Section 11.5
Convection
Fortunately the body possesses another method for transferring heat. Most of the heat is transported from the inside of the body by blood in the circulatory system. Heat enters the blood from an interior cell by conduction. In this case, heat transfer by conduction is relatively fast because the distances between the capillaries and the heat-producing cells are small. The circulatory system carries the heated blood near to the surface skin. The heat is then transferred to the outside surface by conduction. In addition to transporting heat from the interior of the body, the circulatory system controls the insulation thickness of the body.
When the heat flow out of the body is excessive, the capillaries near the surface become constricted and the blood flow to the surface is greatly reduced. Because tissue without blood is a poor heat conductor, this procedure provides a heatinsulating layer around the inner body core.
11.4
Control of Skin Temperature
As was stated, for heat to flow out of the body, the temperature of the skin must be lower than the internal body temperature. Therefore, heat must be removed from the skin at a sufficient rate to ensure that this condition is maintained.
Because the heat conductivity of air is very low (2.02 Cal-cm/m2-hr-C◦), if the air around the skin is confined—for example, by clothing—the amount of heat removed by conduction is small. The surface of the skin is cooled primarily by convection, radiation, and evaporation. However, if the skin is in contact with a good thermal conductor such as a metal, a considerable amount of heat can be removed by conduction (see Exercise 11-6).
11.5
Convection
When the skin is exposed to open air or some other fluid, heat is removed from it by convection currents. The rate of heat removal is proportional to the exposed surface area and to the temperature difference between the skin and the surrounding air. The rate of heat transfer by convection H c (see Eq. 9.4) is given by
H c K cAc(Ts − Ta)
(11.4)
where Ac is the skin area exposed to the open air; Ts and Ta are the skin and air temperatures, respectively; and K c is the convection coefficient, which has a value that depends primarily on the prevailing wind velocity. The value of K c as a function of air velocity is shown in Fig. 11.1. As the plot shows, the convection coefficient initially increases sharply with wind velocity, and then the increase becomes less steep (see Exercise 11-7).
Chapter 11 Heat and Life FIGURE 11.1 Convection coefficient as a function of air velocity.
The exposed area Ac is generally smaller than the total surface area of the body. For a naked person standing with legs together and arms close to the body, about 80% of the surface area is exposed to convective air currents.
(The exposed area can be reduced by curling up the body.)
Note that heat flows from the skin to the environment only if the air is colder than the skin. If the opposite is the case, the skin is actually heated by the convective air flow.
Let us now calculate the amount of heat removed from the skin by con vection. Consider a naked person whose total surface area is 1.7 m2. Standing straight, the exposed area is about 1.36 m2. If the air temperature is 25◦C and the average skin temperature is 33◦C, the amount of heat removed is
H
×
c 1.36K c 8 10.9K c Cal/hr Under nearly windless conditions, K c is about 6 Cal/m2-hr-C◦ (see Fig. 11.1), and the convective heat loss is 65.4 Cal/hr. During moderate work, the energy consumption for a person of this size is about 170 Cal/hr. Clearly, convection in a windless environment does not provide adequate cooling. The wind 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.
11.7 Radiative 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 Life FIGURE 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.
Fortunately the body possesses another method for transferring heat. Most of the heat is transported from the inside of the body by blood in the circulatory system. Heat enters the blood from an interior cell by conduction. In this case, heat transfer by conduction is relatively fast because the distances between the capillaries and the heat-producing cells are small. The circulatory system carries the heated blood near to the surface skin. The heat is then transferred to the outside surface by conduction. In addition to transporting heat from the interior of the body, the circulatory system controls the insulation thickness of the body.
When the heat flow out of the body is excessive, the capillaries near the surface become constricted and the blood flow to the surface is greatly reduced. Because tissue without blood is a poor heat conductor, this procedure provides a heatinsulating layer around the inner body core.
11.4
Control of Skin Temperature
As was stated, for heat to flow out of the body, the temperature of the skin must be lower than the internal body temperature. Therefore, heat must be removed from the skin at a sufficient rate to ensure that this condition is maintained.
Because the heat conductivity of air is very low (2.02 Cal-cm/m2-hr-C◦), if the air around the skin is confined—for example, by clothing—the amount of heat removed by conduction is small. The surface of the skin is cooled primarily by convection, radiation, and evaporation. However, if the skin is in contact with a good thermal conductor such as a metal, a considerable amount of heat can be removed by conduction (see Exercise 11-6).
11.5
Convection
When the skin is exposed to open air or some other fluid, heat is removed from it by convection currents. The rate of heat removal is proportional to the exposed surface area and to the temperature difference between the skin and the surrounding air. The rate of heat transfer by convection H c (see Eq. 9.4) is given by
H c K cAc(Ts − Ta)
(11.4)
where Ac is the skin area exposed to the open air; Ts and Ta are the skin and air temperatures, respectively; and K c is the convection coefficient, which has a value that depends primarily on the prevailing wind velocity. The value of K c as a function of air velocity is shown in Fig. 11.1. As the plot shows, the convection coefficient initially increases sharply with wind velocity, and then the increase becomes less steep (see Exercise 11-7).
Chapter 11 Heat and Life FIGURE 11.1 Convection coefficient as a function of air velocity.
The exposed area Ac is generally smaller than the total surface area of the body. For a naked person standing with legs together and arms close to the body, about 80% of the surface area is exposed to convective air currents.
(The exposed area can be reduced by curling up the body.)
Note that heat flows from the skin to the environment only if the air is colder than the skin. If the opposite is the case, the skin is actually heated by the convective air flow.
Let us now calculate the amount of heat removed from the skin by con vection. Consider a naked person whose total surface area is 1.7 m2. Standing straight, the exposed area is about 1.36 m2. If the air temperature is 25◦C and the average skin temperature is 33◦C, the amount of heat removed is
H
×
c 1.36K c 8 10.9K c Cal/hr Under nearly windless conditions, K c is about 6 Cal/m2-hr-C◦ (see Fig. 11.1), and the convective heat loss is 65.4 Cal/hr. During moderate work, the energy consumption for a person of this size is about 170 Cal/hr. Clearly, convection in a windless environment does not provide adequate cooling. The wind 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.
11.7 Radiative 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 Life FIGURE 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.