Page 227 - Industrial Ventilation Design Guidebook

1 88 CHAPTER 5 PHYSIOLOGICAL AND TOXICOLOGICAL CONSIDERATIONS

5.1.7 Thermal Radiation and Operative Temperature
In buildings away from outside perimeter walls, air and surface tempera-
tures are usually approximately equal. The heat losses from a person by ra-
diation (q r) and convection (q c) 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 sed-
entary 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
(T a) the person will feel warmer or colder than in a thermally uniform space
where MRT = T a .
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 (T a — MRT) that
has the same total dry heat loss (convection 4- radiation) as the actual environ-
ment where T a & MRT.
Dry heat losses (q^ TJ} from the person's surface at temperature T, can be
expressed as

where the convective (h c) and linearized radiation (h r) heat transfer coeffi-
cients are

and

where
e = emissivity of clothing-body surface « 0.9,
8 2
a - Stefan-Boltzmann constant, 5.67xlO" W/m K
2
A r = effective radiation area of body, m (A r /A D ) ~ 0.7
A r is less than the skin area A D 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

6
where T Q is the operative temperature, evaluated as T 0 = [h c • T a + h r • T r]/
(h c + h r). 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 h c = h r and op-
erative temperature becomes the simple average of the air and mean radiant
temperatures,