The basic data measurements for SHED's surface temperature at 30 or 35°C, placed vertically in the air, were performed under climate chamber conditions (less than 0.1 m/s wind, 25°C air temperature, and 40, 60, and 80% RH). The k dry and k wet values are listed in Table 1. k dry showed -10 kcal/m2/h/°C regardless of the humidity and SHED surface temperature, k wet decreased with increasing humidity and converged at -30 kcal/m2/h/°C regardless of the surface temperature of the SHED. The k wet indicates that heat exchange on the wet surface will be more complex. DQ, derived Q wet minus Q dry, showed direct correlation with T surface, but not with RH%. T surface is considered to be a major regulator of evaporative heat dissipation when T ambient is lower than the T surface (Table 1).
Figure 2 shows the results of calibration using the Leslie cube. Since the SHED did not touch an object, its total output (Q) did not include the conduction heat exchange at all and consisted solely of R and (C+E). A minor effect of thin paper on each slope and section was observed (data not shown). These regression equations could be used within the calibrated Q range (-500 to +200 kcal/m2/h).
Table 1 and Figure 2 insert near here.
The environmental condition during this experiment was followed; Tambient: 25.4 ±0.5; %RH: 35.5 ±3.1. Figure 3, Panel 3A shows seven Q values obtained by changing the surface temperature of the SHED in the order of 8.2, 13.2, 13.4, 18.4, 18.5, 28.8, and 34.5°C. When the SHED is covered with dry paper, Q dry is constantly flowing onto SHED. However, when it is covered with wet paper, Q wet only flows into SHED when the surface temperature is below 30 °C. The two Qs coincide at a surface temperature of around 13.5 °C. When these data are fractionated by our calibration (Figure 2), the C wet (= Q wet – R wet) is not fully explained by the theoretical estimate of convection caused by temperature differences between the surface and the ambient air plus evaporative cooling (Figure 3, Panel 3B). This is in agreement with a geoscientific theory that states that wetlands absorb more solar radiation than dry lands (Budyko, 2008). This is a simple experiment, but it shows that surface temperature has a strong influence on heat exchange and that humidity or water vapor partial pressure is the determinant. I would like to show the whole picture under the environmental conditions of a wider temperature and humidity range.
Table 1. SHED specific k and DQ measurements at 25°C.
T ambient (°C), and RH%
|
T surface (°C)
|
Q dry
(kcal/m2/h)
|
k dry
(kcal/m2/h/°C)
|
Q wet
(kcal/m2/h)
|
k wet (kcal/m2/h/°C)
|
DQ
= Q wet - Q dry
(kcal/m2/h)
|
25, 40
|
30
|
-48.5
|
-9.8
|
-225.9
|
-44.5
|
-177.4
|
35
|
-134.7
|
-14.5
|
-391.9
|
-39.0
|
-257.2
|
25, 60
|
30
|
-47.4
|
-10.0
|
-185.2
|
-36.6
|
-137.8
|
35
|
-120.1
|
-12.6
|
-307.2
|
-30.7
|
-187.1
|
25, 80
|
30
|
-53.4
|
-10.6
|
-147.4
|
-29.1
|
-94.0
|
35
|
-101.1
|
-10.1
|
-280.4
|
-28.0
|
-179.3
|
Mean ± SD
|
30
|
-49.8±3.2
|
-10.1±0.4
|
-186.2±39.2
|
-36.7±7.7
|
-136.4±41.7
|
35
|
-118.6±16.8
|
-12.4±2.2
|
-326.5±58.2
|
-32.6±5.7
|
-207.9±42.9
|
All
|
|
-11.3±1.9
|
|
-34.6±6.5
|
-172.1±54.4
|
DQ = -17.527 x T surface +412.61 (R2 = 0.867); DQ = 2.037 x RH%-191.64 (R2 = 0.100)
Table 2. Results of Experiment 2. The differences of Q induced by the surface water (DQ1 (kcal/m2/h) = Q wet - Q dry), and those induced by the radiation (△Q2 (kcal/m2/h) = △Q1 L rad - △Q1 L n-rad) are listed in this table. When DQ is negative, it indicates more lamp-radiated heat flow into the wet SHED surface, but when DQ is positive it indicates heat flow out from the wet SHED surface. Multiple regression equations for DQ1 and △Q2 on T surface and T ambient are shown below this table.
Ambient temperature
(T ambient)
|
Measurement and treatment
|
Lamp non-radiated (L n-rad)
|
Lamp radiated (L rad)
|
SHED surface temperature (T surface)
|
SHED surface temperature (T surface)
|
15 °C
|
20 °C
|
25 °C
|
30 °C
|
35 °C
|
15 °C
|
20 °C
|
25 °C
|
30 °C
|
35 °C
|
12.2±1.4 °C
|
Q dry
|
-7.4
|
-80.6
|
-118.3
|
-228.9
|
-312.0
|
946.7
|
939.1
|
773.9
|
739.1
|
674.1
|
Q wet
|
-80.6
|
-194.4
|
-368.2
|
-539.7
|
-699.8
|
1046.9
|
1001.9
|
629.6
|
408.3
|
314.7
|
△Q1 = Q wet - Q dry
|
-73.2
|
-113.9
|
-249.9
|
-310.7
|
-387.7
|
100.2
|
62.9
|
-144.2
|
-330.8
|
-359.4
|
△Q2 = DQ1L rad –DQ1L n-rad
|
-
|
|
|
|
|
173.4
|
176.8
|
105.7
|
-20.1
|
28.3
|
17.3±0.9 °C
|
Q dry
|
-
|
-3.3
|
-52.5
|
-112.9
|
-184.3
|
-
|
1081.2
|
1032.5
|
992.2
|
935.9
|
Q wet
|
-
|
-89.4
|
-189.9
|
-301.8
|
-432.8
|
-
|
1167.9
|
1055.8
|
898.1
|
718.5
|
△Q1
|
-
|
-86.1
|
-137.4
|
-189.0
|
-248.5
|
-
|
86.7
|
23.3
|
-94.1
|
-217.5
|
△Q2
|
-
|
|
|
|
|
-
|
172.8
|
160.4
|
94.9
|
31.0
|
21.1±1.7 °C
|
Q dry
|
-
|
-12.8
|
-69.3
|
-90.4
|
-146.5
|
-
|
1072.2
|
1052.5
|
1040.2
|
994.8
|
Q wet
|
-
|
-43.7
|
-125.4
|
-223.2
|
-346.4
|
-
|
1181.5
|
1043.8
|
900.0
|
740.6
|
△Q1
|
-
|
-30.9
|
-56.1
|
-132.8
|
-199.9
|
-
|
109.2
|
-8.7
|
-140.2
|
-254.2
|
△Q2
|
-
|
|
|
|
|
-
|
139.9
|
47.4
|
-7.4
|
-54.3
|
27.1±1.4 °C
|
Q dry
|
-
|
73.8
|
28.0
|
-26.3
|
-82.5
|
-
|
1308.7
|
1247.0
|
1216.3
|
1170.5
|
Q wet
|
-
|
64.5
|
-48.4
|
-165.5
|
-278.8
|
-
|
1440.2
|
1307.2
|
1166.3
|
1013.0
|
△Q1
|
-
|
-9.3
|
-74.6
|
-165.5
|
-278.8
|
-
|
131.6
|
60.2
|
-50.0
|
-157.4
|
△Q2
|
-
|
|
|
|
|
-
|
140.9
|
134.8
|
115.5
|
121.4
|
30.6±1.7 °C
|
Q dry
|
-
|
-
|
58.7
|
11.0
|
-53.2
|
-
|
-
|
1231.3
|
1225.7
|
1211.5
|
Q wet
|
-
|
-
|
19.1
|
-100.2
|
-243.1
|
-
|
-
|
1307.4
|
1194.1
|
1014.4
|
△Q1
|
-
|
-
|
-39.6
|
-111.3
|
-189.9
|
-
|
-
|
76.1
|
-31.6
|
-197.1
|
△Q2
|
-
|
-
|
|
|
|
-
|
-
|
115.7
|
79.7
|
-7.2
|
△Q1 indicates the difference between Q wet and Q dry at each ambient temperature and surface temperature; △Q2 indicates the difference in △Q1 between the lamp is on and off, of each T surface condition; -: No data due to Q dry cannot be distinguished from Q wet in these experimental conditions; Multiple regression equations: △Q1 = – 24.1 x T surface + 10.3 x T ambient + 378.7 (R2=0.905, F=0.000, P<0.001), and △Q2 = – 10.1 x T surface + 0.1 x T ambient + 361.7 (R2=0.611, F=0.000, P<0.001).
Figure 3. insert near here.
In a room with the temperature of 12 °C, a tissue paper-covered and thermally radiated SHED with surface temperatures of 15, 20, 25, 30, and 35 °C gained more heat than the dry surface with additional water and sustained these values until the water dried up (Figure 4). The device gained heat when radiated by a lamp; however, it absorbed additional heat (~100 kcal/m2/h) when water was added to the radiated surface. Another SHED, which was not covered with paper and non-radiated (dashed line in Figure 4), exhibited more heat loss (HL) as the surface temperature increased. Similar measurements were performed in rooms at 17, 21, 27, and 31 °C (Supplement 1. – 4.), and the results are summarized in Table 2.
Table 2 and Figure 4 insert near here.
In summary of Experiment 2, multiple regressions of DQ1, and △Q2 listed in Table 2 are provided. This shows that both the T surface and T ambient are important factors in determining the amount of absolute radiated heat afflux on a wet surface. The inclusion of T surface and T ambient variables explains 74% of the data fluctuation.
A multiple regression equation shows how T surface and T ambient affect the increment of heat inflow when 1000 kcal/m2/h of heat is irradiated onto a wet surface (Table 2). The value △Q1 increased as the surface temperature decreased, and the ambient air temperature increased. The difference between radiated and non-radiated (△Q2) was negatively correlated with T surface, and T ambient. These results suggest that the transfer of radiant heat to the human body is negatively regulated by the skin surface temperature.
Representative data for conducting this experiment on humans are shown in Supplement 5. Two heat flow meters covered with dry tissue paper were attached to human skin, and the output of the heat flow meters was stabilized while irradiating heat with a lamp (value A'). After that, water was sprayed on one of the meters, and approximately 3 min later, the output became stable (value B'). The output of the heat flow meter temporarily decreased immediately after the water was applied; however, it rapidly increased to reach a new equilibrium. No change in output was observed on the 'dry' heat flow meter during this period. An increment in heat flow due to sprayed water (DQ hs) is the residue from B’ minus A’. The average skin temperature (S1) during “dry” heat irradiation (A') and the average skin temperature (S2) during “wet” heat irradiation (B’) were determined to be S because no significant change was observed. The values of S, A', B', DQ, and a regression equation of DQ hs by lamp radiation and sprayed water showed a linear function with skin temperature (S) in Table 3.
Table 3. Absolute differences between heat flow (DQ hs) of lamp-irradiated dry skin (A’) and wet skin (B’) of ten human subjects. Positive values indicate higher lamp-irradiated heat inflow, and negative values indicate loss of heat from their skin surface. Two trials in a warmer room or colder room were performed on the same day. Supplement 5 is helpful how to analyze the individual data.
Subjects
|
Measurement &
treatment
|
Trial 1
|
Trial 2
|
|
Subjects
|
Measurement &
treatment
|
Trial 1
|
Trial 2
|
Sub. A
|
S1: Skin temp. pre-radiation (°C)
|
29.5
|
29.4
|
Sub. E
|
S1
|
28.5
|
27.7
|
S: Skin temperature (°C)
|
38.2
|
40.6
|
S
|
39.0
|
37.1
|
A’ (kcal/m2/h)
|
530.3
|
466.8
|
A’
|
357.3
|
278.0
|
B’ (kcal/m2/h)
|
96.6
|
-55.3
|
B’
|
104.9
|
2.9
|
△Q hs = B’-A’ (kcal/m2/h)
|
-433.7
|
-522.2
|
△Q hs
|
-252.4
|
-275.1
|
Sub. B
|
S1
|
31.5
|
29.2
|
|
Sub. F
|
S1
|
30.0
|
29.1
|
S
|
37.5
|
36.5
|
S
|
39.4
|
37.9
|
A’
|
221.7
|
331.6
|
A’
|
400.1
|
342.9
|
B’
|
-68.2
|
-128.8
|
B’
|
109.9
|
-30.3
|
△Q hs
|
-289.9
|
-460.4
|
△Q hs
|
-290.2
|
-312.6
|
Sub. C
|
S1
|
29.3
|
30.7
|
Sub. G
|
S1
|
28.5
|
27.7
|
S
|
38.5
|
37.5
|
S
|
38.4
|
37.6
|
A’
|
507.4
|
330.1
|
A’
|
350.5
|
220.6
|
B’
|
80.4
|
-33.6
|
B’
|
24.6
|
-72.8
|
△Q hs
|
-427.0
|
-363.7
|
△Q hs
|
-325.9
|
-293.4
|
Sub. D
|
S1
|
30.7
|
29.3
|
Sub. H
|
S1
|
30.0
|
28.6
|
S
|
41.4
|
39.7
|
S
|
39.6
|
37.8
|
A’
|
653.4
|
637.1
|
A’
|
601.6
|
293.0
|
B’
|
287.2
|
215.7
|
B’
|
221.4
|
80.5
|
△Q hs
|
-366.2
|
-421.4
|
△Q hs
|
-380.2
|
-212.5
|
DQ hs = −27.864 S + 710.85 (R² = 0.226)
The visible light transmittances for dry and wet tissue paper were 70% and 85%, respectively. The reflectance of the surfaces of dry and wet tissue papers were 28% and 13%, respectively. That is, surface water on tissue paper affected both the transmission of visible light through the paper and the reflection of visible light off the paper.
The absolute value of k dry at SHED surface temperatures of 30 °C and 35 °C in a room (25 °C, 80% RH, and <0.2 m/s air velocity) was approximately 10 kcal/m2/h/°C, which is similar to that of a thermal mannequin (Mochida, 1982; Kurazumi, et al., 2008). The k wet measured by the same method was approximately thrice the value of k dry. It was expected to be equivalent to the sum of k dry and evaporative cooling rates (Nishi and Gagge, 1970). However, there were some recommendations on the evaporative cooling rate (7.86 kcal/m2/h/°C) of a standing subject in a specific condition (30 °C, 60% RH, airflow 0.2 m/s) (Nag, 1984); 10 kcal/m2/h/°C was obtained by applying the regression equation (Colin and Haudas, 1967), and it was similar to the measured k wet. However, in our calibration using a Leslie cube, the heat exchange of the water-covered 35 °C SHED surface had a mean k wet of 29.8 kcal/m2/h/°C, which was compatible with the previous measurements (28.0–44.5 kcal/m2/h/°C) in a room with an artificial climate (Table 1). Because k dry was close to hc in the absence of wind, it is reasonable that k wet is thrice the value of k dry based on the Lewis relation (Gagge and Nishi, 1977).
k dry is the sum of the convective heat transfer coefficient hc and radiant heat transfer coefficient hr on a dry vertical surface. When a vertical plane receives radiant heat, the temperature of the surface increases, which affects convection and conduction. Thus, a new thermal balance of the entire sensor is established. However, in the SHED, heat recovery or release is performed in a separate circuit, and the surface temperature is constantly buffered so that the output depends only on the prevailing environmental conditions. In the SHED calibration that used a Leslie cube as the radiant heat source, the R and C derived from Q minus R were positively correlated to Q. The value of Q minus R fluctuates greatly when the surface is wet, so convective heat exchange is considered to account for most of the fluctuation. The surface of human skin is rich in blood vessels and acts as a buffer against heat invasion from the external environment. Skin temperature during exercise is even more strongly buffered by increased blood flow and sweating. Therefore, because the SHED output maintains a constant surface temperature, it closely represents the amount of heat exchanged between the human skin surface and the external environment.
The following important points were obtained by analyzing the amount of heat exchange (Q dry or Q wet) in Experiment 1 conducted at 25 °C. [1] Q dry cannot dissipate heat when T surface is ≤40 °C, and Q wet can dissipate heat when T surface is <28 °C. [2] The Q dry and Q wet attained equivalence when T surface was <22 °C, and our theoretical estimation of C’ (sum of evaporation and convection caused by the temperature difference between the SHED surface and ambient air) cannot exceed C which was obtained from Experiment 1 (dashed line in Panel 3B). That is, at ambient temperature of 25 °C, Q dry and Q wet with a surface temperature of 13.5 °C or less always match regardless of the dry / wet state of the surface. It is presumed that one of the causes of [2] is that the value, Q minus R, increases owing to the aggregation of water vapor on the SHED. In the case of this experiment, it was shown that Q wet does not promote cooling but instead promotes heat absorption. Moreover, it works remarkably when T surface is between 20 °C and 30 °C. Geoscientific studies have already shown that moist soil absorbs 10% more sunlight than dry soil (Budyko, 2008), and the results of our experiment support this. We believe that this is evidence of a similar phenomenon that occurs in relation to sweating human skin. During cold days, runners and outdoor workers absorb more solar heat than previously predicted when their skin surface is wet. The authors referred to this phenomenon as the hidden heat inflow (HHI), whereby greater heat flows into wet skin surfaces than dry ones when radiant heat is applied.
The results of Experiment 2 were significant. They showed a significant difference between the wet and dry surfaces of the heat inflow (Figure 4). In this experiment, fluctuations in airflow, room temperature, and humidity were minimized, so the surface temperature was the only factor invoking the heat inflow or HHI. It was confirmed that vaporization cooling was restored when the surface temperature of the SHED was 25 °C or higher, and below that, the HHI was expressed. The experiment also showed that DQ, the difference between Q wet and Q dry, decreased with increasing T ambient (Table 2). The bulb used as the heat source in this study is a high-temperature and point-radiant source; Q is not calibrated by Stefan–Boltzmann’s equation, but the fluctuation of Q can be read.
The results of the three experiments are summarized in Figure 5. This shows that DQ is inversely proportional to the T surface, or skin temperature. It also shows that when the surface temperature of the SHED is below 25 °C, the surface must be lost its water evaporation, or occurring condensation of water vapor in the ambient air. This phenomenon is also expected to occur on the skin running in cold air (Maron, Wagner, and Horvath, 1977). These results explain the cause of the EHS that occurred during the marathon race held on a cold day and suggests that Roberts' case report is by no means a misdiagnosis (Roberts, 2000).
Figure 5 insert near here.
Wind direction is another important factor. The winds in the Northern Hemisphere have different velocities, but their directions are mostly westerly. The running courses in which EHS cases have been reported often include long straight ways heading east-northeast. The Hakone Ekiden in Japan is no exception. The body temperature balance of runners running under such environmental conditions tends to be negative, increasing the risk of EHS. An 18-year epidemiological analysis of a seven-mile (11 km) road race in a summer resort (outside temperature, 23 ± 2.5 °C; 70 ± 19% RH) showed a high rate of EHS (2.13 ± 1.62/1000 runners) (DeMartini et al., 2014). The course is designed to run east-northeast, and we hope that it will be re-analyzed from the perspective of wind direction and radiant heat.
We believe that minimizing the HHI will protect runners from the EHS and help improve marathon running records. Runners should wear light-colored clothing, and caps to block solar radiant heat as personal protection against hyperthermia. However, it should be noted that radiant heat protection with clothing is not an efficient HHI countermeasure for runners, considering their sparse running attire, and regular running caps are prone to heat accumulation because of their poor ventilation. Our goal is to protect runners from solar radiation, HHI, and EHS by recommending the running course designs based on local wind history, and by promoting the best materials for solar protection.
Maintaining high athletic performance during competitive endurance sports is desirable for athletes as well as their coaches and spectators. However, the reduction in air-cooling capacity due to tailwinds is a major environmental EHS risk factor for long-distance runners. In this study, a new direct heat exchange estimator for the body surface was developed and thermally characterized. When this device is exposed to a cold and thermally radiated environment, water placed on its surface accelerates heat flow into the surface. Contrary to the well-known phenomenon of heat dissipation due to sweating on the body surface, a wet and low-temperature surface receives more heat than a dry surface when thermally radiated (Clark, Mullan, and Pugh, 1977; Tanda, 2016). A water-induced lowered thermal conductivity (Chen, Fan and Zhang, 2003) and diminished sweat evaporation by the lowered skin temperature, are causative factors for this phenomenon. Thus, cooled skin surfaces add an unknown heat source for runners in cold air, causing an occasional EHS and decreased endurance. Further studies are necessary to find ways to protect outdoor athletes from radiant heat and to enable them to maintain their level of performance.