3.1. Thermal Sensation Analysis
The percentages of overall thermal sensation votes (TSVs), not the local votes, in response to the twelve scenarios (given in
Table 3) are shown in
Figure 6. In all but scenario S1, the majority of overall TSVs lay between “slightly cool, −1” and “slightly warm, +1”, reaching more than 84% for three scenarios related to the ceiling surface temperatures set to 33 °C. Most of the participants voted between “slightly cool, −1” and “cold, −3” in the scenarios, where the ceiling surface temperature was set to 28 °C (S1, S4, S7, S10). Such voting behavior is most prominent for the scenario with the distance of 1m to the cool artificial window (1st), where more than 80% voted as such and less than 40% voted between “slightly cool, −1” and “slightly warm, +1”. In contrast to the ceiling surface temperatures of 28 and 33 °C, more participants responded “slightly warm” as well as “warm” in all four scenarios (S3, S6, S9, and S12) with the radiant ceiling operating at 38 °C, and it is most apparent for the scenario with warm window (S9 and S12).
In reality, the temperature of the window is strongly associated with the window type and thereby especially its U-value. Comparing the distribution of overall TSVs shown in
Figure 6 between the scenarios with cold window (S1–S6) and warm window (S7–S12) with each other, i.e., S1 with S7, S2, with S8, and so on, the temperature of the window had the highest influence on overall TSVs when the ceiling surface temperature was set to 28 °C. The window temperature’s impact on the votes in the scenarios with the ceiling surface temperature of 33 °C was slightly lower, but it is still noticeable, particularly at the positions near to the window (FP: S1–S3, S7–S9). The impact of the window temperature was minimum when the ceiling surface temperature was set to 38 °C.
Additionally, concerning the distance to the artificial window, the comparison among the scenarios shows that the participants sitting in the front felt cooler than the other group sitting in the rear when having other factors fixed. However, this comparison needs to be done with cautiousness, because the participants who sat near to the artificial façade were different from the participants who sat at the rear positions.
Figure 7 presents the averages of overall and local thermal sensation votes in each scenario (listed in
Table 3). The four plots are separated based on the thermal status of artificial windows (warm and cool) and the positions of participants (front and rear positions). Each plot contains the overall and local thermal sensation votes acquired at different ceiling surface temperatures (28, 33, 38 °C). According to the PMV calculations presented in
Table 3, the overall thermal condition is within a narrow range between “slightly cool” and “neutral”. Therefore, it can be assumed that the observed differences between local thermal sensation can be attributed mainly to differences in the radiant temperature asymmetry and not to those of the overall thermal environmental parameters.
Figure 7 shows that, in general, the overall and local sensation had the highest values in the scenarios when the ceiling surface temperature was set to 38 °C (red lines), especially at the scenario with warm window and rear position. The lowest votes occurred at the ceiling surface temperature of 28 °C (blue lines), especially for the scenario with the distance of 1m to the cool artificial window.
In these four plots shown in
Figure 7a–d, the average overall TSVs for the scenarios with the ceiling surface temperature of 28 °C (blue lines) are in the cold zone [−2.0 and −1.0]. At the ceiling surface temperature of 28 °C, the average values of votes at the upper-body parts (except hand and forearm) lay between “slightly cool, −1” and “neutral, 0”, and the votes at the lower parts (except thigh) are between “cold, −2” and “slightly cool, −1”. At this ceiling temperature, the temperature of the window/façade, corresponding to the type of window/façade, influenced the participants’ votes slightly, and it has the minimum impact at the parts that are cool/cold. At the ceiling temperature of 28 °C as well as other temperatures, the head and forehead have the highest average value of votes compared to the other limbs which are about “neutral”. The coldest parts are the feet and then hands.
At the ceiling temperature of 33 °C, in general, the average of votes at the majority of body parts except for the cold extremities (feet and hands) is about “neutral”. The participants voted local feet and hands between “slightly cool, −1” and “neutral, 0” for the four group-scenarios (
Figure 7a–d). Forehead and head were slightly warmer than the other upper limbs, and the feet and the hands are the coolest limbs. The temperature of the window at the ceiling temperature of 38 °C had a minimum impact on the global and local TSVs for both positions. At this temperature, the temperature of the window slightly influenced the local thermal sensations votes at cool body parts for the participants who sat in the front positions (
Figure 7a,c), and its influence at the participants’ perception who sat the front positions was weak. In general, the global and local thermal sensation votes (except feet and hands) related to the ceiling temperature of 38 °C lay between “neutral, 0” and “slightly warm, +1”. At this ceiling temperature, averages of votes at cold extremities (feet and hands) were between “slightly cool, −1” and “neutral, 0”, and the warmest votes at these limbs occurred for the 12th scenario shown in
Figure 7d.
Comparison among these scenarios indicates that although the radiant ceiling at the temperature 38 °C provides about “neutral” conditions at majority of body parts even at extremities, the ceiling temperature of 33 °C can provide fairly “neutral” conditions at majority of body parts (except extremities) if the temperature of the envelope is relatively high (e.g., 20 °C). Such conditions occur, e.g., when standard building envelopes with relatively low U-values are applied.
Table 4 presents the p-values derived from the non-parametric Friedman ANOVA test. For this test, four scenario groups were created, distinguished by the distance to the window (DW: 1 m (FP) or 3 m (RP)) and the window temperature (WT: 15.5 °C (cool) or 19 °C (warm)). Note that these groups relate to the four sub-figures of
Figure 7, e.g., scenario group-1 relates to
Figure 7a. In this test, the ceiling temperature is the independent variable and the null hypothesis states that there is no significant difference in thermal sensation votes for the three ceiling temperatures (28, 33 and 38 °C) at each scenario group. As seen in
Table 4, there is a significant difference between the ceiling temperatures for overall thermal sensation at three of four group-scenarios.
Table 5 presents the results of the Wilcoxon signed rank test to determine the statistical significance of the difference between each pair of ceiling temperatures. The results indicate that there is a significant difference between the ceiling temperatures of 28 °C and 38 °C for all 4 group-scenarios. It means that the overall thermal sensation votes are significantly different at the ceiling temperatures of 28 °C and 38 °C, while overall calculated PMV values (see
Table 3) are very close to each other.
At the same time, in the 2nd and 3rd scenario groups, there is no significant difference in thermal sensation votes between the ceiling temperatures of 28 °C and 33 °C. Moreover, the influence of rising the ceiling temperature from 33 °C to 38 °C on the overall thermal sensation votes is insignificant for all scenario groups except the 2nd.
Additionally, the results of the Friedman test presented in
Table 4 indicate that, in general, the difference in thermal sensation votes between the ceiling temperatures is insignificant for the majority of body parts in four group-scenarios, particularly the first 3 group-scenarios.
The analysis of data for local thermal sensation votes indicates that although, according to the Freidman test, there is no significant difference between some scenarios, the averages of local thermal sensation votes shown in
Figure 7 varied from one scenario to another. There are some possible reasons to explain these findings: (i) the body limbs, particularly clothed limbs and non-extremities, were not sensitive to the changes of radiative room surfaces and slight changes of room air temperature [
28]. These findings are in contrast with other results related to local thermal sensation and comfort done by Zhang et al. in which the averages of local thermal sensation votes strongly depend on the experimental conditions [
23,
24]. They observed the significant reaction of the local body limbs to the changes of surrounding air conditions, and the local thermal sensation votes were selected as significant parameters to predict the overall thermal sensation. This contrast between the two studies may be explained by the fact that heat exchange between the local body surface and the surrounding thermal environment was only through the convection in their study, while in our experiments both radiation and convection occurred. The second reason (ii) for the insignificant difference between the scenarios might be the type of scale used for the evaluation of local thermal sensation. The thermal sensation scale is symmetrical (from “cold, −3” over “neutral, 0” to “hot, +3”) and the tendency of majority of participants to select the central three categories (“slightly cool, −1” to “slightly warm, +1”) is high [
29,
30,
31]. Consequently, the median values of votes related to different experimental conditions are close to each other and within the central three categories (see
Figure A1 in
Appendix A). The closeness of the median values in different scenarios may result in insignificant differences between the median distribution and the hypothetical median. Different types of thermal sensation scales such as visual analogue scales may lead to more pronounced differences between the scenarios, but cannot be compared directly to existing data as discussed earlier [
31]. The possible third reason (iii) is that the participants may vote at some body parts based on a reference (extreme) cold or warm body parts. For example, the participants may vote the chest differently if the extremities are cold or hot, even the surrounding thermal conditions around the chest are the same. It may influence the accuracy of local votes.
3.2. Thermal Comfort Analysis
Figure 8 presents the percentage of overall thermal comfort votes (TCVs) observed in the twelve different scenarios listed in
Table 3. The four scenarios related to the ceiling temperature of 28 °C (S1, S4, S7, S10) had the least percentage of “comfortable” and “just comfortable” votes, particularly the scenario with the cool window and a front position (S1). At this ceiling temperature, the percentage of “comfortable” and “just comfortable” votes was highest if the position of participants was 3 m away from the artificial window and a warm temperature (19 °C) of the artificial window (S10). At the ceiling temperature of 33 °C, the percentages of “comfortable” were more than the same votes at the ceiling temperature of 38 °C, except for the scenario with warm window and rear position (S11).
At least 50% of participants voted “comfortable” for the four scenarios related to the ceiling temperature of 33 °C. At this temperature, the position of participants and the temperature of the window slightly influenced the “comfortable” votes but their effects were notable for “just comfortable” and “just uncomfortable” votes. In contrast, at the ceiling temperature of 38 °C, the “comfortable”, “just comfortable” and “just uncomfortable” votes were influenced noticeably by the position of participants and the temperature of the window (differences between S3 and S6, and between S9 and S12). Participants felt more comfortable if they sat in a rear position and in a room with a warm window (S12). The results presented in
Figure 8 and
Figure 9 clearly indicate that radiant heating ceiling systems operating with the temperatures of 33 °C and 38 °C have about equal influence on the overall thermal comfort of occupants having least “just comfortable” conditions. The comfort conditions can slightly be improved if the temperature (thermal performance) of the window/façade is increased.
Figure 9 presents the average of overall and local thermal comfort votes (TCVs) at 10 body parts associated with each scenario. Similar to
Figure 7, this figure shows four groups of scenarios related to the temperature of the artificial window and the position of participants.
Each scenario group consists of the corresponding scenarios distinguished by three ceiling temperatures. As seen from the four plots, the body parts excluding the hand, calf, and feet were voted close to “just comfortable, +2” at the ceiling temperature of 28 °C. At this ceiling temperature, the extremities and the calf were on average voted between “just uncomfortable, +1” and “just comfortable, +2”. Similar to the overall thermal comfort votes, the averages of local thermal votes in response to the ceiling temperatures 33 and 38 °C are about similar. At the ceiling temperatures of 33 and 38 °C, it is quite unexpected to see that thermal comfort votes of the lower limbs (except foot and hand) have a similar average like the upper limbs, particularly if the artificial window temperature was 19 °C. The ceiling temperature of 38 °C provided conditions perceived as slightly more comfortable at all body limbs compared to a ceiling temperature of 33 °C and lead to a “comfortable, +3” vote at all body parts only if the 4th group-scenario took place. The results imply that improving thermal performance of the window has a positive influence in providing thermal comfort conditions for occupants.
Friedman test results indicate that there is a significant difference between the three ceiling temperature for scenario group 1 (
p = 0.05) and 4 (
p = 0.008). The changes in ceiling temperature have a significant influence on few limbs including the back in the 1st scenario group (related to
Figure 9a), foot in the 2nd scenario group, and hand, thigh, calf, and foot in 4th scenario group (
p < 0.04). The Wilcoxon signed rank test was performed for the aforementioned scenario groups to determine whether there is a significant difference in thermal comfort votes between each pair of ceiling temperatures. The test indicates that there is a significant difference between the ceiling temperatures of 28 °C and 38 °C for all cases. There is a significant difference between 28 °C and 33 °C for the two overall thermal comfort votes (
p < 0.04); however, the test suggested no significant differences between the 28 °C and 33 °C as well as 33 °C and 38 °C for the aforementioned limbs.