H EADII:9 DC I=: EHN8=GDB:IG>8 8=6GI ;DG 6 B:6C G69>6CI I:BE:G6
IJG: I6@:C  3$4 67DK: I=: 6>G I:BE:G6IJG: L=:G:6H I=: L>C9 K:AD8>IN
G:B6>CH 6I 6  3BHYV4 ;DG >CHI6C8: >C I=: 86H: D; 6 W 30BYV4
>C8>9:CI HDA6G G69>6I>DC 6C9 HI>AA 6>G -=: >HDK6AJ: A>C:H D; I=: DG><>
C6A )- 6G: HA><=IAN DK:G:HI>B6I>C< 8DBE6G:9 ID I=: 8DGG:8I:9 K:GH>DC
-=>H G:A6I:H ID I=: ;68I I=6I JCA>@: >C I=: 6B:C9:9 EGD8:9JG: I=: H@>C
L:II:9C:HH >H CDI 86A8JA6I:9 6<6>C >C I=: DG><>C6A K:GH>DC L=>8= 6;;:8IH
I=: A6I:CI =:6I SJM via :K6EDG6I>DC 6I H@>C HJG;68:  H>B>A6G IG:C9 86C
7: D7H:GK:9 >C DE:G6I>K: I:BE:G6IJG: 8DC9>I>DCH 6H L:AA 6H L>C9N 8DC
9>I>DCH L>I= ADL:G 9>;;:G:C8:H 7:IL::C I=: /" B:I=D9 6C9 >IH 8DGG:8
I>DC
CDI=:G H>BEA>R86I>DC L6H B69: ;DG I=: HDAK>C< D; I=: :FJ6I>DCH I=:
I=G:: I:BE:G6IJG:H -8-H@-8A 6G: HJEEDH:9 ID 7: >C9:E:C9:CI L=>8=
B:6CH I=: 8DJEA>C< 7:IL::C H@>C 6C9 8DG: I:BE:G6IJG:H >H CDI 8DCH>9
:G:9 >C I=: BD9:A ':MI H:8I>DC 9:6AH L>I= I=>H 6HE:8I D; I=: HJ7?:8I
4. Comparisons with an improved model
"C I=>H ,:8I>DC I=: B:I=D9 ;DG 86A8JA6I>C< I=: )- ;GDB I=: 8DJEA:9
HNHI:B D; :FJ6I>DCH >H RGHI EG:H:CI:9 -=: G:HJAIH D7I6>C:9 L>I= I=: DG><
>C6A B:I=D9 EG:H:CI:9 >C ,:8I>DC  >C8AJ9>C< I=: 8DGG:8I>DC D; :GGDGH
B:CI>DC:9 >C ,:8I>DC  6G: I=:C 8DBE6G:9 ID I=: )- D7I6>C:9 L>I=
I=: 8DJEA:9 HNHI:B D; :FJ6I>DCH H I=: DG><>C6A K6EDJG 9>;;JH>DC BD9:A
6EE:6GH ID 7: >CH:CH>I>K: ID I=: A:K:A 8ADI=>C< 6C >BEGDK:B:CI D; I=:
:FJ6I>DC ;DG 9>;;JH>DC >H EGDEDH:9 -=: G:HJAIH 6G: 8DBE6G:9 L>I= I=DH:
D; I=: 8DGG:8I:9 DG><>C6A BD9:A
4.1. Resolution of the non-linear model
"C HI:69NHI6I: =:6I SDLH ;GDB I=: 8DG: ID I=: 6B7>:CI 6IBDHE=:G:
I=GDJ<= I=: H@>C A6N:G 6C9 I=: 76G: H@>C 688DG9>C< ID I=: :FJ>K6A:CI
:A:8IG>8 H8=:B: EG:H:CI:9 DC ><  -=: H@>C 8DG: 6C9 8ADI=>C< I:BE:G
6IJG:H 6G: 9:E:C9:CI DC :68= DI=:G G:HJAI>C< >C 6 HNHI:B D; I=G:: :FJ6
I>DCH
-=: 8DG: CD9: :FJ6I>DC >H I=: 6A<:7G6>8 HJB D; B:I67DA>8 G6I: G:HE>
G6IDGN ADHH:H 6C9 8DG: ID H@>C =:6I IG6CH;:G

-=: =:6I 76A6C8: DC I=: H@>C CD9: H=DLH I=: :FJ6A>IN 7:IL::C I=:
=:6I SJM ;GDB 8DG: ID H@>C 6C9 I=: =:6I IG6CH;:GG:9 ;GDB H@>C ID I=: :C
K>GDCB:CI :>I=:G 9>G:8IAN ;DG 76G: H@>C DG I=GDJ<= I=: 8ADI=>C<

-=: 76A6C8: DC I=: 8ADI=>C< CD9: N>:A9H I=: :FJ6A>IN D; SJM 7:IL::C
I=: 8ADI=:9 ;G68I>DC D; H@>C 6C9 I=: :CK>GDCB:CI

-=: HNHI:B D; :FJ6I>DCH  >H CDCA>C:6G 6H I=: 8D:;R8>:CIH q7
6C9 EHL G:EG:H:CI>C< I=: =JB6C I=:GB6A G:<JA6I>DC >C FJ6I>DC 
9:E:C9 DC I=: K6AJ:H D; TH@ 6C9 T86H 9:H8G>7:9 EG:K>DJHAN -=>H 8GDHH:9
CDC A>C:6G HNHI:B >H HDAK:9 L>I= 6 =N7G>9 )DL:AA H8=:B: ;GDB I=: HI6C
96G9 )NI=DC ;JC8I>DC fsolve I=: GDJI>C: JH:9 >H EGDK>9:9 >C 6EE:C9>M
Y
;I:G I=: K6AJ:H ;DG T8ATH@ 6C9 T86G: @CDLC I=: )- >H 86A8JA6I:9
7N 9>8=DIDBN HDAK>C< ;DG I=: HI:69N HI6I: FJ6I>DC  L>I= I=: G:;
:G:C8: 6B7>:CI 8DC9>I>DCH 9:RC:9 >C ,:8I>DC  -=: 9>8=DIDBN B:I=D9
EGDK:H ID 7: :;R8>:CI >C I=>H 86H: 6H >I DCAN G:FJ>G:H 6 H:6G8= >CI:GK6A
>CHI:69 D; 6C >C>I>6A K6AJ: -=: )- 86A8JA6I>DC 86C 7: >AAJHIG6I:9 >C ;DA
ADL>C< ;G6B:
4.2. In?uence of the resolution method
-=G:: H>IJ6I>DCH 6G: :M6B>C:9 >C DG9:G ID :K6AJ6I: I=: >CSJ:C8: D;
I=: CJB:G>86A H>BEA>R86I>DC DC I=: G:HJAI>C< 8DB;DGI -=: 86A8JA6I:9
)- K6AJ:H 6G: EADII:9 DC I=: EHN8=GDB:IG>8 8=6GI ;DG 6C 68I>K>IN A:K:A
D;  304 6C9  38AD4 >CHJA6I>DC D; 8ADI=>C< -=: H@>C 9>;;JH>DC ADHH:H
E9>U L:G: @:EI 6H E:G I=:>G DG><>C6A 9:;>C>I>DC >C FJ6I>DC  6C9 CD
6B:C9B:CIH L:G: B69: :M8:EI ;DG I=: INEDH B:CI>DC:9 >C 6EE:C9>M

Operative temperature environment: -=: DG><>C6A BD9:A L6H 8DB
E6G:9 L>I= I=: HIG>C<:CI G:HDAJI>DC ;DG DE:G6I>K: I:BE:G6IJG:8DC
9>I>DCH id est L>I= CD 9>;;:G:C8: 7:IL::C I=: 6>G I:BE:G6IJG: 6C9 I=:
B:6C G69>6CI I:BE:G6IJG: -=: 6>G K:AD8>IN L6H 8=DH:C 6H v 
3BHYV4 ><  H=DLH I=: 9>;;:G:C8: 7:IL::C I=: ILD G:HDAJI>DC B:I=
D9H >C 6C DE:G6I>K: I:BE:G6IJG: :CK>GDCB:CI >H8G:E6C8>:H 86C 7:
D7H:GK:9 D; 67DJI V  ID   9:<G:: 7:IL::C I=: DG><>C6A BD9:A
6C9 I=: EG:H:CI LDG@
High mean radiant temperature environment: I=: B:6C G69>6CI
I:BE:G6IJG: >H I6@:C  3$4 =><=:G I=6C I=: 6>G I:BE:G6IJG: 6C9 I=:
L>C9 K:AD8>IN G:B6>CH 6I 6 ADL K6AJ: D;  3BHYV4 -=:H: 8DC9>I>DCH
8DJA9 8DGG:HEDC9 ID 6 W 30BYV4 HDA6G G69>6I>DC 6C9 HI>AA 6>G -=:
>HD)- K6AJ:H 9G6LC DC ><  H=DL I=6I I=: )- 8DBEJI6I>DC 6;I:G
I=: /" CDGB DK:G:HI>B6I:H I=: )- K6AJ: 6;I:G I=: EG:H:CI LDG@ 7N
.H>C< 6 HI6C96G9 ':LIDC+6E=HDC EGD8:9JG: EGDK:9 ID 7: >C:T8>:CI <>K:C I=:
I=:GB6A G:<JA6I>DC D; B:I67DA>HB 6C9 I=: 9:E:C9:C8N D; H@>C 6C9 8ADI= I:BE:G6IJG: ID
I=: EDL:G D; ;DJG I=: 6A<DG>I=B >H A>@:AN ID 9>K:G<: >; 6C >BEGDE:G >C>I>6A K6AJ: D; T8A >H
8=DH:C
UNCORRECTED PROOF
E. Walther, Q. Goestchel Building and Environment xxx (2018) xxx-xxx
Table 1
)- K6AJ:H D7I6>C:9 L>I= I=: 8DGG:8I:9 EGD8:9JG: 8DBE6G:9 ID 34 ;DG  304 68I>K>IN 6C9  38AD4
-air 34 -mrt 34 /air 3BHYV4pv3=)64 )-6;I:G34 DGG:8I:9)- >U:G:C8:34
     
V     V
V V V V 
      
      V
Fig. 2. !><= B:6C G69>6CI I:BE:G6IJG: 8DC9>I>DCH  (G><>C6A K:GHJH 8DGG:8I:9 )- "HD)-
K6AJ:H    6C9 °
Fig. 3. (E:G6I>K: I:BE:G6IJG: 8DC9>I>DCH  )- 6;I:G I=: 8DGG:8I:9 /" K:GHJH EG:H:CI
LDG@ "HD)- K6AJ:H    6C9  °
Fig. 4. !><= B:6C G69>6CI I:BE:G6IJG:  )- 6;I:G I=: 8DGG:8I:9 /" K:GHJH EG:H:CI LDG@
"HD)- K6AJ:H    °
V  ID W 3$4 6I I=: B6M>BJB >C :CK>GDCB:CIH L>I= =><= B:6C
G69>6CI I:BE:G6IJG:H -=: 9>;;:G:C8: >C8G:6H:H L>I= :A:K6I:9 I:BE:G6
IJG:H 6H L:AA 6H :A:K6I:9 K6EDJG EG:HHJG:H id est =><= G:A6I>K: =JB>9>
I>:H
Windy environment:  8DBE6G>HDC L6H 6AHD B69: 7:IL::C I=: 8A6H
H>86A )- 6C9 I=: HIG>C<:CI 8DJEA:9 HDAJI>DC >C 6C :CK>GDCB:CI L>I=
6C 6>G K:AD8>IN D;  3BHYV4 L=:G: 6>G 6C9 B:6C G69>6CI I:BE:G6
IJG:H 6G: :FJ6A -=: G:HJAIH 6G: EG:H:CI:9 DC ><  "C I=>H H>IJ6I>DC 6
H>B>A6G I:C9:C8N 86C 7: ;DJC9 7:IL::C 7DI= B:I=D9H 6C9 I=: )- 9:
K>6I:H 7N 67DJI   3$4 6I I=: B6M>BJB "C :CK>GDCB:CIH L>I= =><=
L>C9 HE::9 I=: H6B: IG:C9 86C 7: D7H:GK:9 I=: 8A6HH>86A 86A8JA6I>DC
<>K:H 6 HA><=I DK:G:HI>B6I>DC D; I=: )- 86A8JA6I:9 6;I:G I=: 8DJEA:9
HNHI:B 6H >AAJHIG6I:9 DC ><  -=: 9>;;:G:C8: G6C<:H ;GDB V  3$4
ID  3$4
-=: B:I=D9 ;DG G:HDAJI>DC JH:9 >C I=: DG><>C6A )- =:C8: >C9J8:H 6
7>6H :K6AJ6I:9 7:IL::C V  6C9   3$4 >C I=: 8DC9>I>DCH HIJ9>:9
,JGEG>H>C<AN I=: )- 9D:H CDI :M=>7>I 6C >BEDGI6CI H:CH>I>K>IN ID =JB>9
>IN I=: >HD)- A>C:H 6G: 6ABDHI K:GI>86A ;DG 7DI= 86A8JA6I>DC B:I=D9H "C
I=: A>I:G6IJG: I=: 8DB;DGI >C9:M:H 76H:9 DC I=: H6B: ILDCD9: BD9:A
HJ8= 6H I=: - DG ,- H=DL 6 BJ8= HIGDC<:G 9:E:C9:C8: ID =JB>9>IN
H:: I=: <G6E=H >C +:;H 34 -=: L:6@ >CSJ:C8: D; 8ADI=>C<
6C9 =JB>9>IN DC )- L6H 6AHD JC9:GA>C:9 7N +:; 34
-=>H 7:=6K>DJG 86C 7: :MEA6>C:9 7N I=: :FJ6I>DC 8=DH:C ;DG I=: BD9
:AA>C< D; 9>;;JH>DC 6I H@>C HJG;68: 6C9 L>AA 7: 9:6AI L>I= >C I=: C:MI ,:8
I>DC
4.3. Di@usion heat transfer Edi@
"C I=>H H:8I>DC I=: 9>;;JH>DC =:6I SJM E9>U L6H 6B:C9:9 6;I:G FJ6
I>DC  8DGG:HEDC9>C< ID I=: HI6I: D; I=: 6GI 34 >CHI:69 D; JH
>C< FJ6I>DC  ;DG L=>8= CD ?JHI>R86I>DC 8DJA9 7: ;DJC9 FJ6I>DC
 6AHD =6H I=: 69K6CI6<: D; 688DJCI>C< ;DG I=: 8ADI=>C< G:H>HI6C8: ID
K6EDJG IG6CH;:G L=>8= FJ6I>DC  9D:H CDI 6AADL
-=: G:HJAIH D7I6>C:9 ;DG I=: ILD 9>;;JH>DC =:6I IG6CH;:G BD9:AH
6G: H=DLC ;DG  38AD4 6C9  38AD4 8ADI=>C< A:K:A DC ><  -=:
8DJEA:9 G:HDAJI>DC EG:H:CI:9 >C ,:8I>DC  L6H JH:9 ;DG I=: 8DB
EJI6I>DC D; I=: )-
Fig. 5. 0>C9N :CK>GDCB:CI )- 6;I:G I=: 8DGG:8I:9 /" K:GHJH EG:H:CI LDG@ "HD)-
K6AJ:H   °
UNCORRECTED PROOF
E. Walther, Q. Goestchel Building and Environment xxx (2018) xxx-xxx
Fig. 6. DBE6G>HDC D; I=: DG><>C6A H@>C 9>;;JH>DC BD9:A K:GHJHE9>U 6;I:G FJ6I>DC 
L>I= 6C9 68I>K>IN A:K:A D;  304
ID G:9J8: I=: 9>H8G:E6C8N >C9J8:9 7N I=: CJB:G>86A EGD8:9JG: "I 86C
7: H::C DC ><  I=6I I=: >HD)- 9:E:C9 BDG: HIGDC<AN DC =JB>9>IN
8DBE6G:9 ID I=: DG><>C6A ;DGBJA6I>DC -=: 9>;;:G:C8: 7:IL::C  6C9 
38AD4 >H 6AHD HA><=IAN C6GGDL:G ;DG I=: DG><>C6A E9>U BD9:A L=:G:6H >I >H
BDG: H><C>;>86CI ;DG I=: 9>;;JH>DC BD9:A D; FJ6I>DC 
-=: >CSJ:C8: D; I=: 8=D>8: D; I=: 9>;;JH>DC BD9:A L6H 8DBE6G:9 ;DG
I=: I=G:: :CK>GDCB:CIH HIJ9>:9 >C ,:8I>DC  -=: H6B: 68I>K>IN 6C9
8ADI=>C< A:K:AH L:G: JH:9 -=: K:GH>DC D; I=: )- GDJI>C: EGDK>9:9 >C
EE:C9>M  L6H JH:9 >C8AJ9>C< I=: 8DGG:8I>DCH D; :GGDGH B:CI>DC:9 >C
,:8I>DC 
Operative temperature: "C HJ8= :CK>GDCB:CIH I=: >CSJ:C8: D; I=:
9>;;JH>DC BD9:A H=DLH H:K:G6A 9:<G::H 9>;;:G:C8: 6I =><= 6C9 ADL G:A
6I>K: =JB>9>I>:H H:: ><  -=: 9>;;:G:C8: 7:IL::C 7DI= B:I=D9H
G6C<:H ;GDB V  ID  3$4
High mean radiant temperature environment: -=: 8DBE6G>HDC D;
I=: B:I=D9H ;DG =><= B:6C G69>6CI I:BE:G6IJG: :CK>GDCB:CIH EG:H:CI:9
DC ><  G6C<: ;GDB V  ID   3$4
Windy environment: -=: 8DBE6G>HDC D; I=: B:I=D9H ;DG L>C9N :C
K>GDCB:CIH EG:H:CI:9 DC ><  G6C<: ;GDB V  ID  3$4
"C I=: HIJ9>:9 8DC9>I>DCH I=: 9>;;:G:C8: 7:IL::C I=: 8DGG:8I /" 6C9
I=: 8DJEA:9 G:HDAJI>DC L>I= >BEA:B:CI6I>DC D; I=: 9>;;JH>DC =:6I IG6CH
;:G 6;I:G FJ6I>DC  G6C<:H V  ID   3$4 -=: )- 8DB;DGI ODC:
7:>C<  3$4 7GD69 ;GDB  ID ° )- >H 8DCH>9:G:9 ID 7: I=: G6C<:
L>I=DJI I=:GB6A HIG:HH I=>H K6G>6I>DC G:EG:H:CIH 6 H><C>;>86CI 9>H8G:E
6C8N
Fig. 7. (E:G6I>K: I:BE:G6IJG: :CK>GDCB:CI (G><>C6A H@>C 9>;;JH>DC BD9:A K:GHJHE9>U 6;
I:G FJ6I>DC  "HD)- K6AJ:H    6C9  °
Fig. 8. !><= B:6C G69>6CI I:BE:G6IJG: :CK>GDCB:CI (G><>C6A H@>C 9>;;JH>DC BD9:A K:G
HJHE9>U 6;I:G FJ6I>DC  "HD)- K6AJ:H    6C9 °
Fig. 9. 0>C9N :CK>GDCB:CI (G><>C6A H@>C 9>;;JH>DC BD9:A K:GHJHE9>U 6;I:G FJ6I>DC 
"HD)- K6AJ:H   °
5. Conclusion & perspectives
-=>H LDG@ EG:H:CIH 6 ;JAA 9:H8G>EI>DC D; I=: )- BD9:A L=>8= 86C 7:
E6GI>6AAN ;DJC9 >C 9>;;:G:CI 6GI>8A:H D; I=: A>I:G6IJG: -=: 6C6ANH>H D; I=:
BD9:A L>I= G:;:G:C8: EJ7A>86I>DCH EGDK:9 I=6I I=: 8D9: EGDK>9:9 7N I=:
:GB6C /" HI6C96G9 8DCI6>CH H:K:G6A :GGDGH
-=: B6>C RC9>C<H D; I=>H LDG@ 6G: I=: ;DAADL>C<
-=: EGD8:9JG:H >C +:;H 34 H=DJA9 CDI 7: JH:9 6H I=:N 8DCI6>C :G
GDGH 6C9 >C8D=:G:C8:H -=: 6JI=DGH D; I=>H E6E:G EG:H:CI 6 G:K>H:9 K:G
H>DC D; I=: 8D9: EGDK>9:9 >C EE:C9>M 
>K:C I=: ;:L 6K6>A67A: CJB:G>86A IDDAH 6I I=: I>B: I=: )- DJI9DDG
8DB;DGI >C9>86IDG L6H 8DCHIGJ8I:9 I=: H>BEA>R:9 ;DGBJA6I>DC D; I=:
EGD7A:B >H :A:<6CI "I 6AADLH ;DG I=: G:HDAJI>DC D; I=: CDCA>C:6G :FJ6
I>DC HNHI:B N>:A9>C< I=: E=NH>DAD<>86A :FJ>K6A:CI I:BE:G6IJG: JH>C<
H:8DC9DG9:G EDANCDB>6AH !DL:K:G ;DG DJI9DDG :CK>GDCB:CIH I=:
6HHJBEI>DC I=6I H@>C 6C9 8DG: I:BE:G6IJG: 6G: >C9:E:C9:CI 6H HJ<
<:HI:9 6I I=: :C9 D; 34 EGDK:9 ID 7: >C688JG6I: <>K:C I=: CJB:G>
86A G:HJAIH D7I6>C:9 >C I=>H LDG@ -=: >CSJ:C8: DC I=: 86A8JA6I:9 )-
G6C<:H ;GDB V  ID   3$4 6C9 >H 9:I6>A:9 >C ,:8I>DC 
-=: EGD8:9JG: JH:9 ;DG G:HDAJI>DC =6H 6 A>B>I:9 :;;:8I DC 688JG68N
=DL:K:G JH>C< JE ID 96I: IDDAH ;DG I=: G:HDAJI>DC D; CDC A>C:6G HNHI:BH
D; :FJ6I>DCH EGDK:9 ID 7: ;6HI:G 7N 6 ;68IDG D; ILD K:GHJH I=: 8A6HH>
86A DC: L>I= 6 BDG: G:6967A: 6C9 8DBE68I 8D9: -=: 8DJEA:9 HDAK>C<
EGD8:9JG: ;DG )- >H EGDK>9:9 >C I=: 6EE:C9>M  D; I=: EG:H:CI LDG@
-=: H:CH>I>K>IN ID =JB>9>IN D; I=: DG><>C6A BD9:A >H K:GN ADL 6C9 86C
7: :MEA6>C:9 7N 6 HJGEG>H>C< 8=D>8: ;DG I=: :FJ6I>DC D; K6EDJG 9>;;J
UNCORRECTED PROOF
E. Walther, Q. Goestchel Building and Environment xxx (2018) xxx-xxx
H>DC I=6I 9D:H CDI 9:E:C9 DC I=: 8ADI=>C< A:K:A >C I=: DG><>C6A )-
BD9:A -=: 9>;;JH>DC BD9:A H=DJA9 =:C8: 7: BD9>R:9 ;DG >CHI6C8: 6;
I:G I=: HI6I: D; I=: 6GI 34 6C >BEA:B:CI6I>DC >H EGDK>9:9 >C I=: 8D9:
D; EE:C9>M  -=: 9>;;:G:C8: 7:IL::C 7DI= K6EDJG 9>;;JH>DC BD9
:AH EGD9J8:H 6 H><C>;>86CI K6G>6I>DC >C I=: )- G6C<>C< ;GDB V  3$4
ID   3$4 6H H=DLC >C ,:8I>DC 
"I L6H H=DLC I=6I I=: =:6I 6C9 B6HH IG6CH;:G 9:E:C9:C8N L>I= 6B
7>:CI 6>G K:AD8>IN 86C 86JH: 6C >BEDGI6CI H=>;I D; I=: 8DB;DGI ODC:
34 -=: =:6I 6C9 K6EDJG IG6CH;:G BD9:AA>C< >C 8DB;DGI >C
9>8:H H=DJA9 =:C8: 7: >BEGDK:9 6;I:G 34 ID >C8AJ9: L>C9 :;;:8I DC
8ADI=:H EGDE:GI>:H -=: )- K6EDJG IG6CH;:G BD9:A H=DJA9 6AHD 7: BD9>
R:9 ;DG >CHI6C8: 6;I:G I=: HI6I: D; I=: 6GI 34
-=: K6G>:IN D; 8DCHI6CIH ;DJC9 >C I=: A>I:G6IJG: e.g. G:<6G9>C< 7D9N
H:I ED>CI I:BE:G6IJG:H 34 DG 9>A6I6I>DC8DCHIG>8I>DC 8D:;R8>:CIH ;DG
7ADD9 SDL A:69H JH ID I=>C@ I=6I K6G>67>A>IN H=DJA9 7: I6@:C >CID 68
8DJCI L=:C BD9:AA>C< I=: =JB6C B:I67DA>HB :HE:8>6AAN ;DG 8DB;DGI
EJGEDH:H 34 -=: >BE68I D; E=NH>DAD<>86A K6G>67>A>IN DC I=: 9>H
E:GH>DC D; ILDCD9:BD9:AH76H:9 8DB;DGI >C9:M:H >H 8JGG:CIAN :MEADG:9
6C9 L>AA 7: EG:H:CI:9 >C 6CDI=:G LDG@
Acknowledgements
-=: 6JI=DGH LDJA9 A>@: ID I=6C@ )G G &>8=6:A GJH: '/"&-
6C9 )G =G>HI>6C "C6G9 .C>K %6 +D8=:AA: ;DG H=6G>C< I=:>G :ME:G>:C8:
6C9 K>:LH JEDC I=: )- 6H L:AA 6H &6M DA>CDI L=D >BEA:B:CI:9 I=:
fsolve B:I=D9 ;DG I=: )- 86A8JA6I>DC
Nomenclature
λ8A :FJ>K6A:CI 8DC9J8I>K>IN D; 8ADI= 30BYV$YV4
ρb7ADD9 9:CH>IN 3@<BYV4
σDAIOB6CCH 8DCHI6CI  X V 30BYV$YV4
ε8A :B>HH>K>IN D; 8ADI=:H 34
εH@ :B>HH>K>IN D; H@>C 34
A7D9N HJG;68: 6;I:G J7D>H A mXH3BY4
A76G: 76G: HJG;68: D; I=: 7D9N 3BY4
A8A 8ADI=:9 HJG;68: D; I=: 7D9N 3BY4
c6HE:8>R8 =:6I 86E68>IN D; 6>G 3#@<YV$YV4
C76G: DCK:8I>DC ADHH:H ;DG 76G: 6G:6 30BYV4
c7HE:8>R8 =:6I 86E68>IN D; 7ADD9 3#@<YV$YV4
C8AD DCK:8I>DC ADHH:H ;DG 9G:HH:9 6G:6 30BYV4
C99>A6I6I>DC 8D:;R8>:CI 3%BYV=YV$YV4
CG:HE H:CH>7A: =:6I ADHH 7N I=: 6>G :ME>G:9 30BYV4
CH0 HL:6I>C< 8D:;R8>:CI 3<BYV=YV$YV4
CHHIG>8I>DC 8D:;R8>:CI 3$YV4
cKHE:8>R8 =:6I 86E68>IN ;DG D; L6I:G K6EDJG
3#@<YV$YV4
E9>U =:6I ADHH 7N 9>;;JH>DC 30BYV4
EG:HE %6I:CI =:6I IG6CH;:G 7N 7G:6I=>C< 30BYV4
EH@ IDI6A A6I:CI H@>C =:6I ADHH 30BYV4
EHL =:6I ADHH 7N HL:6I>C< 30BYV4
f68A ;G68I>DC D; I=: 7D9N 8DK:G:9 7N 8ADI=>C< 34
f8A JGIDC ;68IDG ;DG I=: >C8G:6H: D; :M8=6C<: HJG;68: L>I= 8ADI=
>C< >CHJA6I>DC 38ADYV4
f:U ;68IDG ;DG I=: :;;:8I>K: HJG;68: HJ7?:8I ID G69>6I>DC :M 
L=:C HI6C9>C<
H=:><=I D; I=: >C9>K>9J6A 3B4
h8A 8ADI=>C< 8DC9J8I6C8: 30BYV$YV4
h88DCK:8I>K: =:6I IG6CH;:G 8D:;R8>:CI 30BYV$YV4
A6I:CI =:6I IG6CH;:G 8D:;R8>:CI ;DG 8ADI=>C< 30BYV)6YV4
A6I:CI =:6I IG6CH;:G 8D:;R8>:CI ;DG 6>G 30BYV)6YV4
hGG69>6I>K: =:6I IG6CH;:G 8D:;R8>:CI 30BYV$YV4
i8A 8ADI=>C< >CHJA6I>DC A:K:A 38AD4
im0DD98D8@H E:GB:67>A>IN >C9:M I6@:C 6H 
LKA6I:CI =:6I D; L6I:G 3#<YV4
Le %:L>H CJB7:G 34
LR %:L>H G6I>D W 3$)6YV4 ;DG JHJ6A 6B7>:CI 8DC9>I>DCH
MB:I67DA>8 =:6I G6I: 30BYV4
mB6HH D; I=: >C9>K>9J6A 3@<4
Mf;:B6A: B:I67DA>HB 304
MmB6A: B:I67DA>HB 304
p6K6EDJG EG:HHJG: D; 6B7>:CI 6>G 3)64
K6EDJG EG:HHJG: D; :ME>G:9 6>G 3)64
pKK6EDJG EG:HHJG: D; 6>G 3)64
q77ADD9 B6HH SDL G6I: ;GDB 8DG: ID H@>C 3%BYV=YV4
H:I 7ADD9 SDL G6I: ;GDB 8DG: ID H@>C 3%BYV=YV4
SDL G6I: D; >CHE>G:9 6>G 3@<BYV=YV4
HL:6I>C< G6I: 3@<BYV=YV4
QG:HE ,JB D; I=: =:6I :M8=6C<:H 7N 7G:6I=>C< 30BYV4
R6>G 8DCK:8I>K: 6C9 G69>6I>K: =:6I IG6CH;:G G:H>HI6C8: ID I=: :CK>
GDCB:CI 3BY$0YV4
r6>CI:GC6A G69>JH D; 8ADI=>C< 3B4
R76G: +69>6I>DC ADHH:H ;DG 76G: 6G:6 30BYV4
r7:MI:GC6A G69>JH D; 8ADI=>C< 3B4
R8AD +69>6I>DC ADHH:H ;DG 9G:HH:9 6G:6 30BYV4
R8A 8ADI=>C< =:6I IG6CH;:G G:H>HI6C8: 3$0YV4
T6I:BE:G6IJG: D; 6B7>:CI 6>G 3Y°4
T77D9N I:BE:G6IJG: 3Y°4
7D9N H:I I:BE:G6IJG: 3Y°4
T8A 8ADI=>C< I:BE:G6IJG: 3Y°4
T88DG: I:BE:G6IJG: 3Y°4
8DG: H:I I:BE:G6IJG: 3Y°4
T:ME I:BE:G6IJG: D; :ME>G:9 6>G 3Y°4
TBGI B:6C G69>6CI I:BE:G6IJG:
TH@ H@>C I:BE:G6IJG: 3Y°4
H@>C H:I I:BE:G6IJG: 3Y°4
UH@ H@>C =:6I IG6CH;:G 8D:;R8>:CI 30BYV$YV4
V6>G K:AD8>IN 3BHYV4
wH@>C L:II:9C:HH 34
y8ADI=:9 ;G68I>DC D; I=: 7D9N 34
Appendix A. Respiration losses
FJ6I>DC  6HHJB:H I=6I  -=>H
6AADLH ;DG 6 H>BEA>R:9 K:GH>DC D; I=: K6EDJG IG6CH;:G 7:IL::C :ME>G:9
6>G 6I BD>HIJG: 8DCI:CI w:ME 3@<YL6I:G@<Y6>G4 6C9 DJIH>9: 6>G L>I= BD>HIJG:
8DCI:CI w6<>K:C >C FJ6I>DC 
UNCORRECTED PROOF
E. Walther, Q. Goestchel Building and Environment xxx (2018) xxx-xxx


-=: H:CH>7A: =:6I G:FJ>G:9 ;DG I=: I:BE:G6IJG: K6G>6I>DC D; L6I:G
K6EDJG >H 6AHD C:<A:8I:9 >C FJ6I>DC   HIG>C<:CI :MEG:HH>DC LDJA9
7: 6H E:G FJ6I>DC 

-=: >CSJ:C8: D; I=: 6HHJBEI>DC >H =DL:K:G A>B>I:9 9:E:C9>C< DC
I=: :CK>GDCB:CI 8DC9>I>DCH I=: 7>6H >C9J8:9 7N FJ6I>DC  >H D; W
 8DBE6G:9 ID FJ6I>DC  9:E:C9>C< DC I=: 6>G I:BE:G6IJG: 6C9
K6EDJG EG:HHJG: 6H EG:H:CI:9 DC ><  -=: >BE68I DC I=: )- 86A8JA6
I>DC 8DJA9 7: CDC C:<A><>7A: >C HE:8>R8 8DC9>I>DCH "C9::9 IDI6A 7G:6I=
>C< ADHH:H 688DJCI ;DG W ID  D; I=: G:HI>C< B:I67DA>HB >C I=: B:6
HJG:B:CIH 7N +:; 34
Appendix B. Analysis of the VDI original code
-=: JH:G B6N RC9 >I 9>;R8JAI ID JC9:GHI6C9 I=: 8D9: EGDK>9:9 L>I=
I=: /" CDGB 34 "I >H >C9::9 EDDGAN 8DBB:CI:9 6C9 EGD;JH>DC D; CJ
B:G>86A 8DCHI6CIH 6G: JH:9 -=>H H:8I>DC B><=I EGDK: ID 7: JH:;JA ;DG
L=DB =6H I=: HDJA D; 6 =6BEDAA>DC 6C9 LDJA9 L>H= ID 9:8D9: I=: /"
DG><>C6A 8D9: ID 7: ;DJC9 ;DG >CHI6C8: >C I=: 6EE:C9>M D; 34 6H >I EGD
K>9:H I=: DG><>C D; HDB: CJB:G>86A 8DCHI6CIH
B1. Explanation of the numerical constants and errors
-=: 8DGG:HEDC9:C8: 7:IL::C CJB:G>86A 8DCHI6CIH 6C9 A>I:G6A :MEG:H
H>DCH =6G9 8D9:9 >C !öEE:H DGIG6C 8D9: 6G: EGDK>9:9 =:G:6;I:G

Fig. 10. >;;:G:C8: 7:IL::C I=: H>BEA>R:9 I=: :M68I :MEG:HH>DC D; QG:HE 9:E:C9>C< DC G:A
6I>K: =JB>9>IN 6C9 6>G I:BE:G6IJG:


,:K:G6A INED<G6E=>86A B>HI6@:H 86C 6AHD 7: CDI:9
-=: H@>C H:I I:BE:G6IJG: >H I6@:C 6H 34 L=:G:6H >I H=DJA9 7:
 34 ;DG I=: H6@: D; 8D=:G:C8: I=GDJ<=DJI I=: EGD<G6B A>C:H 
6C9  D; I=: DGIG6C 8D9:
-=: 7D9N H:I I:BE:G6IJG: >H I6@:C 6H 34 L=:G:6H >I H=DJA9
7:  34 ;DG I=: H6@: D; 8D=:G:C8: A>C:  D; I=: DGIG6C 8D9:
-=: 8DCHI6CI :MEA6>C:9 >C FJ6I>DC  >H B>HINE:9 6H
I=GDJ<=DJI I=: /" 8D9:
B2. Corrected version of VDI code
-=: 6B:C9B:CI EGDEDH:9 86C 7: ;DJC9 I=:G:6;I:G >C )NI=DC A6C
<J6<: =IIEH<>I=J78DB:99:H+)7AD7B6HI:G/"5)-5
8DGG:8I:9EN
B3. Coupled resolution of the code
-=: 6B:C9B:CI :MEDH:9 >C ,:8I>DC  86C 7: ;DJC9 I=:G:6;I:G >C
)NI=DC A6C<J6<: -=: K:GH>DC EGDEDH:9 >H BDG: 8DBE68I 6C9 :M=>7>IH
6 ;6HI:G 8DBEJI6I>DC I>B: =IIEH<>I=J78DB:99:H+)7AD7
B6HI:G)-5;HDAK:58D9:EN
References
34 ) !öEE: !:6I 6A6C8: &D9:AA>C< ME:G>:CI>6 
34 ) !öEE: -=: E=NH>DAD<>86A :FJ>K6A:CI I:BE:G6IJG: 6 JC>K:GH6A >C9:M ;DG I=: 7>D
B:I:DGDAD<>86A 6HH:HHB:CI D; I=: I=:GB6A :CK>GDCB:CI "CI # >DB:I:DGDA
 
34 /" CK>GDCB:CI6A &:I:DGDAD<N &:I=D9H ;DG I=: !JB6C >DB:I:DGDAD<>86A K6A
J6I>DC D; A>B6I: 6C9 >G *J6A>IN ;DG .G76C 6C9 +:<>DC6A )A6CC>C< 6I +:<>DC6A
%:K:A )6GI " A>B6I: KDA  /:G:>C :JIH8=:G "C<:C>:JG:  A6II 
34 & ,69:<=>EDJG +DJ9H6G> & )6@ %69N7J< 6 E6G6B:IG>8 :CK>GDCB:CI6A EAJ<>C ;DG
G6HH=DEE:G ID =:AE 9:H><C:GH 8G:6I: 6C :CK>GDCB:CI6AAN8DCH8>DJH 9:H><C "C I=
"CI:GC6I>DC6A "), DC;:G:C8: J< 
34 ! &6N:G # !DAHI ) DHI6A  "B7:GN  ,8=>C9A:G !JB6C I=:GB6A 8DB;DGI >C
HJBB:G L>I=>C 6C JG76C HIG::I 86CNDC >C :CIG6A JGDE: &:I:DGDA 2 
34 $ ,:I6>= ' !6BO6 - -DLCH=:C9 HH:HHB:CI D; (JI9DDG I=:GB6A 8DB;DGI >C JG
76C B>8GD8A>B6I: >C =DI 6C9 6G>9 6G:6H "C )GD8::9>C<H D; , 
34  DB:O ) J:K6 & /6A8J:C9:  &6IO6G6@>H +:H:6G8= DC :8DAD<>86A 9:H><C
ID :C=6C8: 8DB;DGI >C DE:C HE68:H D; 6 8>IN /6A:C8>6 ,E6>C .I>A>IN D; I=: E=NH>D
AD<>86A :FJ>K6A:CI I:BE:G6IJG: 8DA C<  
34 -) %>C  &6IO6G6@>H -DJG>HB 8A>B6I: >C;DGB6I>DC 76H:9 DC =JB6C E:G8:EI>DC
>C -6>L6C 6C9 6HI:G =>C6 -DJG>HB &6C6<  
34 :E6GIB:CI D; G8=>I:8IJG: .!$ .G76C A>B6I>8 &6E 6C9 ,I6C96G9H ;DG 0>C9
CK>GDCB:CI  :6H>7>A>IN ,IJ9N I:8= G:E  =IIELLLEA6C9<DK=@EA6C95
:CE5HIJ9NEGD<5HJ8B6EL:7J8B6E5EGD?:8I8DCI:CIG:EDGIHDB;DGI5%:K:A5
,JGK:NE9; (CA>C:  688:HH:9 :7GJ6GN 
34  6<<: # ,IDAL>?@ 1 '>H=> C :;;:8I>K: I:BE:G6IJG: H86A: 76H:9 DC 6 H>BEA:
BD9:A D; =JB6C E=NH>DAD<>86A G:<JA6IDGN G:HEDCH: J>A9 C<  
34  6<<:  D7:A:IH % :G<AJC9 HI6C96G9 EG:9>8I>K: >C9:M D; =JB6C G:HEDCH:
ID I=: I=:GB6A :CK>GDCB:CI J>A9 C<  
34 ) !öEE: >;;:G:CI 6HE:8IH D; 6HH:HH>C< >C9DDG 6C9 DJI9DDG I=:GB6A 8DB;DGI C
:G<N J>A9  
34 ) 6C<:G -=:GB6A DB;DGI &8 G6L !>AA ':L1DG@ 
34 ) !öEE: >: C:G<>:7>A6CO 9:H &:CH8=:C &üC8=C:G .C>K:GH>IäIHH8=G>;I:C &:I:D
GDA "CHI 0>HH &>II  
34 ,!+ -=:GB6A CK>GDCB:CI6A DC9>I>DCH ;DG !JB6C (88JE6C8N ',"
,!+ 699:C9JB 7 ID ',",!+ ,I6C96G9  
34 # 6>C , %>K>C<HIDC: + 'DA6C  $::;: +:HE>G6IDGN =:6I ADHH 9JG>C< LDG@ 6I
K6G>DJH 6B7>:CI I:BE:G6IJG:H +:HE>G )=NH>DA  CD   Q
34 ,!+ >C "C8=)DJC9 :9 9 ,!+ !6C97DD@ JC96B:CI6AH =6EI:G 
-=:GB6A DB;DGI B:G>86C ,D8>:IN D; !:6I>C< +:;G><:G6I>C< 6C9 >GDC9>I>DC>C<
C<>C::GH 
34 " !DABéG ! '>AHHDC !6K:C>I= $ )6GHDCH ADI=>C< 8DCK:8I>K: =:6I :M
8=6C<: EGDEDH6A ;DG >BEGDK:9 EG:9>8I>DC >C HI6C96G9H 6C9 BD9:AH CC (88JE
!N<  CD  

UNCORRECTED PROOF
E. Walther, Q. Goestchel Building and Environment xxx (2018) xxx-xxx
34 -# D=:GIN  G:CH K6AJ6I>DC D; I=: E=NH>DAD<>86A 76H:H D; I=:GB6A 8DB;DGI
BD9:AH J>A9 C< 
34 1 '>H=>  6<<: &D>HIJG: E:GB:6I>DC D; 8ADI=>C< 6 ;68IDG <DK:GC>C< I=:GB6A
:FJ>A>7G>JB 6C9 8DB;DGI &:B 68JA C< !D@@6>9D .C>K KDA  ,JEEA
 Q
34 )+ D7:A:IH ) 6<<: +6I>DC6A>O6I>DC D; I=: :;;:8I>K: I:BE:G6IJG: - 6H 6
B:6HJG: D; I=: :CI=6AEN D; I=: =JB6C >C9DDG :CK>GDCB:CI J>A9 C<  
34 ,!+ >C "C8=)DJC9 :9 9 ,!+ !6C97DD@ JC96B:CI6AH =6EI:G 
&6HH -G6CH;:G B:G>86C ,D8>:IN D; !:6I>C< +:;G><:G6I>C< 6C9 >GDC9>I>DC>C<
C<>C::GH 
34 !6K:C>I= " !DABéG  :C !6GID< $ )6GHDCH ADI=>C< :K6EDG6I>K: =:6I
G:H>HI6C8: EGDEDH6A ;DG >BEGDK:9 G:EG:H:CI6I>DC >C HI6C96G9H 6C9 BD9:AH CC
(88JE !N<  CD  
34  6<<: 1 '>H=> ':K>CH -=: GDA: D; 8ADI=>C< >C B::I>C< ;:6 :C:G<N 8DCH:GK6
I>DC <J>9:A>C:H J>A9 C<   Q
34 ,/ ,OD@DA6N "CIGD9J8I>DC ID G8=>I:8IJG6A ,8>:C8: H:8DC9 :9 G8=>I:8IJG6A
EG:HH 
34 1 =:C  &6IO6G6@>H &D9>R86I>DC D; E=NH>DAD<>86AAN :FJ>K6A:CI I:BE:G6IJG:
# !:6I "HA6C9 "CHI "CI   
34  06AI=:G & D<96C DB;DGI BD9:AA>C< >C H:B>DJI9DDG HE68:H +!/ #

34 & GJH: "I8B6 H>BEA: 9NC6B>8 CD9: BD9:A D; I=: =JB6C I=:GBDG:<JA6IDGN
HNHI:B 6C9 >IH 6EEA>86I>DC >C 6 BJAI>6<:CI HNHI:B CC &:I:DGDA  
Q
34  $>C<B6 0 K6C &6G@:C %>8=I:C7:AI C:G<N 8DCHJBEI>DC >C 7J>A9>C<H 6C9 ;:
B6A: I=:GB6A 9:B6C9 '6I A>B =6C<:  CD   Q
34  &>H=G6 & %DDB6CH # !:CH:C -=:GB6A 8DB;DGI D; =:I:GD<:C:DJH 6C9 9N
C6B>8 >C9DDG 8DC9>I>DCH6C DK:GK>:L J>A9 CK>GDC   Q

... Fanger's PMV index is commonly used in field measurement and simulation studies for assessing thermal comfort in semi-outdoor environments [5,7,8,23,24,29,30]. Other studies use Gagge's SET* and PMV* indices [20,28,[31][32][33][34][35], as well as the Physiological Equivalent Temperature (PET) [35][36][37][38][39][40][41][42], because these indices are based on the two-node model of the human thermal regulation system and thus better suited for semi-outdoor environments [37,[43][44][45]. Additional indices have been proposed for assessing thermal comfort in semi-outdoor spaces: (1) the Universal Thermal Climate Index (UTCI) [46], and (2) the OUT_SET* [2,47]. ...
... Fanger's PMV index is commonly used in field measurement and simulation studies for assessing thermal comfort in semi-outdoor environments [5,7,8,23,24,29,30]. Other studies use Gagge's SET* and PMV* indices [20,28,[31][32][33][34][35], as well as the Physiological Equivalent Temperature (PET) [35][36][37][38][39][40][41][42], because these indices are based on the two-node model of the human thermal regulation system and thus better suited for semi-outdoor environments [37,[43][44][45]. Additional indices have been proposed for assessing thermal comfort in semi-outdoor spaces: (1) the Universal Thermal Climate Index (UTCI) [46], and (2) the OUT_SET* [2,47]. ...
... Third, the Physiological Equivalent Temperature (PET) thermal index was used. It is also based on Gagge's two-node model from which SET* was derived [37], which is defined as the air temperature at which, in a typical indoor setting (without wind and solar radiation), the heat budget of the human body is balanced with the same core and skin temperature as under the complex outdoor conditions to be assessed [74]. Gagge's SET* and PMV* were calculated using calcSET() and calcPMVStar() functions within the comf 0.1.11 ...
Article
Full-text available
The lack of green open spaces undermines the environmental and social quality of tropical highly-dense cities (i.e. raises urban temperatures, limits social interaction). The goal of this study, which focused on environmental aspects, was to identify underlying factors (i.e. hypothetical constructs) in semi-outdoor spaces within building forms that explain their microclimatic behaviour, thermal comfort levels, and clustering. Sixty-three semi-outdoor spaces in four high/mid-rise building forms of Singapore were studied using microclimatic data collected from field measurements and analysed via inferential statistical methods (e.g., exploratory factor analysis, multivariate regression analysis, and hierarchical clustering analysis). Findings demonstrate: (1) that spatial attributes (i.e. height, depth, void, solid, total frontage, open frontage, area, volume, perimeter, sky view factor, green plot ratio) are manifestations of three underlying factors: volume porosity (VP), perimeter openness (PO) and exposure to sky (ES); (2) that VP and PO are significantly associated with air velocity and predicted thermal comfort; and (3) that vertical breezeways appear to be the most thermally comfortable cluster due to high VP and low PO. This study sheds new light on the spatial nature of semi-outdoor spaces, which designers can consider in order to enhance wind movement for promoting thermally comfortable semi-outdoor environments in highly-dense Singapore.
... According to HOPPE (1999), PET is defined as the physiological temperature equivalent to the air temperature, the thermal balance of the human body to maintain central and skin temperature to the evaluated conditions. The use of urban vegetation impacts directly to the cooling of the urban environment, hence it influences the PET values in that analyzed environment (LUCCHESE, 2016;MORAKINYO et al., 2019;WALTHER;GOESTCHEL, 2018). ...
... According to HOPPE (1999), PET is defined as the physiological temperature equivalent to the air temperature, the thermal balance of the human body to maintain central and skin temperature to the evaluated conditions. The use of urban vegetation impacts directly to the cooling of the urban environment, hence it influences the PET values in that analyzed environment (LUCCHESE, 2016;MORAKINYO et al., 2019;WALTHER;GOESTCHEL, 2018). ...
Article
Full-text available
Green infrastructure is presented in several research as an urban strategy necessary to minimize the negative effects arising from the urbanization process and provide outdoor thermal comfort. The urban revitalization project "Reviva Centro" , proposes the increase of vegetation along "14 de Julho" street, located in downtown Campo Grande, Mato Grosso do Sul, Brazil. In this sense, the aim of this study is to compare two scenarios, corresponding to the previous situations and after the implementation of the urban revitalization project. To compare the scenarios , the Envi-met program was used for 3D modeling and microclimatic simulation. The program simulates climatological interactions between surfaces, plants, and atmosphere, considering four fundamental variables of urban thermal comfort (temperature, relative humidity and wind speed and direction). The analysis and visualization of the results is based on the equivalent physiological temperature (PET), that classifies outdoor human thermal comfort conditions. Based on the results of the simulations, the increase in thermal comfort was provided in relation to cold and heat. At 8 am., an air temperature increases of 6 °C, decreasing the discomfort caused by the cold. At 16 hours the comfort gain is obtained by decreasing the air temperature, with a difference of 4.98 °C, optimizing thermal comfort in the scenario that represents the state after revitalization. The results presented in this research show the benefits of urban vegetation as a strategy to balance the urban microclimate and increase comfort for pedestrians.
... The Raspberry Pi calculates PET (°C) on the device based on the Python script by Walther and Goestchel [42]. The meteorological input variables for the PET calculations are Ta, ρv, Tmrt, and v. ...
... The Raspberry Pi calculates PET ( • C) on the device based on the Python script by Walther and Goestchel [42]. The meteorological input variables for the PET calculations are T a , ρ v , T mrt , and v. ...
Article
Full-text available
The MoBiMet (Mobile Biometeorology System) is a low-cost device for thermal comfort monitoring, designed for long-term deployment in indoor or semi-outdoor occupational contexts. It measures air temperature, humidity, globe temperature, brightness temperature, light intensity, and wind, and is capable of calculating thermal indices (e.g., physiologically equivalent temperature (PET)) on site. It visualizes its data on an integrated display and sends them continuously to a server, where web-based visualizations are available in real-time. Data from many MoBiMets deployed in real occupational settings were used to demonstrate their suitability for large-scale and continued monitoring of thermal comfort in various contexts (industrial, commercial, offices, agricultural). This article describes the design and the performance of the MoBiMet. Alternative methods to determine mean radiant temperature (Tmrt) using a light intensity sensor and a contactless infrared thermopile were tested next to a custom-made black globe thermometer. Performance was assessed by comparing the MoBiMet to an independent mid-cost thermal comfort sensor. It was demonstrated that networked MoBiMets can detect differences of thermal comfort at different workplaces within the same building, and between workplaces in different companies in the same city. The MoBiMets can capture spatial and temporal differences of thermal comfort over the diurnal cycle, as demonstrated in offices with different stories and with different solar irradiances in a single high-rise building. The strongest sustained heat stress was recorded at industrial workplaces with heavy machinery.
... Here, scenarios beyond annually averaged spatial diversity [15] are explored to understand the dynamics of sun-wind diversity in various seasons. Furthermore, a new index is proposed, the net diversity d%, scaled by the physiological equivalent temperature (PET) [16]. The PET has been widely utilised to evaluate heat and cold stress on a linear scale [17], [18]. ...
Conference Paper
Full-text available
Urban microclimatic diversity is of significance to understanding outdoor thermal satisfaction, as it offers a degree of freedom of choice for comfort-seeking behaviour, thermal stimulation and potential alliesthesia. The existing assessment of thermal diversity has shown strong relation to urban 3D geometry. A new workflow is proposed based on previous methods for strengthening the reliability in mapping urban microclimatic diversity. Two new indicators, the gross sun-wind diversity (D%) and the net diversity (d%) have been tested in three urban district models via Envi-MET simulation. The results are segmented by 9 grades of physiological equivalent temperature (PET), showing the value of including the range and variety of thermal sensations in the assessment of urban comfort. The preliminary findings point to a stronger link between microclimatic diversity and thermal neutrality in transitional seasons than in summer or winter.
... Using the actual values of skin and core body temperatures, the energy balance of Eq. (4) can be solved to estimate the air temperature Ta (or PET) in equilibrium conditions with: v=0.1 m/s, vp=12 hPa and Tmrt=Ta. In this work, PET was calculated with ENVI-met introducing some new improvements for outdoor environments [17]. ...
Article
Full-text available
Download link: https://www.iieta.org/journals/ijht/paper/10.18280/ijht.400104. Improving outdoor thermal comfort of the urban spaces is one of the most important challenges that cities have to carry out in the next years. The aim of this work consists of assessing the impact of urban variables and to quantify the influence of greening on outdoor thermal comfort conditions. The work compares six neighborhoods in the city of Turin characterized by different urban forms, contexts, and green areas. External thermal comfort conditions were measured by evaluating a series of indicators with the support of the ENVI-met tool. Through the analysis of various scenarios, outdoor thermal comfort conditions were measured using green mitigation measures, like vegetated areas, trees, and green roofs. The results allow the evaluation on how outdoor thermal comfort varies in relation to urban form and greenery. By comparing neighborhoods with different urban characteristics, it was possible to define the most effective form for the city of Turin. Higher levels of mean radiant temperature were obtained with open form neighborhoods with a prevalent East-West orientation, a low buildings’ density, and a low height-to-width ratio. However, thermal comfort conditions can be mitigated by court-form districts and the presence of greenery, to increase the livability of the urban outdoor environment.
... At each site, the 10-min climate values were used to assess the thermal comfort levels by means of the PET (Physiological Equivalent Temperature) heat stress index (Höppe, 1999;Matzarakis et al., 1999), considering standarized data for human metabolic heat rate and other personal parameters (i.e., age: 35, height: 1.75 m; metabolic rate: 80 W/m 2 ; clothing: 0.9 clo; weight: 75 kg; sex: male). Calculation of PET was performed with a Python code freely available (Walther and Goestchel, 2018). Results were validated with Rayman model, commonly used to estimate PET Matzarakis et al., 2007). ...
Article
In the context of climate change, outdoor thermal comfort is an important component in many urban areas, especially in cities located in hot and humid climates. Climate-responsive urban design, including adequate building morphologies, can create novel urban spaces with better thermal comfort. In this study we compare simultaneous climate measurements taken during several months in different outdoor and semi-outdoor spaces. Results show the improvement of thermal comfort levels in semi-outdoor spaces of tropical areas like Singapore. During the midday/afternoon period air temperature in the semi-outdoor space (sheltered from solar radiation) can be reduced by ~2 °C (as a reference mean value) with respect to a non-urban reference site. However, in certain meteorological conditions the reduction can reach ~4 °C. During the same period of the day, mean radiant temperature is ~28 °C lower than in outdoor spaces of low-rise developments. The mean thermal comfort levels in the semi-outdoor space show significantly less variation during the diurnal cycle and the mean values are always within the acceptable thermal comfort range for Singapore. Mean PET differences reach ~14 °C with respect to low-rise developments. For cities like Singapore, the current study presents the benefits on thermal comfort of promoting the development of semi-outdoor spaces.
... In simple terms, the comfort index, be it the PET or SET * , is then computed as the operative temperature of a "typical indoor" (id est low air velocity, 50% relative humidity and appropriate clothing for the metabolic activity level) that provokes the same physiological response as the actual environment. The open-source version of the PET that can be found in Walther and Goestchel (2018) serves for the computations. ...
Conference Paper
Full-text available
The present work deals with the determination of thermal comfort maps in large enclosures. Currently no specific approach is proposed to this end as building simulation relies on a nodal approach, where the computed scalar values (e.g. temperature, humidity, solar flux) are homogeneously distributed in zones whatever their size. We present here a method allowing for the calculation of a spatial distribution of thermal comfort, enhancing the classical approach by a precise determination of indoor solar fluxes and isothermal air velocities.
... Knowing the skin and core temperatures, the MEMI balance can be solved to evaluate PET that is the air temperature Ta with v = 0.1 m/s, vp = 12 hPa and Tmrt = Ta. ENVI-met calculates PET according to a new model introduced by [44]. The main improvements refer to: (i) turbulent exchange coefficients for heat and water vapour fluxes calculated with the internal air velocity and the outdoor value; (ii) the sweat rate and the amount of sweat on the skin is set to zero when starting to calculate the indoor environments. ...
Article
Extensive and intensive green roofs and vegetated walls should be used to improve the livability in cities, especially in densely built-up context, in order to optimize their contribution on energy savings and greenhouse gas emissions, improving thermal comfort conditions and ensuring a greater storm-water runoff. The aim of this study is to evaluate the effect of urban morphology and to quantify the impact of green surfaces and plants on outdoor thermal comfort conditions. The analysis was applied to six neighborhoods in the city of Turin, identified as typical districts with different building geometries, urban contexts and green presence. The outdoor thermal comfort conditions were assessed calculating a set of indicators, such as the predicted mean vote and the physiological equivalent temperature, with the support of ENVI-met tool. Retrofit scenarios were hypothesized, and outdoor thermal comfort conditions were investigated before and after the installation of green roofs and vegetated areas. The result allowed to understand how thermal comfort vary, considering the building geometry, urban morphology, and green areas in different zones of the city of Turin. By analyzing neighborhoods, it is possible to identify the optimal built environment that ensure better thermal comfort conditions. These models and tools could support urban planners in defining the best measures to improve the liveability and quality in the built environment considering local constraints and the real characteristics of the territory or in designing new neighborhoods. https://www.iieta.org/journals/ti-ijes/paper/10.18280/ti-ijes.652-433
Article
Trees play an essential role in improving outdoor thermal comfort amidst rapid urbanization and impending climate change. Physiological Equivalent Temperature (PET) is used as the thermal comfort metric, derived based on a combination of in-situ measured meteorological parameters and numerically simulated pedestrian-level radiant exchange. The numerical model is developed based on surface energy balance coupled with the Monte Carlo ray-tracing technique and is validated with in-situ measurements. We study the thermal comfort enhancement potential of four typical tree morphologies at varied planting densities in the residential precincts in tropical Singapore. Firstly, we examine the temporal evolution and spatial distribution of PET in a matured residential precinct (MRP) on a typical hot day. Trees with large canopies either in diameter or height, i.e., umbrella and oblong trees, are most effective in improving outdoor thermal comfort. In particular, the umbrella trees improve the precinct mean PET by 1 class from “Warm” to “Slightly warm” at 14:00. Amongst different land features, the mean reduced PET is highest on land features near trees, i.e., grass, by up to 4.35 °C. Secondly, we evaluate the effects of varied planting densities in a new residential precinct (NRP), where open grass patches exist between buildings. At 14:00, tree planting densities of 2.20, 12.20, 29.33, and 36.76 trees per 10,000 m² are needed per 1 °C of mean reduced PET for umbrella, oblong, round to inverted cone trees, respectively. Our findings provide insights on the choice of tree morphology and planting density to mitigate the thermal stress of high-density living.
Article
Among the problems caused by the increase of the urban heat island phenomenon, the worsening of the outdoor thermal comfort at pedestrian level was addressed to improve urban resilience. Starting from the analysis of a real urban area in Venice, Italy, the study was extended to different urban forms classified by the Local Climate Zones (LCZs) method. The Physiological Equivalent Temperature (PET) calculated with the ENVI-met code was used to evaluate outdoor thermal comfort. Different mitigation strategies were compared for the whole summer period. For this purpose, a monthly assessment was performed using the monthly mean day approach rather than the usual single days analysis. A new index (%DPET) was proposed, indicating the percentage reduction in the discomfort rate in PET of the original scenario achieved by mitigation measures. The results show that the largest PETs, corresponding to very hot human thermal sensation, for the original scenario occur in the case of lowrise buildings. In this case, green and cool roofs provide their best performances and the seasonal %DPETs reach 9.1% and 7.5%, respectively. Green wall technology is the most effective in all urban forms studied with %DPET values ranging from 28% to 115%, sometimes reaching the neutral comfort level.
Article
Full-text available
Indoor comfort modelling is well known and mastered thanks to empirical indices or heat balance equations of the individual. In open buildings, called semi-outdoor spaces, assessing comfort is a considerable effort as rapid variations of ambient conditions require the transient modelling of human metabolism.
Article
Full-text available
The buildings sector, being a leading energy consumer, would need to lead in conservation efforts as well. There is a growing consensus that variability in indoor conditions can be acceptable to occupants, improve comfort perception, and lower building energy consumption. This work endeavours to scrutinise and summarise studies that examined human thermal and comfort perception to such variations in the indoor environment: spatial transients, non-uniformities, and temperature drifts. We also briefly discuss personalised comfort systems since they work on an occupant's micro-climate and create non-uniformities in the indoors. Perusal of works done on effect of non-thermal factors on thermal comfort, point to the need for synchronizing the overall indoor environment's quality – in terms of décor, air quality, lighting etc. – to improve occupant thermal comfort. Essence of the overall discussions come out to be that indoor thermal environment can be variable and still agreeable, implying existence of energy saving avenues, hitherto precluded from earnest consideration.
Article
Full-text available
you can download the article here: http://www.nature.com/nclimate/journal/vaop/ncurrent/full/nclimate2741.html
Article
Full-text available
Thermal indices have been applied in the field of human-biometeorology since several decades (e.g. for environmental evaluations, climate assessment for tourists, as well as assessments of climate change). Physiologically Equivalent Temperature (PET), which is based on a time-saving and two-node model, is a widely applied thermal index. However, variations in air humidity and clothing insulation show weak influence on PET. Other thermal indices also show limitations in their applicability. Thus, this study aims to develop a modified PET (mPET) on thermo-physiological mechanisms and clothing factors for universal applications in all climate zones. Physiological thermoregulation of mPET is adapted to a simple multi-segment body model including a blood pool element and a bio-heat transfer principle instead of the two-node human body model used in PET. Furthermore, a multi-layer clothing model with clothing insulation and vapour resistance is established for mPET. It replaces the single-layer clothing model applied in PET. Due to those two modifications, mPET can evaluate thermal conditions influenced by vapour pressure and clothing insulation.
Conference Paper
Full-text available
Due to rapid and intensified urbanisation in cities, the characteristics of outdoor urban microclimates have been detrimentally influenced, altering the perception and satisfaction of pedestrians, especially in hot and dry climates. This poses challenges to many researchers and urban space designers in finding appropriate methods to reduce the urban heat stress and thus to enhance the thermal comfort level of outdoor pedestrian spaces, to prolong the period of their use of space and viability as urban retreats. However, there is limited research conducted on outdoor urban spaces in hot arid climate. Therefore, the purpose of this current research is to review the outdoor thermal comfort interaction factors, as well as to contribute to the knowledge of the literature by conducting a case study of a pedestrian street in the hot dry city of Madinah, Saudi Arabia. It also aims to find out the available methods to increase the outdoor pedestrian thermal comfort level in hot and dry urban microclimates, in addition to understand how CFD simulation method can influence the urban space design and planning processes. This review covers the effect of the moderation of the built environment’s components on the microclimatic parameters on pedestrians’ scale, with the aim for optimising the thermal comfort level in outdoor urban spaces. The literature also covers the use of simulation tools used to simulate environmental conditions outdoors with specific focus on CFD simulation for outdoor thermal comfort applications. Finally, this paper expects to highlight the limitations of both the microclimatic enhancement approach and the CFD simulation as a tool in the field of urban design.
Article
The general feasibility of using various levels of clothing insulation to meet the FEA guideline temperatures in combination with various levels of humidity and air movement are indicated in the series of charts. Effect of Clothing insulation on air temperatures for thermal comfort and acceptability at constant relative humidity at 40 - 60%, effect of relative humidity on thermal acceptability for various clothing insulations and effectiveness of low levels of air movements on thermal acceptability in warmth are discussed.
Article
The ASHRAE Effective Temperature (ET ~) describes the temperature of a standard environment at 50~ relative humidity in which the total skin heat exchange (dry and latent) is equal to that in the real environment. The significance of ET* is reexamined here in terms of basic thermodynamics and transport theory. Dry-bulb (DBT) and wet-bulb (WBT) temperatures measure the potential of the environment to exchange dry heat and total heat with wet surfaces thr~,gh convection.. The Lewis Rclation lii~ks ~he coeffici~fi£S ~f hea~ and mass transport. By analogy, operative temperature (to) and * measure th e po tential fo r dr y he at an d to tal he at ex change by convection and radiation with a human whose skin is partially wet and protected by clothing. Here, the Lewis Relation must be modified by the nondimensional factor i m, a function of the air layer and clothing transfer coefficients. This analogy substantiates the use of ET* as a more accurate index of the energy transfer potential and enthalpy for the total environment surrounding the skin than either t or WBT.
Article
Keywords: Ecological urban planning Urban climate Outdoor thermal comfort Human biometeorology Physiologically equivalent temperature (PET) Valencia (Spain). a b s t r a c t For many years now, research has focused on issues concerning making cities easier to live in and some of the most important of these concern climatology and thermal comfort issues. There is also a growing awareness of the importance of open spaces and green areas, as key elements in providing opportunities for human interaction, leisure and physical exercise. They are important for all inhabitants, but particu-larly so for children and the elderly population. Of especial interest are the studies which have examined the interaction of comfort with the urban climate. This issue was studied throughout the twentieth cen-tury, but recently the role which can be played by biometeorological indices has come to be recognized, especially because of the better understanding them for those responsible for the design of these urban spaces. This study explores the application of the PET index to urban micro-spaces (urban structures), where general values for cities are not valid and where there is a need to know the PET values in order to measure the impact of all items of the urban environment which can provide an increase in comfort. The study was carried out in Valencia (Spain) with the aim of discovering, through these indices, the natural and ecological effects of urban design which can improve comfort. The study focused on: the role of water features, streets with and without trees, squares with hard and soft street surfaces, the effect of different street orientations and the impact of breezes on the city. We have found that the sheets of water, or ponds, provide a cooling effect for the space in which they are located because they have a lower albedo than its surrounding area. In narrow streets, the trees may have a blanket effect and prevent the passage of breezes. Water jets of the fountains should be designed to take advantage of the effect of the breeze to improve the thermal comfort in the surrounding area. The use of hard surfaces and light colors causes a great thermal stress in summer due to higher solar reflexivity that involves higher heat load.