# Thermal Radiation and Operative Temperature

In buildings away from outside perimeter walls, air and surface tempera­tures are usually approximately equal. The heat losses from a person by ra­diation (qr) and convection (qc) are then flowing to the same temperature level. In such uniform spaces, the radiant and convective losses are about equal and together account for about 80-90% of the total heat loss of a sed­entary comfortable individual. In the presence of hot or cold surfaces, as may occur in perimeter or other locations in a building, the average surface temperature of the surroundings (called mean radiant temperature) as seen by the person’s body may be substantially different from air temperature. If the mean radiant temperature (MRT) is greater or less than air temperature (TJ the person will feel warmer or colder than in a thermally uniform space where MRT = Ta.

To simplify the effects of radiation and convection on dry heat transfer, the concept of operative temperature is often used. By definition operative temperature is the temperature of a uniform environment (Ta — MRT) that has the same total dry heat loss (convection + radiation) as the actual environ­ment where Ta * MRT.

Dry heat losses (<jdry) from the person’s surface at temperature T,. can be expressed as

<?dry = <lc + <lr = hc-(Ts-Ta) + hr-(Ts-MRT) , (5.15)

Where the convective (hc) and linearized radiation (hr) heat transfer coeffi­cients are

Hc = 8.5z/°’5W/m2 K with v in m/s (5.16)

And

Hr = 4eo-(Ar/AD)[273.2 + (Ts + MRT)/2]3 W/m2 K, (5.17)

Where

E = emissivity of clothing-body surface -0.9, a = Stefan-Boltzmann constant, 5.67 x 10~8 W/m2K Ar = effective radiation area of body, m2 (Ar/AD ) ~ 0.7

Ar is less than the skin area AD because some of the skin of fingers, arms, legs, and feet radiates to other skin and is not as effective for radiant heat loss. Equation (5.15) can be rearranged to

<7dry = (kc + hr) ■ [Ts+ Ta] (5.18)

Where T0 is the operative temperature,6 evaluated as T0 = [hc ■ Ta + hr • Tr]/ (hc + br). The equation shows that operative temperature is the average of air and mean radiant temperatures weighted by their respective heat transfer coefficients. It is the temperature of a uniform environment that physically and mathematically represents the actual environment. Fortunately, for the low air speeds (v < 0.25 m/s) of most indoor environments hc = hr and op­erative temperature becomes the simple average of the air and mean radiant temperatures,

(5.19)

At higher air speeds hc > h„ convective hear loss becomes greater than radia tion and TG approaches Tr For such conditions Eq. (5.20) is recommended:»

T0= ATt,+{ — A)MRT,

Where A depends on air speed («’):

1/ (m/s) 0-0.2 (U-0.6 0. ft-1.0

0.5 0.6 0.7

The above indicates that to maintain a constant level of comfort when MRT decreases, Ta must be increased an equal amount. This is the difficulty of pe­rimeter zones. In many such environments the air and surface temperatures differ and operative temperature is a convenient way to characterize the envi­ronment.

How is mean radiant temperature (MRT) determined? One could calcu­late or measure the surface temperatures of the room and calculate MRT from

MRT — ■ TОw + Fp-f Јu-c ’ 7?r) + + +

Where Tr„ is the absolute temperature (K) of the radiating surface n and hp. n is the angle factor from the person to surface w.6-18 and Fp_„ is the fraction of radiation leaving p that strikes n.

If the surface temperatures are not widely different, Eq. (5.21) can be sim­plified to

At a location MRT and T(l are often measured with a sphere or ellipsoid repre­senting the person, as shown in Fig. 5.10. In the diagram the energy balance on the globe at steady state is qc — qr, or

Hc ■ ( TK — TJ = hr • ( MRT — Tg) ,

For T, > T,

R.

And after rearranging:

MRT = Tg+[hc/hr)-(Tg-Ta) (5.24)

Substituting numerical values for hc and br with d = 15 cm and v in m/’s,

MRT = Tg + 0.247v{T,, — T„) . (5.25)

Further, from the definition of operative temperature (T0),

T0 = (hc’ Ta + hT ■ MKT)/(hc + hr), (5.26)

Substituting Eq. (5.24) into Eq. (5.26) and rearranging,

,.r _Ta + [hr+bc]b-Tg + [hr/hc]hhc+hrg-(Tg-Til) ,c ^ 0 1 + hr/bjh ’

Where subscripts h and g designate the human and globe. For 15 to 20 cm di­ameter globes [hr/hc] =[hr/hch, which after substituting and rearranging Eq. (5.27) simplifies to

Tn = Tg. (5.28)

Globes can be made of any opaque material. A globe of low mass is help­ful to provide a short time constant for transient conditions. Globes are typi­cally gray or black, but color is not important if they do not receive high temperature radiation from the sun or other glowing objects. If significant high-temperature radiation is present, then they should have a color similar to that of the occupant. The comfort zones of Fig. 5.7b should be entered w ith TG when it is known that MRT ^ Ta because T0 is the temperature that the envi­ronment feels like to the occupant of the space.

Warm Discomfort and Skin Moisture

In warm environments or situations with prolonged activities above about

1.2 met there is sweating. The sweat glands put water on the skin for evapora­tive cooling. Since the latent heat of evaporation of water is so high very little water is consumed in this cooling process. In the process the skin gets wet. If the conditions are very good for evaporation the skin can remain nearly dry while sweating occurs, as for example in windy desert conditions. In humid still-air conditions a larger surface of water is necessary to evaporate the sweat and the skin becomes wetter. The fraction of the surface of the skin that is cov­ered with water for evaporation is called skin wettedness ( w).X9 It is a measure of the physiological strain or effort of evaporative cooling and has long been associated with warm discomfort (Fig. 5.11). It is rare that a person feels com­fortable with a skin wettedness above 20 to 25%.

 (5,29)

Some of the discomfort of warm environments, the perception of skin moisture, and the interactions of clothing fabrics with the skin may be due to the moisture itself. The skin’s outer layer of dead squamous cells of the stra­tum corneum can readily absorb or lose water. With moisture addition, the cells swell and soften. With drying, they shrink and become hard. In this set­ting the skin’s moisture may be better indicated or characterized by the rela­tive humidity of the skin (RHsk) rather than skin wettedness,24

 Intolerable

 G O O 3 S

 Comfortable g

 1 met, Gonzalez 3 met, Gonzalez 1 met, Berglund 1 met, Cunningham 1 & 5 met, Hoeppe

 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Mean Skin Wettedness FIGURE 5.11 Warm discomfort related to skin wettedness from various studies.20

RHsk = pm/pStSk,
where Pm is the average vapor pressure of the skin and Ps sk is the saturated vapor pressure of water at skin temperature. Typically, the water content (water/dry skin) of the stratum corneum is about 10% but it can absorb as much as four times its dry weight.

Skin moisture may be detected by mechanoreceptors of the skin and hair follicles or some other neural mechanism that senses the skin’s swelling and shrinking. At high levels of skin moisture the swelling is sufficient to close or reduce the lumen of sweat glands and reduce sweating (called hydromeiosis). Hydromeiosis occurs at RHsk s 0.9.25 Conversely, under good drying condi­tions the skin can shrink to the extent that lesions form.

As mentioned previously, the other term for characterizing skin moisture is skin wettedness (w) or the size of the water film as a fraction of total skin area that is necessary to account for the observed evaporative heat loss from the skin (Esk),

Esk = w — Adu — he — (PSjSk-Pt!), (5.30)

Where A&a is total skin area, he is evaporative heat transfer coefficient, and Pa is the ambient vapor pressure.

Skin wettedness and skin relative humidity are related by

RHsk = w + (l-w)(Pa/P^sk) . (5.31)

From Eq. (5.30) it is clear that RHsk will be greater than u> except when w = 1. It is also evident that with a constant w, RHsk increases with ambient absolute humidity. Thus, though the ET* temperature boundaries have con-

 4—I—H
 +
 23 24 25 16 Air Temperature (
 27 ’C)
 28 29 30
 20 21 22
 Very humid 6 Humid 5 Slightly humid 4 Neutral 3 Slightly dry 2 Dry 1 Very dry 0

 Dew point = 20 °C ♦ *11 °C 2 °C

FIGURE 5.12 Perceived ambient humidity by sedentary subjects.

Stant skin wettedness levels, the RHsk, swelling, and softening of the skin in­crease with increasing ambient absolute humidity.

Humans are sensitive to moisture and can reliably describe the humidity of the environment using word scales as demonstrated in Fig. 5.12.10 The sub­ject’s humidity judgments appear to be functions of the air’s dew point, a mea­sure of absolute humidity, and are relatively unaffected by the ambient temperature. Further, people are also good at perceiving skin moisture, as il­lustrated in Fig. 5.13, where perceived skin wettedness is seen to correlate well with measured skin wettedness.

In situations of prolonged sweating, skin wettedness slowly increases with time because of accumulating salt on the skin. The increasing sait oc­curs because the water in perspiration evaporates while the dissolved materi­als, principally sodium chloride, remain on the surface. The salt lowers the vapor pressure of the sweat film, decreasing its rate of evaporation per unit area. The area of the film then naturally increases in order that evaporation will equal the rate of sweat secretion. It is thought that part of the relief that bathing brings after a warm day or strenuous activity is that by cleaning the skin, perspiration can then evaporate more efficiently with reduced skin wet­tedness.

Clothing can be one of the detractors from acceptability in humid envi­ronments. Measurements by Gwosdow26 reveal that the friction between skin and clothing increases abruptly for skin wettedness levels above 25%. Further, fabrics are perceived to be rougher or to have a coarser texture and to be less pleasant with increasing skin moisture. This may be one of the rea­sons that, in the comfort studies cited earlier, the people have rarely indi­cated they were comfortable when they had skin wettedness levels near and above 25%.

Low humidity also affects comfort and health. Comfort complaints about dry nose, throat, eyes, and skin occur in low-humidity conditions, typically when the dew point is less than 0 °C. Low humidity can lead to drying of the skin and mucous surfaces. On respiratory surfaces, drying can concentrate mucus to the extent that ciliary clearance and phagocytic activities are re-

Measured Skin Wettedness W

FIGURE S. 13 Perceived skin moisture correlated to measure skin wettedness for activities from I to 3 met.

Duced, increasing susceptibility to respiratory disease as well as discomfort. Green27 quantified that respiratory illness and absenteeism increase in winter with decreasing humidity. He found that any increase in humidity from the low winter levels decreased absenteeism. Excessive drying of the skin can lead to lesions, skin roughness, and discomfort and impair the skin’s protective functions. Dusty environments can further exacerbate low-humidity dry skin conditions.28

Liviana et al.29 found that drying from low humidity can contribute to eye irritation. Eye discomfort increased with time in low-humidity environments

Tdp < 2 °C.

Comfort is reduced by elevated humidity levels. It is recommended30 that on the warm side of the comfort zone the relative humidity should not exceed 60% to prevent warm discomfort. On the cool side of the comfort zone, high humidity is less important because there is no sweating to increase skin mois­ture. For these reasons the upper boundaries of comfort zones in Fig. 5.7b are wet bulb temperatures of 18 and 20 °C for the winter and summer comfort zones respectively.