Thermal comfort
“That condition of mind in which satisfaction is expressed with the thermal environment ” ANSI/ASHRAE Standard 55-1992:
Thermal Environmental Conditions for Human Occupancy
The following gives a few facts about human beings:
• Heat generated from a human body:
• Human body temperature:
O
• One would wake up from sleep if this person loses 24 W or more. In this case, the skin temperature decreases 2.8 °C.
• One would feel uncomfortable or sick, if the person’s body temperature is 1 K higher.
• O
• O
Human body obeys the first law of thermodynamics. Energy balance for human body: Heat production — Mechanical work = Heat losses
2
M — Rate of metabolic heat production (W/m body surface area) (Table 4-1, textbook)
W — Rate of mechanical work
Q — Heat losses
C — Convective heat losses
R — Radiative heat losses
E — Evaporative heat losses
Sk — Skin
Res — Respiration
Heat production: measured in metabolic or met units.
1 met = 58.2 W/m2 = 18.4 Btu/(hft2) body surface area
|
Table 4 Typical Metabolic Heat Generation for Various Activities
More and Dumin (1967), and Webb (1964). al met = 58.2 W/m2 : Buskirk (1960), PM**. •jq* |
Environmental and personal comfort variables Environmental factors
O
Air temperature ~
Relative humidity ~
Air velocity near a human body, V ~
Surface temperature of the enclosure and other objects ~
Personal factors
Activity (rate of metabolic)
Clothing (insulation)
1 clo = 0.88 F-ft2-hr/Btu
Determination of individual heat loss/gain
2
W = Active work and shivering (involuntary work) (W/m body area)
•2
M = Rate of metabolic heat production (W/m )
(M is given in Table 4-1 of the textbook. 1 met = 58.2 W/m body area)
Csk = he (Tdoth — Tair) Acioth/Abody (W/m2 body area)
|
)0’25 > 12.1 V0’5 )0’25 < 12.1 V0’5 |
Hc = 2.38 (Tdoth — Tair)0’25 when 2.38 (Tcioth — Ta„-
Hc = 12.1 V0’5 when 2.38 (Tdoth — Tair
Tdoth = 35.7 — 0.0275 (M — W) — {(M — W)
— 3.05 [ 5.73 — 0.007 (M — W) — pv]
— 0.42 [ (M — W) — 58.15] — 0.0173 M (5.87 — pv)
— 0.0014 M (34-Tair)}
Abody = 0.202 m0’425 10’725 (m2)
M — Body weight (kg)
1 — Height (m)
Adoth/Abody = f(Garment insulation value)
= 1.0+ 0.3 Id
Rcioth = Cloth thermal resistance (m K/ W)
Rcioth = 0.155 Id
1 clo = 0.155 m2 K/W
Ici can be found in Table 8, Chapter 8 of ASHRAE Fundamentals, 1997
Rsk G Ecloth Eeiiclosure [ ( Tcl0th + 273 ) — (Tenclosure + 273 ) ] Adoth/Abodv
G — Stefan-Boltzmann constant (5.67×10"8 W/m2K4) e — Emittance (a value between 0 and l)
Rsk = 3.96xl0’8 [ ( Tdoth + 273 )4 — (Teiidosure + 273 )4] Adoth/Abodv (W/m2)
Esk nisk ifg
= 3.05 [ 5.73 — 0.007 (M — W) — pv]
+ 0.42 [ (M — W) — 58.15] (W/m2)
Pv — Vapor pressure (kPa)
Cres — nires Cp. a (Tres — Tair)
= 0.0014 M (34 — Tair) (W/m2)
Eres nires ifg
= 0.0173 M (5.87 — pv) (W/m2)
Note: Body energy balance ^ Always thermally comfort Thermal comfort = Always body energy balance
Only in a limited range of environmental parameters, thermal comfort can be achieved.
•
|
PMV = |
Predicted Mean Vote (PMV)
|
+ 3 |
Hot |
|
+ 2 |
Warm |
|
+ 1 |
Slightly warm |
|
0 |
Neutral |
|
-1 |
Slightly cool |
|
-2 |
Cool |
|
-3 |
Cold |
|
O O |
L — Thermal load on the body
L = Internal heat production — heat loss to the actual environment
• Predicted Percentage Dissatisfied (PPD)
PPD = 100 — 95 exp [ — (0.03353 PMV4 + 0.2179 PMV2)]
|
PMV |
PPD |
|
0 |
5% |
|
± 0.5 |
10% |
|
± 1.0 |
25% |
Example:
The environmental parameters in an office are:
Tair = 25 °C Twaii = 25 °C
Pv = 2500 Pa he = 3 W/m2K
Niperson — 70 kg lperson — 1.86 m
Id, person =1.0 clo (Business suit)
Determine the comfort level in the office.
Solution:
From Table 4-1 of the textbook (or handouts), M = 60 W/m2 Since Tair is 25 °C and person does not do physical work, W = 0.
Rdoth = 0.155 1 = 0.155 x 1.0 = 0.155 m2K/W
Abodv= 0.202 m0-425 10’725
= 0.202 x 70°’425 x 1,860-725 = 1.927 m2
Adoth/Abody = 1.0 + 0.3 I = 1.0 + 0.3 x 1.0 = 1.3
Tdoth = 35.7 — 0.0275 (M — W) — Rdoth {(M — W)
— 3.05 [ 5.73 — 0.007 (M — W) — pv]
— 0.42 [ (M — W) — 58.15] — 0.0173 M (5.87 — pv)
— 0.0014 M (34-Tair)}
= 35.7 — 0.0275 x (60 -0) — 0.155{(60 — 0)
— 3.05 [ 5.73 — 0.007 (60 — 0) — 2.5]
— 0.42 [ (60 — 0) — 58.15] — 0.0173 x 60 (5.87 — 2.5) -0.0014×60 (34-25)}
= 26.86 °C
Csk — hc (Tdoth — Tair) Adoth/Abodv = 3 x (26.85 — 25) x 1.3 = 7.254 W/m2
Rsk — 3.96xl0’8 [ ( Tdoth + 273 )4 — (Tenciosure + 273 )4] Adoth/Abody = 3.96xl0"8 [(26.86 + 273)4 — (25+273)4] x 1.3 = 10.23 W/m2
Esk =3.05 [5.73 -0.007 (M-W)-pv]
+ 0.42 [(M-W) -58.15]
= 3.05 [ 5.73 — 0.007 (60 — 0) — 2.5]
+ 0.42 [(60-0)-58.15]
= 9.348 W/m2
Cres = 0.0014 M (34 — Tair)
= 0.0014 x 60 (34 — 25)
= 0.756 W/m2
Eres =0.0173 M (5.87-pv)
= 0.173 x60( 5.87-2.5 )
= 3.50 W/m2
L = M — W — [( Csk + Rsk + Esk ) + ( Cres + Eres )]
= 60 — 0 — [( 7.254 + 10.23 + 9.348) + (0.756 + 3.5)]
= 29 W/m2
PMV = [0.303 exp ( -0.036 M ) + 0.028 ] L
= [0.303 exp ( -0.036 x 60 ) + 0.028 ] x 29
= 1.825 => Warm
PPD = 100 — 95 exp [ — (0.03353 PMV4 + 0.2179 PMV2)]
= 100 — 95 exp [ — (0.03353 x 1.8254 + 0.2179 x 1.8252)]
= 68%
|
|
Ure 2.4: At lower temperatures heat loss by convection and radiation dominate, but >ve 80°F air and surface temperature evaporation begins to dominate. (After. Flynn ISegil, 1970.).
|
Table 2.1: Clo Values for Various Men’s Clothing Ensembles |
|
|
Clothing Ensemble |
Dovakit |
|
Nude |
0 |
|
Shorts |
0.1 |
|
Tropical dothing: shorts, open-neck short-sleeved shirt, Dght socks and sandals |
03-0.4 |
|
Light summer dothing: long light-weight trousers, open-nsck short-sleeved shirt |
OS |
|
Tight working dothing: athletic shorts, wool soda, opervnsck short sleeved cotton shirt, long cotton trousers |
OlB |
|
Light outdoor sportswear: T-shirt, cotton shirt, cotton undaisiiorts, cotton trousers, cotton socks, shoes; and single-pty, light-weight popiin Jacket |
0.7 |
|
Typical business suit |
1J0 |
|
Typical business suit with cotton topcoat (or heavy wool suit without topcoat) |
1J5 |
|
U. S. Army standard cold-wet uniform: cotton-wool undershirt and undershorts, wool/nylon flannel shirt, wind-resistant, water-repellent trousers and field coat, doth mohair and wool coat, and wool socks |
1Л-2Л |
|
Heavy wool pile ensemble: (Polar weather suit) |
ЗЛ-4.0 |
|
(Reproduced from Fanger, 1882, by permission.) |
|
Fig. 11 Predicted Percentage of Dissatisfied (PPO) as Function of Predicted Mean Vote (PMV) |
• Operative temperature (T0)
• Effective temperature (ET*)
• ASHRAE comfort zone
Operative temperature (TO):
O
Tmrt — Mean radiant temperature Tmrt = I AjTj /1 A,
T; — Surface temperature of enclosure i A; — Area of surface i
Effective temperature (ET*):
The temperature of an environment at 50% relative humidity that results in the same total (sensible + latent) heat loss from the skin as in the actual environment. It combines operative temperature and humidity into a single index.
ASHRAE comfort zone (Fig. 4-2):
The “comfort zone” represents combinations of air temperature and relative humidity that most often produce comfort for a seated North American adult in shirtsleeves, in the shade.
Winter: T0 = 20-23.5°C (68-74°F) at 60% relative humidity and Tc = 20.5-24.5°C (69- 76°F) at 2°C (36°F) dew point. Slanting side boundaries correspond to ET* of 20°C (68°F) and 23.5°C (74°F).
Summer: To = 22.5-26°C (73-79°F) at 60% relative humidity and Tc = 23.5-27°C (74- 80°F) at 2°C (36°F) dew point. Slanting side boundaries correspond to ET* of 23°C (73°F) and 26°C (79°F).
Conditions: Typical summer and winter clothing
Light and primarily sedentary activity (<=1.2 met)
10% dissatisfaction
|
OPERATIVE TEMPERATURE. "C Fig. 5 Standard Effective Temperature and ASHRAE Comfort Zones |
Adjustment of the comfort zone
(1) . Clothing (e. g., minimum clothing such as briefs Tc = 26-29°C (79-84°F)
(Table 4-3)
(2) . Air speed VО -> Tot (Fig. 4-3)
(3) . Activity (met)T -> Toi (Fig. 4-4)
(4) Adaptation
Draft is related to air temperature, air velocity, and turbulence intensity. Percentage dissatisfied people due to draft can be expressed as:
PD = 3.143 (34 — Tair) (V — 0.05)0’622
+ 0.3696 (34 — Tair) (V — 0.05)0’622 V Tu
When V < 0.05 m/s, use V = 0.05.
When PD > 100%, insert PD = 100%.
|
18% DISSATISFIED PD — Percentage dissatisfied people due to draft (%) V — Air velocity (m/s) Tair — Air temperature (°C) °-8 Tu — Turbulence intensity (%) Tu = 100 Vstandard deviation /V (0/.
Fig. 13 Percentage of People Dissatisfied as function F|g u Dnrfl Conditions Dissatisfying 15% of Population Of Mean Air Velocity 22 24 AIR TEMPERATURE. *C 0 I O. t 0.9 0 4 MEAN AIR VELOCITY, n* |
Asymmetry of thermal radiation
|
10 16 20 25 30 35 40 RADIANT TEMPERATURE ASYMMETRY, *C |
|
W ALL |
|
WARM CEILING |
|
COOL WALL |
|
Fig. 12 Percentage of People Expressing Discomfort Due to Asymmetric Radiation |
Asymmetry Warm ceiling (—) Cool wall (—) Cool ceiling (—) Warm wall (-)
Thermal stratification
Temperature difference < 3-4 K between head and feet
For large temperature gradients, local warm discomfort can occur at the head, and/or cold discomfort can occur at the feet, although the body as a whole is thermally neutral.
|
AIR TEMPERATURE DIFFERENCE BETWEEN HEAD AND FEET "C |
Rg. 15 Percentage of People Dissatisfied as Ruction of Vertical Air Temperature Difference between Head and Ankles
Warm or cold floors
|
Fig. 16 Percentage of People Dissatisfied as Function of Floor Temperature |
|
Increased MK Textends comfort zone
Dry Mb temperature (TJ Figure 2.7: Effect of mean radiant temperature on comfort zones. (After Arends etal., 1980, modified to current ASHRAE comfort zone.) |
|
Increased air motion extends comfort zone
D/y buib temperature (TJ Figure 2.8: Effect of air motion on the summer comfort zone. (After Arends et al., 1960, modified to current ASHRAE comfort zone.) |
Posted in Fundamentals of Heating. Ventilating, and Air-Conditioning