The metabolic heat generated in the body is dissipated to the environment through the skin and the lungs by convection and radiation as sensible heat and by evaporation as latent heat (Fig. 10). Latent heat represents the heat of vaporization of water as it evaporates in the lungs and on the skin by absorbing body heat, and latent heat is released as the moisture condenses on cold surfaces. The warming of the inhaled air represents sensible heat transfer in the lungs and is proportional to the temperature rise of inhaled air. The total rate of heat loss from the body can be expressed as
Therefore, the determination of heat transfer from the body by analysis alone is difficult. Clothing further complicates the heat transfer from the body, and thus we must rely on experimental data. Under steady conditions, the total rate of heat transfer from the body is equal to the rate of metabolic heat generation in the body, which varies from about 100 W for light office work to roughly 1000 W during heavy physical work.
Sensible heat loss from the skin depends on the temperatures of the skin, the environment, and the surrounding surfaces as well as the air motion. The latent heat loss, on the other hand, depends on the skin wettedness and the relative humidity of the environment as well. Clothing serves as insulation and reduces both the sensible and latent forms of heat loss. The heat transfer from the lungs through respiration obviously depends on the frequency of breathing and the volume of the lungs as well as the environmental factors that affect heat transfer from the skin.
Sensible heat from the clothed skin is first transferred to the clothing and then from the clothing to the environment. The convection and radiation heat losses from the outer surface of a clothed body can be expressed as
hconv = convection heat transfer coefficient, as given in Table 3
hrad = radiation heat transfer coefficient, 4.7 W/m2 · ºC for typical indoor conditions; the emissivity is assumed to be 0.95, which is typical
Aclothing = outer surface area of a clothed person
Tclothing = average temperature of exposed skin and clothing
Tambient = ambient air temperature
Tsurr = average temperature of the surrounding surfaces
The convection heat transfer coefficients at 1 atm pressure are given in Table 3. Convection coefficients at pressures P other than 1 atm are obtained by multiplying the values at atmospheric pressure by P0.55 where P is in atm. Also, it is recognized that the temperatures of different surfaces surrounding a person are probably different, and Tsurr represents the mean radiation temperature, which is the temperature of an imaginary isothermal enclosure in which radiation heat exchange with the human body equals the radiation heat exchange with the actual enclosure. Noting that most clothing and building materials are very nearly black, the mean radiation temperature of an enclosure that consists of N surfaces at different temperatures can be determined from
where Ti is the temperature of the surface i and Fperson-i is the view factor between the person and surface i.
Total sensible heat loss can also be expressed conveniently by combining the convection and radiation heat losses as
where the operative temperature Toperative is the average of the mean radiant and ambient temperatures weighed by their respective convection and radiation heat transfer coefficients and is expressed as (Fig. 11)
Note that the operative temperature will be the arithmetic average of the ambient and surrounding surface temperatures when the convection and radiation heat transfer coefficients are equal to each other. Another environmental index used in thermal comfort analysis is the effective temperature, which combines the effects of temperature and humidity. Two environments with the same effective temperature evokes the same thermal response in people even though they are at different temperatures and humidities.
Heat transfer through the clothing can be expressed as
where Rclothing is the unit thermal resistance of clothing in m2 · ºC/W, which involves the combined effects of conduction, convection, and radiation between the skin and the outer surface of clothing. The thermal resistance of clothing is usually expressed in the unit clo where 1 clo = 0.155 m2 · ºC/W = 0.880 ft2 · ºF · h/Btu. The thermal resistance of trousers, long-sleeve shirt, long-sleeve sweater, and T-shirt is 1.0 clo, or 0.155 m2 · ºC/W. Summer clothing such as light slacks and short-sleeved shirt has an insulation value of 0.5 clo, whereas winter clothing such as heavy slacks, long-sleeve shirt, and a sweater or jacket has an insulation value of 0.9 clo.
Then the total sensible heat loss can be expressed in terms of the skin temperature instead of the inconvenient clothing temperature as (Fig. 12)
At a state of thermal comfort, the average skin temperature of the body is observed to be 33ºC (91.5ºF). No discomfort is experienced as the skin temperature fluctuates by -1.5ºC (2.5ºF). This is the case whether the body is clothed or unclothed.
Evaporative or latent heat loss from the skin is proportional to the difference between the water vapor pressure at the skin and the ambient air, and the skin wettedness, which is a measure of the amount of moisture on the skin. It is due to the combined effects of the evaporation of sweat and the diffusion of water through the skin, and can be expressed as
mvapor = the rate of evaporation from the body, kg/s
hfg = the enthalpy of vaporization of water – 2430 kJ/kg at 30ºC
Heat loss by evaporation is maximum when the skin is completely wetted. Also, clothing offers resistance to evaporation, and the rate of evaporation in clothed bodies depends on the moisture permeability of the clothes. The maximum evaporation rate for an average man is about 1 L/h (0.3 g/s), which represents an upper limit of 730 W for the evaporative cooling rate. A person can lose as much as 2 kg of water per hour during a workout on a hot day, but any excess sweat slides off the skin surface without evaporating (Fig. 13).
During respiration, the inhaled air enters at ambient conditions and exhaled air leaves nearly saturated at a temperature close to the deep body temperature (Fig. 14). Therefore, the body loses both sensible heat by convection and latent heat by evaporation from the lungs, and these can be expressed as
mair, lungs = rate of air intake to the lungs, kg/s
cp, air = specific heat of air = 1.0 kJ/kg · ºC
Texhale = temperature of exhaled air
ω = humidity ratio (the mass of moisture per unit mass of dry air)
The rate of air intake to the lungs is directly proportional to the metabolic rate Qmet. The rate of total heat loss from the lungs through respiration can be expressed approximately as
where Pv, ambient is the vapor pressure of ambient air in kPa.
The fraction of sensible heat varies from about 40 percent in the case of heavy work to about 70 percent during light work. The rest of the energy is rejected from the body by perspiration in the form of latent heat.
EXAMPLE 1 – Effect of Clothing on Thermal Comfort
It is well established that a clothed or unclothed person feels comfortable when the skin temperature is about 33ºC. Consider an average man wearing summer clothes whose thermal resistance is 0.6 clo. The man feels very comfortable while standing in a room maintained at 22ºC. The air motion in the room is negligible, and the interior surface temperature of the room is about the same as the air temperature. If this man were to stand in that room unclothed, determine the temperature at which the room must be maintained for him to feel thermally comfortable.
SOLUTION – A man wearing summer clothes feels comfortable in a room at 22ºC. The room temperature at which this man would feel thermally comfortable when unclothed is to be determined.
Assumptions – 1 Steady conditions exist. 2 The latent heat loss from the person remains the same. 3 The heat transfer coefficients remain the same.
Analysis – The body loses heat in sensible and latent forms, and the sensible heat consists of convection and radiation heat transfer. At low air velocities, the convection heat transfer coefficient for a standing man is given in Table 3 to be 4.0 W/m2 · °C. The radiation heat transfer coefficient at typical indoor conditions is 4.7 W/m2 · °C. Therefore, the surface heat transfer coefficient for a standing person for combined convection and radiation is
The thermal resistance of the clothing is given to be
Noting that the surface area of an average man is 1.8 m2, the sensible heat loss from this person when clothed is determined to be (Fig. 15)
From a heat transfer point of view, taking the clothes off is equivalent to removing the clothing insulation or setting Rclothing = 0. The heat transfer in this case can be expressed as
To maintain thermal comfort after taking the clothes off, the skin temperature of the person and the rate of heat transfer from him must remain the same. Then setting the equation above equal to 95.2 W gives
Therefore, the air temperature needs to be raised from 22 to 26.9ºC to ensure that the person will feel comfortable in the room after he takes his clothes off (Fig. 16).
Discussion – Note that the effect of clothing on latent heat is assumed to be negligible in the solution above. We also assumed the surface area of the clothed and unclothed person to be the same for simplicity, and these two effects should counteract each other.