3. Heat Transfer from the Human Body

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

where

h_conv = convection heat transfer coefficient, as given in Table 3
h_rad = radiation heat transfer coefficient, 4.7 W/m2 · ºC for typical indoor conditions; the emissivity is assumed to be 0.95, which is typical
A_clothing = outer surface area of a clothed person
T_clothing = average temperature of exposed skin and clothing
T_ambient = ambient air temperature
T_surr = 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 P^0.55 where P is in atm. Also, it is recognized that the temperatures of different surfaces surrounding a person are probably different, and T_surr 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 T_i is the temperature of the surface i and F_person-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 T_operative 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 R_clothing 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

where

m_vapor = the rate of evaporation from the body, kg/s
h_fg = 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

where

m_{air, 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 Q_met. The rate of total heat loss from the lungs through respiration can be expressed approximately as

where P_{v, 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.