Handbook of air conditioning and refrigeration / Shan K

Steady-State Thermal Equilibrium
Transient Energy Balance
When the human body is maintained at a steady-state thermal equilibrium, i.e., the heat storage
at the body core and skin surface is approximately equal to zero, then the heat exchange between
the human body and the indoor environment can be expressed by the following heat balance
equation:
M � W � C � R � E sk � E res
where M � metabolic rate, Btu/h�ft 2 (W/m 2 )
W � mechanical work performed, Btu/h�ft 2 (W/m 2 )
C � R � convective and radiative, or sensible heat loss from skin surface,
Btu/h�ft 2 (W/m 2 )
E sk � evaporative heat loss from skin surface, Btu/h�ft 2 (W/m 2 )
E res � evaporative heat loss from respiration, Btu/h�ft 2 (W/m 2 )
In Eq. (4.1), the ft 2 in the unit Btu/h�ft 2 applies to the skin surface area. The skin surface area of a
naked human body can be approximated by an empirical formula proposed by Dubois in 1916
where A D � Dubois surface area of naked body, ft 2 (m 2 )
m b � mass of human body, lb (kg)
H b � height of human body, ft (m)
(4.1)
A D � 0.657m b 0.425 Hb 0.725 (4.2)
In an air conditioned space, a steady-state thermal equilibrium is usually maintained between the
human body and the indoor environment.
When there is a transient energy balance between the human body and the indoor environment, the
thermal interaction of the body core, skin surface, and indoor environment forms a rate of positive
or negative heat storage both in the body core and on the skin surface.
The human body needs energy for physical and mental activity. This energy comes from the oxidation
of the food taken into the human body. The heat released from this oxidation process is
called metabolic heat. It dissipates from the skin surface of the human body into the surroundings.
In a cold environment, the thermoregulatory mechanism reduces the rate of peripheral blood circulation,
lowering the temperature of the skin and preventing any greater heat loss from the human
body. However, if the heat loss and the mechanical work performed are greater than the rate of
metabolic heat produced, then the temperatures of both the body core and the skin surface fall, and
shivering or other spontaneous activities occur to increase the production of heat energy within the
human body.
On the other hand, in a hot environment, if a large amount of heat energy needs to be dissipated
from the human body, the physiological control mechanism increases the blood flow to the skin
surface. This raises the skin temperature. If the heat produced is still greater than the heat actually
dissipated and the temperature of the body core increased from its normal temperature of about
97.6 to about 98.6°F (36.4 to about 37.0°C), then liquid water is released from the sweat glands for
evaporative cooling.
For a transient state of energy balance between the human body and the indoor environment, the
rate of heat storage in the body core S cr and the skin surface S sk, both in Btu/h�ft 2 (W/m 2 ), can be
calculated as
S cr � S sk � M � W � (C � R) � E sk � E res
INDOOR AND OUTDOOR DESIGN CONDITIONS 4.3
(4.3)