2007, Piran, Slovenia
2007, Piran, Slovenia 2007, Piran, Slovenia
Environmental Ergonomics XII Igor B. Mekjavic, Stelios N. Kounalakis & Nigel A.S. Taylor (Eds.), © BIOMED, Ljubljana 2007 496 A THEORETICAL CONSIDERATION OF SKIN WETTEDNESS Masashi Kuramae, Takafumi Maeda and Shintaro Yokoyama Hokkaido University, Sapporo, Japan Contact person: kuramae@eng.hokudai.ac.jp INTRODUCTION The concept of skin wettedness (Gagge et al., 1977) is often used when calculating evaporative heat loss or evaluating a hot environment. However, in past investigations in this field, inappropriate handling or theoretical confusion of the term “wettedness” is observed as a result of discussions that failed to correctly understand the relationship between the fundamental difference in physical fields based on the difference in scale and macroscopic laws. In this paper, the so-called skin wettedness is discussed from a different viewpoint to clarify its true nature, by considering the heat and mass transfer phenomena on the human body surface from a microscopic viewpoint. METHODS Skin wettedness might be interpreted as the ratio wA of the wet area Aw to the total surface area A of a human body. This skin wettedness can not be measured directly from the human body surface but can be calculated by the ratio wH of actual evaporative heat loss Esk to maximum evaporative heat loss Emax However, there is an essential difference between wA and wH from a physical viewpoint. The value of wH is a macroscopic quantity that requires no information, such as which parts of the human body surface are wet or in what condition. On the other hand, wA is a concept that can only be established from the viewpoint of distinguishing the wet and dry parts of the human skin surface. No actual human body is , for example, soaking wet in the upper half and completely dry in the lower half, but the body usually appears to be uniformly wet uniformly, and it is therefore difficult to distinguish these two conditions by the naked eye. Therefore, it is necessary to reduce the scale of measurement to discuss wA from a microscopic viewpoint. While it is necessary from the above viewpoint to clarify the relationship between the laws in a macroscopic field and the heat and mass transfer mechanisms in the temperature and concentration fields of a microscopic scale, where the wet and dry parts of the human body can be distinguished, strictly theoretical handling is too difficult because of the extremely complex properties of the actual human body surface. However, it is thought that a model of mass transfer from a discontinuous source (Suzuki et al.., 1968) described below will be useful for understanding the actual phenomena. Perspiration from the human body surface is thought to be a problem of mass transfer from a surface consisting of a mixture of areas with mass transfer (wet area) and those without mass transfer (dry area). A model that takes into account the above problems ( see Fig.1 ) was used here to represent the condition of the human body from the microscopic viewpoint. In this model, the semidry body surface is regarded as an assembly of unit cells, each of which contains the skin and outside air layer. The circular area at the center of the skin surface represents the wet surface, while the ring-like area surrounding it corresponds to the dry area. This model can simulate the process by which sweat is released from sweat glands and spreads over the surrounding area. Calculation of skin layer is handled as only a heat transfer problem and that of the air layer as only a mass transfer problem based on the assumptions that thermal conductivity on the skin layer is uniform and that molecular diffusion occurs in the stationary film (thickness: δ) in the air layer.
Air film Skin surface Skin layer δ -L Measurement methods RESULTS Figure 2 shows the relationship between the skin wet area ratioφ calculated by the above method and Esk/Emax. The values used for the calculation are listed in Table 1. The Lewis relation was used to calculate hD, and the value of δ was estimated with the assumption that δ = D/hD. The value of rc was found from the space occupied by one sweat gland, which was obtained by dividing the body surface area (1.75 m 2 ) of an average male subject by the number of sweat glands (2.3 million)(Kuno, 1956). Several combinations of Ta and Ca, were used for the calculation, and TL was determined to make the mean skin surface temperature 35°C. The results shown in Fig. 2 indicate that Esk/Emax does not change greatly regardless of air temperature or humidity and remains close to 1 even ifφ 2 Fig. 1 Model of heat and mass transfer from the human body surface , which is thought to be the real wet area, decreases. Because the vapor generated from the wet area diffuses in the film threedimensionally, the vapor concentration might become almost uniform at a position less than δ from the skin surface in the y direction when δ is greater than rc. Consequently, the concentration field in the film would not accurately reflect the skin surface condition. This is obvious from the results of calculation of vapor the concentration distribution based on the assumption that φ = 0.25 at a temperature of 30°C and relative humidity of 10%, as shown in Fig. 3. Figure 4 shows the results of temperature distribution in the skin layer for the same case. It can also be seen here that, because rc is small, the difference in heat flows of the wet and dry parts of the skin surface does not have much effect on temperature distribution. If the mean skin temperatures of the wet and dry parts of the skin surface are calculated by changing the value of φ from 0.01 to 0.99, the difference between them is only about 1°C at most and is much greater than that in normal conditions. For this reason, the effect of microscopic temperature fields on the skin surface on the amount of evaporation is though to be insignificant. Table 1 The value used for calculation D 2.61×10 -5 [m 2 s -1 ] R v 8.31 [JK -1 mol -1 ] γ 2.44×10 3 [Jkg -1 ] h 2.33 [Jm -2 s -1 K -1 ] λ 0.35 [Jm -1 s -1 K -1 ] Φ rc rc y r 497
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Air film<br />
Skin surface<br />
Skin layer<br />
δ<br />
-L<br />
Measurement methods<br />
RESULTS<br />
Figure 2 shows the relationship between the skin wet area ratioφ calculated by the above<br />
method and Esk/Emax. The values used for the calculation are listed in Table 1. The Lewis<br />
relation was used to calculate hD, and the value of δ was estimated with the assumption that δ<br />
= D/hD. The value of rc was found from the space occupied by one sweat gland, which was<br />
obtained by dividing the body surface area (1.75 m 2 ) of an average male subject by the<br />
number of sweat glands (2.3 million)(Kuno, 1956). Several combinations of Ta and Ca, were<br />
used for the calculation, and TL was determined to make the mean skin surface temperature<br />
35°C. The results shown in Fig. 2 indicate that Esk/Emax does not change greatly regardless of<br />
air temperature or humidity and remains close to 1 even ifφ 2 Fig. 1 Model of heat and mass transfer from the human<br />
body surface<br />
, which is thought to be the real<br />
wet area, decreases. Because the vapor generated from the wet area diffuses in the film threedimensionally,<br />
the vapor concentration might become almost uniform at a position less than δ<br />
from the skin surface in the y direction when δ is greater than rc. Consequently, the<br />
concentration field in the film would not accurately reflect the skin surface condition. This is<br />
obvious from the results of calculation of vapor the concentration distribution based on the<br />
assumption that φ = 0.25 at a temperature of 30°C and relative humidity of 10%, as shown in<br />
Fig. 3. Figure 4 shows the results of temperature distribution in the skin layer for the same<br />
case. It can also be seen here that, because rc is small, the difference in heat flows of the wet<br />
and dry parts of the skin surface does not have much effect on temperature distribution. If the<br />
mean skin temperatures of the wet and dry parts of the skin surface are calculated by changing<br />
the value of φ from 0.01 to 0.99, the difference between them is only about 1°C at most and is<br />
much greater than that in normal conditions. For this reason, the effect of microscopic<br />
temperature fields on the skin surface on the amount of evaporation is though to be<br />
insignificant.<br />
Table 1 The value used for calculation<br />
D 2.61×10 -5 [m 2 s -1 ]<br />
R v 8.31 [JK -1 mol -1 ]<br />
γ 2.44×10 3 [Jkg -1 ]<br />
h 2.33 [Jm -2 s -1 K -1 ]<br />
λ 0.35 [Jm -1 s -1 K -1 ]<br />
Φ rc rc<br />
y<br />
r<br />
497