Section 11.5
Section 11.7 Radiative Heating by the Sun
velocity has to increase to about 1.5 m/sec to provide cooling at a rate of 170 Cal/hr.
11.6
Radiation Equation 9.6 shows that the energy exchange by radiation Hr involves the fourth power of temperature; that is, Hr eσ T 4 − T 4
1
2
However, because in the environment encountered by living systems the temperature on the absolute scale seldom varies by more than 15%, it is possible to use, without much error, a linear expression for the radiative energy exchange (see Exercise 11-8a and b); that is, Hr KrAre(Ts − Tr)
(11.5)
where Ts and Tr are the skin surface temperature and the temperature of the nearby radiating surface, respectively; Ar is the area of the body participating in the radiation; e is the emissivity of the surface; and Kr is the radiation coefficient. Over a fairly wide range of temperatures, Kr is, on the average, about 6.0 Cal/m2-hr-C◦ (see Exercise 11-8c).
The environmental radiating surface and skin temperatures are such that the wavelength of the thermal radiation is predominantly in the infrared region of the spectrum. The emissivity of the skin in this wavelength range is nearly unity, independent of the skin pigmentation. For a person with Ar 1.5 m2, Tr 25◦C and Ts 32◦C. The radiative heat loss is 63 Cal/hr.
If the radiating surface is warmer than the skin surface, the skin is heated by radiation. A person begins to feel discomfort due to radiation if the temperature difference between the exposed skin and the radiating environment exceeds about 6 C◦. In the extreme case, when the skin is illuminated by the sun or some other very hot object like a fire, the skin is heated intensely.
Because the temperature of the source is now much higher than the temperature of the skin, the simplified expression in Eq. 11.5 no longer applies.
11.7Radiative Heating by the Sun
The intensity of solar energy at the top of the atmosphere is about 1150 Cal/ m2-hr. Not all this energy reaches the surface of the Earth. Some of it is reflected by airborne particles and water vapor. A thick cloud cover may reflect as much as 75% of solar radiation. The inclination of the Earth’s axis of
Chapter 11 Heat and LifeFIGURE 11.2 Radiative heating by the sun.
rotation further reduces the intensity of solar radiation at the surface. However, in dry equatorial deserts, nearly all the solar radiation may reach the surface.
Because the rays of the sun come from one direction only, at most half the body surface is exposed to solar radiation. In addition the area perpendicular to the solar flux is reduced by the cosine of the angle of incidence (see Fig. 11.2). As the sun approaches the horizon, the effective area for the interception of radiation increases, but at the same time the radiation intensity decreases because the radiation passes through a thicker layer of air. Still, the amount of solar energy heating the skin can be very large. Assuming that the full intensity of solar radiation reaches the surface, the amount of heat Hr that the human body receives from solar radiation is Hr 1150/2 × e × A cos θ Cal/hr
(11.6)
Here A is the skin area of the person, θ is the angle of incidence of sunlight, and e is the emissivity of the skin. The emissivity of the skin in the wavelength region of solar radiation depends on the pigmentation. Dark skin absorbs about 80% of the radiation, and light skin absorbs about 60%. From Eq. 11.6, a light-skinned person with a skin area of 1.7 m2, subject to intense solar radiation incident at a 60◦ angle, receives heat at the rate of 294 Cal/hr.
Radiative heating is decreased by about 40% if the person wears light-colored clothing. Radiative heating is also reduced by changing the orientation of the body with respect to the sun. Camels resting in the shadeless desert face the sun, which minimizes the skin area exposed to solar radiation.
velocity has to increase to about 1.5 m/sec to provide cooling at a rate of 170 Cal/hr.
11.6
Radiation Equation 9.6 shows that the energy exchange by radiation Hr involves the fourth power of temperature; that is, Hr eσ T 4 − T 4
1
2
However, because in the environment encountered by living systems the temperature on the absolute scale seldom varies by more than 15%, it is possible to use, without much error, a linear expression for the radiative energy exchange (see Exercise 11-8a and b); that is, Hr KrAre(Ts − Tr)
(11.5)
where Ts and Tr are the skin surface temperature and the temperature of the nearby radiating surface, respectively; Ar is the area of the body participating in the radiation; e is the emissivity of the surface; and Kr is the radiation coefficient. Over a fairly wide range of temperatures, Kr is, on the average, about 6.0 Cal/m2-hr-C◦ (see Exercise 11-8c).
The environmental radiating surface and skin temperatures are such that the wavelength of the thermal radiation is predominantly in the infrared region of the spectrum. The emissivity of the skin in this wavelength range is nearly unity, independent of the skin pigmentation. For a person with Ar 1.5 m2, Tr 25◦C and Ts 32◦C. The radiative heat loss is 63 Cal/hr.
If the radiating surface is warmer than the skin surface, the skin is heated by radiation. A person begins to feel discomfort due to radiation if the temperature difference between the exposed skin and the radiating environment exceeds about 6 C◦. In the extreme case, when the skin is illuminated by the sun or some other very hot object like a fire, the skin is heated intensely.
Because the temperature of the source is now much higher than the temperature of the skin, the simplified expression in Eq. 11.5 no longer applies.
11.7Radiative Heating by the Sun
The intensity of solar energy at the top of the atmosphere is about 1150 Cal/ m2-hr. Not all this energy reaches the surface of the Earth. Some of it is reflected by airborne particles and water vapor. A thick cloud cover may reflect as much as 75% of solar radiation. The inclination of the Earth’s axis of
Chapter 11 Heat and LifeFIGURE 11.2 Radiative heating by the sun.
rotation further reduces the intensity of solar radiation at the surface. However, in dry equatorial deserts, nearly all the solar radiation may reach the surface.
Because the rays of the sun come from one direction only, at most half the body surface is exposed to solar radiation. In addition the area perpendicular to the solar flux is reduced by the cosine of the angle of incidence (see Fig. 11.2). As the sun approaches the horizon, the effective area for the interception of radiation increases, but at the same time the radiation intensity decreases because the radiation passes through a thicker layer of air. Still, the amount of solar energy heating the skin can be very large. Assuming that the full intensity of solar radiation reaches the surface, the amount of heat Hr that the human body receives from solar radiation is Hr 1150/2 × e × A cos θ Cal/hr
(11.6)
Here A is the skin area of the person, θ is the angle of incidence of sunlight, and e is the emissivity of the skin. The emissivity of the skin in the wavelength region of solar radiation depends on the pigmentation. Dark skin absorbs about 80% of the radiation, and light skin absorbs about 60%. From Eq. 11.6, a light-skinned person with a skin area of 1.7 m2, subject to intense solar radiation incident at a 60◦ angle, receives heat at the rate of 294 Cal/hr.
Radiative heating is decreased by about 40% if the person wears light-colored clothing. Radiative heating is also reduced by changing the orientation of the body with respect to the sun. Camels resting in the shadeless desert face the sun, which minimizes the skin area exposed to solar radiation.