Evaluation of the convective heat transfer coefficient of human body and its effect on the human thermoregulation predictions Building

Human thermoregulation models, particularly the Fiala model, are well accepted for the prediction of thermo- regulatory responses and the assessment of clothing and building systems with regard to human thermal comfort. However, the convective heat transfer coefficients ( h c ), used for the heat transfer calculations, were obtained from measurements with a thermal manikin with poor body resolution from decades ago, and they were not distinguished between body postures. In this study, the overall and local h c of the human body in both standing and seated postures were evaluated by CFD simulations and implemented in the Fiala model to investigate the resultant influence on the predicted thermoregulatory responses by comparing the predictions with measure- ments of 14 human exposures. It was found that the original h c used in the Fiala model was similar to the simulated h c of the standing body, but higher than that of the seated body at most body parts. In 64% of the investigated human exposures, the root-mean-square-deviation of the skin temperature predicted by the Fiala model with the simulated h c was lower than that achieved with the original h c , indicating an improvement of the accuracy of the Fiala model. Additionally, the higher h c of the standing body resulted in a lower mean skin temperature by up to 1.5 ◦ C when compared to the seated body in the environment of 10 ◦ C and 2.5 m/s. This emphasises the necessity of ensuring the accuracy of the h c in the thermoregulation model in order to improve its validity for specific investigated conditions.


Introduction
The human thermoregulation model, in combination with the thermal sensation model, is an efficient tool for predicting human thermal responses, especially in hazardous environments where human tests are not feasible [1,2]. The conjunction of both models also enables parametric studies that can efficiently serve to optimise the human environment with regard to comfort and contribute to understanding the human-environment interaction. On the technical side, the human physiological parameters of skin temperature and core temperature, which are outputs of human thermoregulation models, are inputs of thermal sensation models. The well accepted thermoregulation model of Fiala (Fiala model) [3][4][5] has an accuracy of ±1 • C and ±0.3 • C for the mean skin temperature and core temperature, respectively, in the environment ranging between − 17 • C and 50 • C. According to the study by Koelblen et al. [6], a deviation of 1 • C in the mean skin temperature and/or 0.2 • C in the core temperature would cause a variation of 3 units and 1.1 units in the predicted vote for thermal sensation by the Thermal Sensation (TS) model by Zhang [7,8] and the Dynamic Thermal Sensation (DTS) model by Fiala [9], respectively, which is higher than the generally accepted error of 1 unit or below [6]. This indicates the great necessity of improving the accuracy of the physiological parameters predicted by human thermoregulation models. The accuracy of any mathematical model, besides the accuracy of the model itself, is closely related to the accuracy of its input parameters. In the case of convective heat exchange between the human body and its surroundings, the convective heat transfer coefficient (h c ) of the human body is a critical factor for the accuracy of the human thermoregulation model.
The convective heat transfer coefficients are sensitive towards the environmental conditions (air speed, direction, temperature and turbulence intensity of airflow) and human body (geometry and posture) [10][11][12][13][14][15]. As a consequence, studies performed in different labs with various thermal manikins under similar environmental conditions have reported dispersed values of h c , such as 3.1-5.1 W/(m 2 K) at an air speed of below 0.5 m/s [16,17] and 12.1-27.4 W/(m 2 K) at an air speed of 2.5 m/s [13,16,[18][19][20][21]. The equation of h c in relation with the air speed and temperature gradient between the human skin and environmental air utilised by the state-of-the-art human thermoregulation models for calculating thermal convection, such as the Fiala model [3][4][5] and University of California, Berkeley (UCB) model [22], came from measurements with full-scale thermal manikins under both natural and forced convection conditions from decades ago [16,23]. Detailed information on the manikin, the local airflow condition and the sensors used for measurements is unfortunately missing in these studies. This makes it difficult to check the accuracy of the h c applied to the investigated conditions. Some recent studies [14,15,24] proposed the equation of global and local h c with detailed background information provided, but no one has considered the parameters of air speed and temperature gradient at the same time.
Besides, the standing and seated postures of the human body were not distinguished by the thermoregulation models in terms of the convective heat transfer. According to a numerical study using CFD technology, the phenomenon of the thermal plume around the human body is substantially different between standing and seated postures at the air speed of 0.2 m/s [10]. Due to the change in the orientation of the lower body, a thicker thermal layer was observed in the vicinity of the upper leg and pelvis for the seated body compared to the standing body. As a result, the h c at the upper leg and pelvis of the seated body was 22.7%-38.3% lower than that of the standing body. Quintela et al. [25], Ihihara et al. [21] and Gao et al. [15,26] also reported a difference in the value of the overall h c by around 10% when the manikin was in a seated posture compared to a standing posture under the natural flow condition. Under forced convection, comparative studies between body postures are scarce. A measurement study by de Dear et al. [16] has shown a slightly higher overall h c of the human body in a seated posture than in a standing posture (0.3 W/(m 2 K), 2% higher at the air speed of 2.5 m/s). This was attributed to the greater distance between the limbs and torso in a seated posture as a speculation from the authors, without giving any evidence. On the contrary, according to the numerical simulations conducted by Gao et al. [15], the overall h c of the standing human body was higher than that of the seated body by 0.8 W/(m 2 K) (6%) at the air speed of 1.5 m/s. The contradiction between studies published so far has made the influence of the body posture on the h c at local body segments as well as its potential of affecting the outputs of the human thermoregulation model remain unclear. Therefore, a database of h c with all the related information clearly stated, including the environmental configuration, local airflow condition, human body geometry and posture, temperature gradient, is needed to increase the reliability of the human thermoregulation models using the h c as one of the input parameters.
In this study, a database of h c of standing and seated human bodies was developed using CFD technology, with a detailed description of the environment condition and human body. Regression equations of h c in relation to the air speed and the temperature gradient between body surface and environment air were generated and incorporated into the Fiala model, replacing its original equation of h c and resulting in two new model variations named 'Fiala model_Xu h c _standing' and 'Fiala model_Xu h c _seated'. Validation of the adjusted Fiala models was conducted by comparing their predictions with experimental measurements and predictions from the original Fiala model. Finally, the influence of the input parameter of h c on the predicted human thermal responses by the human thermoregulation model including the skin temperature and core temperature was investigated.

Virtual models of human body and environment
A rectangular-shaped chamber ( Fig. 1 (a)) representing a generic indoor space (4 m × 6 m × 2.37 m) was designed, with the air inlet and outlet surfaces facing each other. A virtual body was placed in the middle of the domain, and it was located 8.5 cm above the ground and 3.7 m from the inlet surface. The body geometry ( Fig. 1 (b)) was obtained from a scanned (Handyscan 700, resolution: 0.05 mm, precision: 0.03 mm) and post-processed (Geomagic Qualify, Geomagic Inc., North California, USA) thermal manikin (Newton, Thermetrics, Seattle, WA, USA) in standing and seated postures.
The virtual room domain was discretised into two regions ( Fig. 1  (a)), and correspondingly meshed using COMSOL Multiphysics 5.4a (COMSOL, Inc., USA). A tetrahedral domain mesh, triangular surface mesh, and five-layer boundary layer mesh were generated for both regions. The mesh in region 1 surrounding the virtual human body, where the temperature and airflow change dramatically, was denser than in region 2. The settings of the mesh size were consistent with that in our previous study [27], where the same room and human body models and physics were presented and checked to be mesh-independent. Around 2, 600,000 mesh elements in total were finally built (Fig. 2).

Boundary conditions and simulation method
The convective heat transfer regime occurring between the surface of the human body and its surrounding air was simulated using COMSOL Multiphysics 5.4a. The boundary conditions for the simulations are listed in Table 1. Three groups (covering the wide range of airflow condition from pure natural convection (v a ≤ 0.2 m/s) to mixed convection (0.2<v a ≤ 1.5 m/s) and forced convection (v a > 1.5 m/s)) of 34 simulations (the standing human body and seated human body are each incorporated in 17 of them, respectively) are included. Six of them marked with an asterisk were conducted in a previous study [27]. The air is treated as a weakly compressible fluid and the boundary conditions for the inlet and outlet of the air are velocity and pressure, respectively. The wall condition for airflow is considered as non-slip. The surrounding walls of the virtual room are adiabatic. The surface of the virtual human body is set at a constant temperature of 34 • C, mimicking the skin temperature of the human body in a thermo-neutral condition. The turbulent intensity of the airflow at the inlet surface is assumed as 0.05, which is within the range reported in previous relevant studies [16,19].
The low Re k-ε model, which solves the velocity profile completely to the wall [29], is used for simulating the turbulent flow. The turbulence kinetic energy k and turbulent dissipation rate ε were calculated by Eqs.
(1) and (2). The convective heat transfer is simulated in COMSOL by coupling the turbulent flow and heat transfer in fluids based on the temperature gradient. The finite element method was used to discrete the governing equations, i.e. the N-S, continuity and energy conservation equations. The segregated solver and SIMPLE algorithm were used for solving the equations. The value of h c is calculated by Eq. (3).
where k is the turbulence kinetic energy; U ref is the mean stream velocity in m/s; TI is the turbulence intensity, assumed to be 0.05 which is within the range reported in previous relevant studies [16,19]; ε is the turbulent dissipation rate; C μ is the k-ε turbulence model constant equal to 0.0845; L is the characteristic length of the inlet in m; q c is the convective heat flux at the manikin surface in W/m 2 ; T sk is the temperature at the manikin surface in • C; T a is the temperature of the air in • C. The distribution of the dimensionless wall distance (y + ) over the virtual human body is given in the appendix. The y + is supposed to be set below 1 in order to accurately simulate the airflow at the body surface when the low re k-ε model is utilised [28]. In the current study, the y + value at most body segments (head, torso, legs, hand and feet) is below 1. For the rest body segment of arms, the maximum y + value is 3.13.

Validation of the simulation method
As reported in our previous study [27], the simulation method has been fully validated against measurements in a climatic chamber. The geometric models, numerical method and model settings in the validation study [27] are identical with these in the current study. The validated parameters reported include the air speed (v a ) and air temperature (T a ) in the vicinity of the human body, as well as the total heat transfer

Table 1
Numerical simulations of the convective heat transfer between human body and its surroundings.
v a -air speed; △T -temperature gradient between the surface of the human body and its surrounding air; × -simulation is performed. * -the simulation was done previously by the authors [27]. coefficient (h t ), comprising h c and the radiative heat transfer coefficient, at the individual body segments. The standard deviation (SD) for the experimental measurements and the root-mean-square-deviation (RMSD) between the simulations and measurements of these validated parameters were compared for validating the simulation method. The RMSD values for v a and T a in the vicinity of the human body were smaller than SD of experimental data indicating a good accuracy of the simulation for heat transfer. Further information can be found in reference [27].

Generation of the equation of h c
Regression analysis on the simulated h c in relation to the v a and the temperature gradient (△T) between the human body surface and its surrounding air is conducted using Origin11 (OriginLab, Inc., USA) using the same formula as in the original Fiala model (Eq. (4)). The analysis is performed for both standing and seated postures globally and locally for 11 segments (head, chest, back, thorax, pelvis, upper arm, lower arm, hand, upper leg, lower leg, and foot). The goodness of fit is judged by the adjusted R 2 .
where h c is the convective heat transfer coefficient at the surface of the human body in W/(m 2 K); a nat , a frc , a mix are coefficients for the natural convection, forced convection and mixed convection, respectively; T sk is the temperature at the manikin surface in • C; T a is the temperature of air in • C; v a is the air speed in m/s.

Integration of the equation of h c into human thermoregulation model
The Besides, it is found that the coefficients in the original Fiala model are identical for some of the body parts (including the upper arm, lower arm, hand, upper leg and lower leg; Table 5), which means that the convective heat transfer mechanism is treated the same at these different body segments by the Fiala model_original h c . The heat transfer along the hands and arms, however, is affected by a buoyancy effect along the body height in the natural flow condition. The natural convection developing at the upper arm is more obvious than at the lower arm, resulting in a higher value of h c at the upper arm [10]. For forced convection, according to our previous study [27] (in press), the h c at the hands and lower arm is approximately 18% greater than that at the upper arm. We thus expect a better resolution at the arms, hands and legs in terms of the calculation of thermal convection through the newly generated database of h c in the current study.

Human exposures for validating the revised human thermoregulation models
The human exposures selected for the validation included motionless subjects without clothing or with some body parts uncovered, as the database of h c was developed for the nude body. In total, 14 exposures,  including steady-state (10 studies, Table 2) and step-change (4 studies, Table 3) ones, were selected from the literature [30][31][32][33][34][35]. All the experiments were performed in climatic chambers with a controlled thermal environment. No spatial non-uniformity of the environmental conditions has been reported. T a and v a varied from 10 • C to 38.9 • C and 0.1 m/s to 0.8 m/s, respectively. The radiant temperature (T rad ) was approximately equal to T a , with exposure S9 as an exception. The subjects were all asked to be in a sedentary position during the exposures, with only slight body movements allowed. The global f cl , which is used for calculating the thermal resistance of the boundary air layer at the surface of clothing, in exposures S5-S10 and T2-T4 was not given in the original study and is assumed based on the value of I cl according to ISO 9920. The unreported relative humidity in exposure S5 is assumed as 50%, which is a plausible value for a thermally neutral condition. Among the 14 exposures, only 6 (S1, S5, S6, S7, S10 and T1) were reported with recordings of temperatures at local nude segments. Mean skin temperature (T sk,m ) recordings were reported for all 14 exposures, calculated by different methods: a 7-point method (exposures S1-S5 and T1), 8-point method (exposures S7 and T2-T4) and 14-point method (exposure S6). A transient recording of the skin temperature was given for all the exposures, except for exposure S6, from which only an average value over the 90-min exposure was available. The core temperature was not measured in exposure S7, while it was measured as the rectal temperature (T re ) in all the other exposures.

Human exposures for parametric study of body posture
To investigate the influence of body posture on the output of human thermoregulation model, two exposures (HS1 and HT1, Table 4) were designed based on exposures S1 and T1. Two body postures and air speeds of 0.5 m/s and 2.5 m/s were used in each exposure. The clothing condition and human anthropometrics are identical to those of the exposures S1 and T1.

Sensitivity check
The effect of the calculation of convective heat transfer on the prediction of the human thermal response by the thermoregulation model was examined by a clearly defined procedure (Fig. 3). The Fiala model (computing platform of FPCm 5.4) with three different datasets of h c (Fiala model_original h c , Fiala model_Xu h c _standing, and Fiala mod-el_Xu h c _seated) was used for simulating the responses of human when exposed to conditions as described in Tables 2-4.
The RMSDs and bias of the skin temperature and core temperature by the Fiala model with different h c were calculated. Comparison of the RMSDs and bias with the SDs for human data was conducted. Besides, the Two-Related-Samples Non-parametric Test (Wilcoxon test) was employed using IBM SPSS Statistics V21.0 for checking the significance of the difference (significance level is 0.05) between the RMSDs for Fiala model_orignial h c , the RMSDs for Fiala model_Xu h c , and SDs for measurements. A significant difference would suggest a statistical discrepancy between the predictions or prediction and measurement. The performance of the newly generated database of h c in combination with the Fiala model in predicting thermal physiological responses was assessed this way.
where RMSD is the root-mean-square-deviation in • C; T mea is the body temperature from measurements in • C; T pre is the body temperature predicted by the human thermoregulation model in • C; n is the number of data points; bias is the discrepancy of the predicted result from the measured result in • C, where a positive (negative) value of bias means the model overestimates (underestimates) the body temperature.

Table 3
Step   Fig. 4 presents the simulated convective heat flux at the surface of the standing and seated human bodies (Fig. 4 (a)), as well as the simulated air temperature and airflow around the arms (Fig. 4 (b)) and other body segments (Fig. 4 (c)) at the air speed of 2.5 m/s. Table 5 gives the calculated coefficients of Eq. (4) by doing nonlinear surface fitting with the simulated h c , as well as the original coefficients used in the Fiala model. The adjusted R 2 values are all greater than 0.95, showing a good fit. As opposed to the original coefficients of the Fiala model, the new coefficients for the upper arm, lower arm and hand segments are distinct from each other. Besides, the coefficients at the upper leg and lower leg, as well as at the chest and back, are differentiated as well.  Table 6 lists the calculated statistics for all the 14 human exposures (Tables 2 and 3), including the mean RMSDs and SDs of the mean skin temperature, local skin temperature and core temperature. The values of the SD were obtained from the original references of the human data. The statistics for local skin temperatures were only calculated for the measured nude body segments (as indicated in Tables 2 and 3). As only one data point from the measurements was given for exposures S6, S8, S9 and S10, the RMSDs for the skin and core temperatures are unavailable. The results of the Non-parametric test for the RMSDs and SDs revealed that there is a significant (p < 0.05) difference between the RMSDs for the mean skin temperature of Fiala model_original h c and the SDs for the mean skin temperature of the measurements. Fig. 7 shows the predicted and measured skin and core temperatures of exposures S1 and T1, as well as the SD for the measurements and RMSD for the predictions. Fig. 8 shows the predicted and measured mean skin temperatures of exposures S3, S5 and S7, as well as the SD for the measurements and RMSD for the predictions. Fig. 9 shows the predicted mean skin temperature, local skin temperature, and core temperature of the human body for exposures HS1 and HT1 by the Fiala models. The local skin temperature is shown for the head and lower arm to represent body segments with minimum and maximum differences in h c between postures (Fig. 5), respectively.

Overall convective heat transfer coefficient
At the lowest investigated air speed of 0.1 m/s, the overall h c of a standing person is 0.2 W/(m 2 K) (5%) higher than that of a seated person. This difference increases with the increment in air speed. At the highest investigated air speed of 2.5 m/s, the overall h c of a standing person is 3.7 W/(m 2 K) (20%) higher than that of a seated person, denoting that heat is more easily lost from a standing body than a seated body.

Local convective heat transfer coefficient
In order to understand the origin of the difference in the overall h c between postures, a further analysis on local body segments was performed. For a seated human body, the lower arm, hand, upper leg, and pelvis are the most spatially changing segments compared with a standing posture. The lower arm, hand and upper leg are positioned vertically in a standing posture, while horizontally in a seated posture. Such variation in the position of the body segments is expected to result in change of the thermal plume mechanism under the natural flow condition, and change of their orientation towards the inflow air under the forced convection. According to Fig. 5, this variation of orientation has resulted in the greatest difference in h c between postures found at the lower arm, upper leg and pelvis, with the h c of a standing posture being 2.5 W/(m 2 K) (46%), 1.6 W/(m 2 K) (36%), and 0.9 W/(m 2 K) (21%) higher than that of a seated posture, respectively, at the air speed of 0.2 m/s. At the air speed of 2.5 m/s, the difference in h c between postures at the lower arm, upper leg and pelvis increased to 12.2 W/(m 2 K) (69%), 7.2 W/(m 2 K) (49%) and 6.8 W/(m 2 K) (46%), respectively. From Fig. 4 (a), there is more convective heat loss at the anterior sector of the lower arm for the standing body when compared to the seated body, which would explain the great difference in the h c at the lower arm between postures. According to Fig. 4 (b), in the vicinity of the anterior sector of the lower arm of the standing body, the airflow occurring towards the human body brings away the warm air over the anterior surface towards behind the lower arm, resulting in a very thin thermal layer over the anterior surface and a thick thermal layer over the posterior surface. Differently, for the seated body, the air flows along the anterior surface of the lower arm and, due to being blocked by the upper arm, the warm air accumulates over the anterior surface, resulting in a low convective heat loss there. A similar phenomenon is found at the upper leg, the anterior sector of which shows a greater heat loss in the standing posture than the seated posture due to the change of the orientation between the body surface and airflow direction.

Table 4
Exposures for parametric study of body posture. Exposure no.
Initial condition Exposure period According to Fig. 4 (c), as for the pelvis segment, which forms an angle of 90 • with the upper leg in the seated posture, the trajectory of the surrounding thermal flow is distinct from that of the standing posture. Natural flow develops at the edge of the pelvis part and leads to the warm air rising up along the surface of the back. The moving air from the inlet of the chamber goes through the gap between the legs and reaches the area underneath and behind the pelvis. It accelerates the upward flow of the warm air at the posterior of the pelvis, resulting in a much thicker thermal layer around the pelvis and the back of the seated body than the standing body. Therefore, the h c at the pelvis and back is lower in a seated posture.

Comparison with other studies
The lack of detailed information on the body postures and the airflow conditions in the literature has made the comparison with previous experimental results difficult and inconclusive. According to Fig. 6, Ichihara et al. [21] have obtained similar results to ours, demonstrating the convective heat being lost more intensively from the surface of a standing body than a seated body, with the overall h c of a seated body being 21% lower than that of a standing body at the air speed of 1.0 m/s. On the contrary, de Dear et al. [16] have reported a close value of overall h c between the standing (17.4 W/(m 2 K)) and seated (17.7 W/(m 2 K)) postures at the air speed of 2.5 m/s, and Mochida et al. [38] have got a 10.5% higher value for a seated body than a standing body.
By comparing the values of h c obtained in the current study with the original values used in the Fiala model (Fig. 5), it is found that the original h c , which is not differentiated between postures, is closer to the simulated h c of the standing body than the seated body, except at a small proportion of the body surface (head, hands and feet). This might suggest that the predicted skin or core temperature by Fiala model_original h c would be closer to that by Fiala model_Xu h c standing than to that by Fiala model_Xu h c seated.

Mean skin temperature and core temperature
The mean skin temperature predicted by Fiala model_Xu h c for all the exposures is higher than that by Fiala model_original h c , with the greatest difference of 0.8 • C for steady-state exposure (S1) and 1.0 • C for step-change exposure (T1). This is related to the lower h c of the seated body at most of the area of the human body surface (thorax, pelvis, arm and upper leg) used in Fiala model_Xu h c _seated than in Fiala mod-el_original h c , as shown in Fig. 5. This indicates the sensitivity of the human thermoregulation model towards the estimation of the convective heat exchange between the human body and its surroundings.
For the core temperature, the difference between Fiala model_Xu h c and Fiala model_original h c varies slightly within − 0.2 • C and 0.1 • C, which is no greater than the typical standard deviation (0.2 • C) in human subject studies [39]. This signifies that the prediction of the core temperature by the Fiala model is not sensitive towards the estimation of thermal convection. This is reasonable since the core temperature of the human body is more dependent on the personal metabolic heat than on the convective heat loss at the skin surface [40].
By comparing the bias and RMSDs, the Fiala model_Xu h c has shown a closer prediction in the mean skin temperature than Fiala model_original h c to the measurement for 9 (S1, S2, S4, S8, S9 and T1-T4) out of 14 (64%) cases. This indicates the good performance of the Fiala mod-el_Xu h c in predicting the human thermal response of the mean skin temperature. According to Fig. 7, the Fiala model_Xu h c shows a slower rate of change in the mean skin temperature with time than Fiala a nat , a frc , a mix are coefficients for the natural convection, forced convection and mixed convection, respectively, in Eq (4).  Among the exposures (S3, S5, S6, S7 and S10) where the Fiala model_original h c showed more accurate predictions in the mean skin temperature than the Fiala model_Xu h c , only the mean value for T sk_m and T cr was reported from the measurements of exposures S6 and S10, which made the analysis difficult. For the remaining exposures (S3, S5 and S7), the difference of the mean skin temperature between predictions and measurements mainly came from the initial 10-20 min duration of the exposures, in which the predictions are much higher than the measurements, especially for Fiala model_Xu h c _seated, with a lower h c than Fiala model_original h c (Fig. 8). This might be due to the unclearly reported initial states of the subjects before the formal tests [41], i.e. the dressed condition and psychological state. In the final 10-20 min duration of the exposures, Fiala model_Xu h c actually gave values of the mean skin temperature that were closer to the   6. Global convective heat transfer coefficient at the surface of (a) standing and (b) seated human bodies from different studies [16,[18][19][20][21]38]. measurements than Fiala model_original h c for exposures S3 and S5. For exposure S7, in spite of the slightly greater value of RMSD for Fiala model_Xu h c than Fiala model_original h c , the value of RMSD for Fiala model_Xu h c (0.14 • C) is smaller than the value of SD (0.45 • C), denoting an accurate prediction by Fiala model_Xu h c .
Furthermore, according to the Non-parametric test, no statistically significant difference is found between the RMSDs of the mean skin temperature of the Fiala model_Xu_h c and that of the Fiala model_Or-iginal_h c . However, the RMSDs of the mean skin temperature of the Fiala model_Original_h c are significantly (p < 0.05) different from the SDs of the mean skin temperature of the measurements. Besides, the average RMSD of the Fiala model_Original_h c is higher than that of the Fiala model_Xu_h c and the average SD of the measurements. All these evidence together speak in favor of the Fiala model_Xu_h c for the prediction of skin temperature.

Local skin temperature
Locally, the greatest difference in the predicted skin temperature between Fiala model Xu_h c and Fiala model Original h c is found to be 2.0 • C and 1.5 • C at the upper leg for steady-state (S1) and step-change (T1) exposures, respectively, with the Fiala model_Xu h c predicting higher values of skin temperature. This is in line with the greatest difference in h c found at the upper leg between Fiala model_original h c and Fiala model_Xu h c _seated under the investigated air speeds (Fig. 5). A previous validation study of the Fiala model by Martinez et al. [41] reported a great underestimation of the skin temperature at the upper leg by a mean value of 0.87 • C. The Fiala model_Xu h c used in the current study with a lower value of h c at the upper leg is supposed to improve the results.
By comparing the bias and RMSDs, the prediction of the local skin temperature at 11 out of 21 (52%) checked body segments has been improved by Fiala model_Xu h c , compared with Fiala model_original h c . Among the remaining 10 body segments, where the Fiala model_Xu_h c gave worse predictions compared with Fiala model_original h c , 2 of them showed a lower value of RMSD for Fiala model_Xu h c than that of SD for the measurements, which, together with the above mentioned 11 segments, validates the good performance of Fiala model_Xu h c in predicting the local skin temperature.

Steady-state condition
The higher h c , meaning greater convective heat exchange between the human body and the environment at most body segments (head, thorax, pelvis, upper arm, lower arm, hand and upper leg) of a standing person than a seated person, resulted in a lower final mean skin temperature of the standing person than the seated person. The discrepancy of the final mean skin temperature between postures is 1.2 • C and 1.5 • C at the air speeds of 0.5 m/s and 2.5 m/s, respectively, corresponding to a difference in overall h c between postures of 1.5 W/(m 2 K) (17%) and 3.7 W/(m 2 K) (20%), respectively. Also, according to the slope of the curves in Fig. 9, the change rate of the mean skin temperature with time of a seated body is smaller than that of a standing body in the initial 20 min of the exposure HS1. At the head, where there is only a difference of 0.7 W/(m 2 K) (4%) in h c between postures, the difference in skin temperature is no greater than 1 • C between postures. At the lower arm, where the h c of a standing person is greater than that of a seated person by 4.9 W/(m 2 K) (61%) and 12.2 W/(m 2 K) (69%) at the air speeds of 0.5 m/s and 2.5 m/s, respectively, the skin temperature of a standing person is lower by 2.7 • C and 2.9 • C, respectively. The difference in core temperature between the models is within the range of 0.1 • C, which is lower than the typical standard deviation from human subject studies (0.2-0.3 • C).

Table 6
Statistics calculated for the human exposures.
Exposure No. n -the number of data points used for calculating the statistics in Table 6

Step-change exposure
For the exposure of HT1 ( Fig. 9 (b)), where the air condition was periodically constant, the findings are similar to those of the steady-state exposure of HS1, with an exception in the period of 110-140 min, where the human body was first exposed to a hot environment of 38.9 • C (110-130 min) and then suddenly shifted to an environment of 29.4 • C (130-140 min). In the environment of 38.9 • C, the air temperature was higher than the skin temperature and the human body has changed from losing heat to gaining heat according to the rising core temperature from 120 min. In this period, human thermal regulation showed a sweating and evaporation response, which became the predominant pathway of heat dissipation. Hence, the difference in skin temperature caused by h c or thermal convection became minor such that the difference in the mean and local skin temperatures between models was within 0.1 • C.
Besides, it was found that the influence of body posture on the skin temperature gets stronger with higher air speeds. For instance, the greatest discrepancy of the mean skin temperature of exposure HT1 was 0.9 • C at the air speed of 0.5 m/s, and 1.1 • C at the air speed of 2.5 m/s.

Sensitivity of human thermoregulation model towards h c from different studies
According to the varying predicted skin temperatures by Fiala model with different databases of h c , it can be inferred that the greatly varying h c reported by different labs (Fig. 6) will very likely result in distinct skin temperatures of the human body when used in combination with human thermoregulation models. For instance, the discrepancy of the value of h c measured by Nishi  into the Fiala model for calculating human thermal responses separately for exposure HS1, a great difference of more than 1.5 • C in the resultant mean skin temperature between them will be seen. Moreover, such variation of the mean skin temperature would finally cause a variation of over 1 unit in the prediction of subjective thermal sensation. This emphasises the necessity of ensuring the applicability of the h c that is coupled into the thermoregulation model, to the investigated conditions, in order to improve the accuracy of human thermoregulation models and thermal sensation models.

Conclusions
A database of the overall and local h c of standing and seated human bodies was developed in the current study using validated CFD modelling. It was incorporated into the Fiala model for predicting human thermal physiological responses. It was found that: The Fiala model_Xu h c proposed in this study was only validated for the air speeds below 0.8 m/s and the airflow was limited to a frontal direction. This has led to limited applicable scenarios of the results, for example, the wind tunnel condition, industrial settings, and research in the lab simulating skiing, cycling, etc. Generation of the equation of the h c under various airflow directions based on existing simulations [27], and collection of human data in multiple environmental conditions and body postures would help increase the validity of the Fiala model using the simulated h c .

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.