A numerical investigation of the influence of wind on convective heat transfer from the human body in a ventilated room Building and Environment

As an important factor in indoor human thermal comfort, the wind is investigated in the present study using a fully validated human body-environment interface model based on CFD technology. The three parameters of air speed (v a , 0.5 – 2 m/s), turbulence intensity (TI, 5% – 40%) and wind direction (0 ◦ – 180 ◦ ) were simulated to study their influence on the convective heat transfer coefficient (h c ) at the surface of the human body. It was found that v a influenced the value of h c more than TI. The influence of TI on h c reached a steady level when v a was above 1.5 m/s; for example the greatest rate of change of h c at the head remained at 52% as the TI was increased from 5% to 40%. The wind direction had a noticeable influence on the overall h c when the v a was above 0.5 m/s. A 90 ◦ wind (i.e. from the right side) gave a value of h c that was about 20% lower than wind from other directions, and led to an asymmetrical distribution of h c over the body surface. Locally, the wind direction did not influence h c at the head and feet, and influenced the central segments more than the limbs. Two regression equations for the correlations between h c and v a , TI and wind direction were also generated and validated for continuous eval- uation of h c . The resulting database of values for h c can be used in combination with the human thermoregulation models for thermal response prediction in built spaces with increased air speed.


Introduction
As a basic requirement for life, human thermal comfort is a constant focus of research in indoor environments and automotive cabin engineering. The two most widely used methods for evaluating indoor human thermal comfort are human trials and thermoregulation models, such as the Fiala model [1,2], UCB model [3] and Tanabe 65-node model [4], in conjunction with thermal sensation and comfort models [5][6][7][8]. The temperature of the indoor surrounding environment (air temperature and radiant temperature) and the air speed are the two most influential parameters, and are the most easily adjustable using indoor heating, ventilation and air conditioning (HVAC) systems for human thermal comfort. According to Newton's law of cooling and the Stefan-Boltzmann law of radiation, the temperature of the surrounding environment affects both convective and radiative heat exchange between the human body and the environment. The air speed, which changes the airflow pattern around the surface of human skin, mainly influences convective heat exchange. To find a balance between energy consumption and human thermal comfort, plenty of experimental and numerical studies [9][10][11] have been conducted to investigate the relationship between the use of air-conditioning systems and human thermal comfort, and have provided guidance on the design of air-conditioning and ventilation systems for occupational and residential spaces.
The convective heat transfer coefficient (h c ) at the surface of the human body integrates the air speed (v a ), and is used in human thermal regulation models to estimate convective heat exchange between the body and the environment. However, different values of this coefficient have been reported in literature for comparable environmental conditions. Under natural convection (v a < 0.5 m/s) where no extra wind is imposed on the environment, the value of h c for the whole human body has been found to vary within the range 3.1-5.1 W/(m 2 K) in different studies conducted under similar temperature gradients between the body surface and the environment [12,13]. The possible reasons for this variation, such as differences in body geometry, body posture and airflow patterns in the investigated room, have been systematically analysed by Xu et al. [14]. Under forced convection, in which extra wind is imposed on the environment, h c has been found to be a function of the v a (Equation (1)) [10,15]. Fig. 1 depicts the relation between v a and h c obtained from seven independent experimental studies of frontal wind on the human body [12,[16][17][18][19][20]. Large discrepancies can be observed, and these increase even further as the air speed increases. In the same way as for h c under natural convection [14], these discrepancies can only be partially explained by body geometry and body posture, since the difference in the results for standing and seated postures using the same manikin, as reported by de Dear et al. was smaller than the discrepancies shown in Fig. 1. The differing characteristics of the airflow produced in the climatic chamber in different labs can also be considered a factor causing this discrepancy [16]. This hypothesis can be verified by comparing the data obtained from de Dear et al. and Oguro et al. which were recorded in the same lab and are very similar (Fig. 1). A further explanation may involve the turbulence intensity (TI) of the blowing air, which has unfortunately always been neglected or not clearly determined in these studies. Although a TI of below 40% has been shown to have a negligible influence on the value of h c at an air speed lower than 0.5 m/s [21], it may have a more pronounced influence at larger air speeds, according to the study by Ono et al. [22]. For example, the values of h c for the whole human body at 4 m/s wind were 56 W/(m 2 K), and 32 W/(m 2 K) (i.e. 42.9% lower) for values of TI of 40% and 10%, respectively. Additionally, the higher the air speed, the stronger the influence of TI. From the perspective of human thermal comfort, a change in TI may induce a feeling of draft (an undesired local cooling sensation due to air movement) even at the same overall air speed [23]. This demonstrates the uncertainty and inapplicability of the results of such studies when TI is not reported. Moreover, the location of air speed measurement in the climatic chamber and the method of calculation of the average air speed were different in these studies. For instance, the reported air speed was calculated as an average of several measurements at different heights with the same distance to the manikin [12], as a single value at a point at the end of the wind tunnel section [16], or simply not reported [20,22]. These factors mean that each set of experimental results are valid only for the conditions under which they were derived. This imposes a limitation on human thermoregulation models, which need to use the value of h c obtained from experimental studies to estimate the convective heat exchange from the human body in a wide range of environments. (1) where h c is the convective heat transfer coefficient in W/(m 2 K), v a is the air speed in m/s, b and d are constants.
A systematic and cross-validated database of values for h c that takes into account all the influential parameters such as the magnitude of the air velocity, TI and airflow direction would be helpful in improving the predictability of the models. It is also critical to include higher air speeds (inducing both forced and natural convection) in such a database, since they are an unavoidable factor in human thermal comfort and thermal balance in ventilated rooms or vehicles. With its continuously adjustable parameters, numerical simulation would be an efficient method of obtaining such a database. Several simulation studies have been done under indoor conditions [24][25][26][27][28], taking into account the natural airflow, studies in the literature under windy conditions are however incomplete [20,22]. The simulations by Ono et al. [22] were not fully validated against measurements, and the heat transfer of regional body segments was not discussed. Li and Ito [20] mainly focused on air speeds higher than 1.0 m/s, and neglected speeds of between 0.5 and 1.0 m/s, which form an important transition zone from natural to forced convection.
This study aims to build a generic database of h c for the human body by taking into account the three relevant wind parameters of v a , TI and wind direction. Numerical simulation is utilised to create this database. A high-resolution human body, referring to the most common thermal manikins in measurement studies and human geometries in thermoregulation models, is used to investigate the local h c values. The v a is varied between 0.5 and 2.5 m/s, covering the most frequently seen air speeds in ventilated indoor spaces, such as the residential room, industrial workplaces, and climatic chambers in the research labs for mimicking outdoor conditions [16,29]. From the perspective of airflow condition, this range of air speed also covers the transition zone from natural to forced convection. Five levels of TI (5%, 10%, 20%, 30% and 40%) and wind direction (0 • , 45 • , 90 • , 135 • and 180 • ) are investigated. The results of this study can be used in thermoregulation models, and can help improve the predictability of indoor human thermal responses.

Design of the study
We began with the development and systematic verification of the numerical simulation method, before attempting an investigation of h c under windy conditions. First, a wind tunnel test was performed in a climatic chamber (chamber 1), and this was reproduced virtually using a CFD simulation with COMSOL Multiphysics 5.4a (COMSOL, Inc., USA). Comparisons were made between the measured and simulated parameters to verify the accuracy of the CFD method. In the next step, numerical investigations of the wind were carried out in a chamber with a more generic geometry (chamber 2), based on the verified CFD method. The three parameters of air speed, turbulence intensity and wind direction, which are commonly used variables in ventilated rooms [30], were systematically explored in the numerical investigations. A database of values of h c for the investigated parameters was then generated based on the simulated results. A regression analysis on the simulated values of h c in relation to the air speed, TI and wind direction was also conducted, which can help in the prediction of the continuous values of h c .

Wind tunnel test
Measurements were conducted in chamber 1 (length: 6.3 m, width: 3.5 m, height: 2.4 m) with a 22-sector thermal manikin SAM standing inside. SAM mimics human body in macro-scale and has a similar emissivity of 0.95 at its surface with the real human skin. A wind tunnel with four fans arranged vertically was placed in front of SAM, as shown in Fig. 2(a). Average air speeds of 0.5 and 2.5 m/s (the minimum and maximum investigated air speeds in this study) were obtained by adjusting a control panel. The average values were calculated by averaging the air speeds, measured at three height levels (as depicted in Fig. 2(a)) with a set of three omnidirectional anemometers (Sensor Electronic, SENSOANEMO 5100SF, accuracy: ±0.02 m/s±1%). The TI at the outlet of the wind tunnel, determined by the ratio between the standard deviation and average values of v a , was 38.9% for a wind speed of 0.5 m/s and 38.2% for a speed of 2.5 m/s, which indicates the presence of large-scale eddies in the airflow. The air speed was also measured at points 10 cm in front of, 10 cm behind and 10 cm to the side of the manikin, using the same setup involving anemometers at three heights ( Fig. 2(a)) to validate the simulations. The air temperature and relative humidity of the chamber were kept constant at 22.5 ± 0.2 • C and 50% ± 5%, respectively. The surface temperature of the manikin was kept uniform at 34 ± 0.1 • C. The heating power, which was recorded every minute for 30 min, was assumed to be equivalent to the sensible heat loss, which is composed of convective and radiative heat from the manikin's surface. More information on the thermal manikin can be found in Ref. [31,32].

Numerical simulations of wind tunnel tests
A representative virtual geometric model ( Fig. 2(b)), including chamber 1, the wind tunnel and the manikin, was built using COMSOL Multiphysics, based on the wind tunnel experimental test setup ( Fig. 2 (a)). In order to minimise the size of the model and speed up the simulation, two simplifications were introduced to the chamber geometry: a reduction in the part of the chamber in front of the wind tunnel outlet, where the airflow contributes little to the convective heat exchange at the manikin surface, and the use of symmetry in the chamber to reduce its computational volume. The outlet of the wind tunnel was treated as the inlet of the virtual chamber 1, and the height and width were kept the same. The entire wall behind the manikin was treated as the outlet of the virtual chamber 1. A scanned and post-processed human body model ( Fig. 2(b)) based on a full-scale thermal manikin Newton (Thermetrics, Seattle, WA, USA), created using a 3D scanner (Handyscan 700, resolution: 0.05 mm, precision: 0.03 mm) and surface inspection software (Geomagic Qualify, Geomagic Inc., North California, USA), was imported and placed in the middle of the domain. It was located 8.5 cm above the ground and 73 cm in front of and facing the inlet of the virtual chamber 1. We hypothesize that the differences in size and shape between the manikin Newton (for simulation) and manikin SAM (for measurement) can be neglected.
The heat transfer regime inside the virtual chamber 1 under windy conditions was simulated using COMSOL Multiphysics. The boundary conditions for the simulation (Table 1) were set to be consistent with the wind tunnel tests.
.RANS k-ε and low Re k-ε models have been widely used to simulate the turbulent flow in previous studies [33,34]. The turbulence kinetic energy k and the turbulent dissipation rate ε were calculated using Equations (2) and (3). The difference between these two models lies in the way they treat the airflow close to the solid wall. The low Re k-ε model simulates the airflow in the space up to the wall with a good accuracy at the laminar and buffer layers, while the RANS k-ε model employs a wall function to simplify the airflow in the laminar layer near the wall. Theoretically, the low Re k-ε model is expected to give more accurate simulation results than the RANS k-ε model, especially for the conditions in the current study, where the heat transfer at the solid wall (manikin surface) is under investigation. However, a higher computational cost (denser mesh and longer computing time) is needed for the low Re k-ε model.
where k is the turbulence kinetic energy, U ref is the mean stream velocity in m/s, ε is the turbulent dissipation rate, C μ is the k-ε turbulence model constant (here, 0.0845), and L is the characteristic length of the inlet in m.
We first discuss both models, comparing the simulation results with measurements taken in the wind tunnel, and then select the one that predicts the airflow and heat transfer more accurately and economically under the investigated conditions.
The radiative heat exchange is not accounted for in this study, as it is not influenced by wind (the manikin and wall temperatures are kept constant). The convective heat transfer is simulated in COMSOL by coupling the turbulence flow and heat transfer in fluids, based on the temperature gradient. The value of h c is calculated by solving Equation (4): where 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 K, and T a is the temperature of the air in K. The virtual domain was discretised into two regions ( Fig. 2(b)) and meshed. A tetrahedral domain mesh, triangular surface mesh, and fivelayer boundary layer (y + < 5) mesh were generated for both regions. The mesh in region 1 surrounding the virtual manikin, where the temperature and airflow changes dramatically, was denser than in region 2. The finite element method (FEM) was used to compute the governing equations, i.e. the N-S, continuity and energy conservation equations.
A mesh sensitivity study was conducted only with the low Re k-ε model, as it is more sensitive to the quality and density of the mesh near the wall than RANS k-ε model. The results show (Fig. 3) that the simulated convective flux at the human body surface changed with the number of the domain mesh, and reached a steady value when the number of mesh elements reached 1.9 M. A change of only 0.2% in the convective heat flux was observed as the mesh number was increased from 1.9 M to 3.1 M, whereas the computational time increased by 60%. Based on a comprehensive consideration of the simulation accuracy and computational time, a mesh of 1.9 M points was selected for both the wind tunnel simulation and the remaining simulations. Fig. 4 shows the air speed around the manikin, and the total heat transfer coefficient (h t ) from both measurement and simulation. The simulated value of h t is the sum of the simulated h c from the present study and the simulated radiative heat transfer coefficient from our previous study [14], which was conducted in a virtual chamber with an identical configuration to that used in this study. The average standard deviations (SDs) of three quantities (the measured v a and h t over 30 min) and the root mean square deviations (RMSDs) between measurement and simulation are also shown in Fig. 4.

Comparison between measurement and simulation
From Fig. 4, it can be seen that the simulated air speeds using the RANS k-ε and low Re k-ε models are both within the error range of the measurements, except for behind the manikin, where the simulated air speeds (<0.5 m/s) are lower than the measured speeds (by around 1.0 m/s) along the aerodynamic shading area of the back and pelvis at an air speed of 2.5 m/s. In the physical test in the wind tunnel, there is a huge metal-structured box behind the manikin ( Fig. 2(a)) which is needed to affix the walking system; however, this was not simulated in the numerical model, which may have changed the air flow pattern, resulting in the discrepancy in the air speed. Furthermore, the RMSDs of the low Re k-ε and RANS k-ε models are both no greater than the SDs of the measurements, showing that good estimations of the airflow are produced by both models.
The RMSDs of RANS k-ε model and low Re k-ε model for h c are greater than the SDs of the measurements, especially at an air speed of 2.5 m/s. Fig. 4(e) shows that the prediction errors from the low Re k-ε and RANS k-ε models at 2.5 m/s are mainly due to the chest segment, where the simulated values of h t are greater than the measured values by 65% and 45%, respectively, followed by the back segment, with simulated values that are greater by 17.1% and 19.1%, respectively. This could be due to the different methods of averaging the h t at the individual surface. The reported h t from the simulated human body is dependent on the heat flux from each tiny mesh surface, which is kept at a constant surface temperature. For the measured values, the reported h t is dependent on the heating power supplied to the whole body segment, as the average surface temperature of the segment was kept constant. This means that the surface of the manikin in the chest region, where the heat flux is fairly heterogeneously distributed, as shown in Fig. 5, could be locally at different temperatures generating diverging heat loss although the mean temperature was maintained. Additionally, a previous measurement study of Psikuta et al. [35] also reported a smaller h t (by 10%) at the chest segment of manikin SAM than the average result of other commonly used thermal manikins (Newton, Diana, Tore) under a similar natural flow condition (v a < 0.2 m/s). As given in the same study of Psikuta et al. there exists lateral heat transfer inside SAM through joints and guard sectors, which we assume as another possible factor in causing such discrepancy.
When the chest segment was excluded from the calculation of average RMSD, we obtained much lower RMSDs of 3.8 and 3.4 W/(m 2 K) for the RANS k-ε and low Re k-ε models, respectively. Hence, we assume the prediction error in h t is mainly not caused by the inaccuracy of the numerical method.
Despite the greater RMSDs than SDs, the simulated results from both the low Re k-ε and the RANS k-ε models correspond well with the measurements (except for the chest segment), with greater values of h t at the limbs than at the torso. As the RMSDs of the low Re k-ε model are smaller than of the RANS k-ε model, the low Re k-ε model is selected to simulate the turbulent flow for the remaining simulations in this study.

Virtual geometric models and meshing
A rectangular-shaped chamber 2 ( Fig. 6 (a)) representing the generic indoor space (4 m × 6 m × 2.37 m) was established, with the inlet and outlet surfaces facing each other. The same virtual manikin ( Fig. 6 (b)) was used here as in the simulation for the wind tunnel test. It was located 8.5 cm above the floor and 3.7 m from the inlet surface. Five wind directions towards the right half of the manikin, front (0 • ), front diagonal (45 • ), side (90 • ), back diagonal (135 • ), and back (180 • ), were simulated by rotating the manikin in relation to the inlet.
As in the simulation for the wind tunnel test, the virtual domain was discretised into two regions ( Fig. 6(a)) and meshed accordingly. The mesh settings were consistent with those in Section 2.2.2, which was checked as being mesh-independent. A total of around 2.6 M mesh elements were finally obtained (Fig. 7).

Boundary conditions
Five simulation cases (Table 2) were used to investigate the three parameters of air speed, TI and wind direction. The air speed was homogeneous everywhere at the inlet surface, and TI was applied directly  Fig. 3. Mesh sensitivity study for the simulation with low Re k-ε model at an inlet air speed of 2.5 m/s. to the air blowing at the inlet surface. The convective heat transfer between the virtual human body and chamber 2 was simulated for each of the five cases. The low Re k-ε model was coupled using the COMSOL Multiphysics interface with heat transfer in fluids, based on the temperature gradient. Both the thermal plume due to buoyancy force of air and the heat transfer due to blown wind are simulated. The boundary conditions for the simulations are listed in Table 3.

Regression analysis of the correlation between convective heat transfer coefficient and wind conditions
Once the values for h c were obtained from the above-mentioned simulations in Table 2, regression analysis was performed with the resulting h c and v a , TI and wind direction. Two regression equations were expected. One involved the correlation between h c and v a by coupling TI, while the other involved the correlation between h c and v a by coupling wind direction. As the frontal wind was most commonly discussed, the second equation was designed in a form of correction factor of h c based on the h c under a frontal wind of 0.5 m/s. The two formulas were proposed based on the scatter plots of the investigated variables. The values of the coefficients of the formulas were calculated with the approach of non-linear surface fitting using Origin11 (Origin-Lab, Inc., USA). The goodness of fit was judged using R 2 (Equation (5)) or adjusted R 2 (Equation (6)) and the standard error of estimate (SEE, Equation (7)). Furthermore, measurements and equations from previous studies [12,16,17,22] were used for validating the regression equations developed in this study.
where x i ' is the estimated result, x i is the simulated result, R adj 2 is the adjusted R 2 , and df means degrees of freedom.  axis) for the overall and local body segments at various air speeds, with wind from the front at various TI levels. On the secondary y-axis, the change in the value of h c caused by an increase in TI from 5% to 40% is presented. The change in h c was calculated by dividing the difference in h c at 40%TI and 5%TI by the value of h c at 5%TI, i.e. ((h c_40%TI -h c_5%TI )/ h c_5%TI *100%). According to Fig. 8, the h c increases with the increment in v a and TI, and the slope of the curve of h c increases with the TI. Besides, the change rate of h c fluctuates as the air speed is below 1.5 m/s while it maintains at a steady level as the air speed exceeds 1.5 m/s. Locally, the air speed has the greatest influence on h c of the hand, lower arm and chest, and has the lowest influence on h c for the leeward part of back, for every value of TI investigated. In addition, the absolute value of h c for the chest, hand and lower arm segments is over 50% higher than at the back.  Fig. 9(a) are top views at the chest level, and those in the right-hand column are side views. As can be seen from Fig. 9(a), the solid human body effectively blocks the wind blowing towards it, as the air speed in the rear part of the chamber is obviously lower than in the front, especially near the central torso region. Air flow is observed through the gaps between the body segments (between the arm and torso, and between the legs) for all wind directions except for the side.

Convective heat transfer coefficient for various wind directions
In Fig. 9(b), the negative value indicates heat release from the surface of the manikin. Obviously, the wind direction changes the distribution of h c over the body surface. The value of h c is greater on the windward side than on the leeward side. A lower h c is always observed for the central torso segments than for the limbs and extremities, for all wind directions. Fig. 10 shows the data for the simulated h c over the whole body and local body segments, for five wind directions. The difference in h c between wind directions increases with an increment in air speed. For example, at an air speed of 0.5 m/s, the change of the overall h c of the other wind directions is very small compared with a frontal wind     Table 4. According to Table 4, the change in the wind direction has smaller influences on the h c at the head and foot than at the others. Although the human body used in this study has left/right symmetry, h c can be asymmetrical under an asymmetrical wind (i.e. from the side and diagonal directions), as virtually shown in Fig. 9(b). Fig. 11 shows the simulated values of h c for the left and right halves of the body under front diagonal, side and back diagonal winds. The y-axis shows the values of h c for the right half of the body, and the x-axis shows the values for the left half of the body. Data points above (below) the dotted lines indicate that h c for the body part on the right is greater (lower) than for the part on the left. Data points falling on the dotted lines indicate that h c is symmetrically distributed over the body surface. According to Fig. 11, the side wind causes higher h c for the right half of the body segments than for the left half, except at the foot. For the diagonal winds, they cause asymmetric distribution of h c over the head and torso (chest, back and pelvis) segments.  Fig. 8. Simulated values of h c (main y-axis) and change in h c due to an increase in TI from 5% to 40% (secondary y-axis) for (a) the overall surface and (b)-(k) local body surfaces, under frontal wind.

Results of regression analysis
Equation (8), a power function according to the scatter plots, is the newly generated formula for overall and local h c in relation to v a and TI. Table 5 gives the coefficients, the adjusted R 2 and the SEE for Equation (8). The adjusted R 2 is above 0.998. Fig. 12 (a) shows the validation results of Equation (8) for 5% TI by comparing the predicted results by Equation (8) and equations in previous studies [12,16,17,19,22]. For a TI higher than 5%, Equation (8) in this study was compared only with the correlation of Ono et al. [22], due to a lack of more relevant data in the literature. Exemplary results of a comparison for 20% TI and 40% TI are shown in Fig. 12(b) and (c), respectively.
According to the scatter plots in Fig. 10, the correlation between h c and v a and wind direction was found to be a bivariate polynomial function (Equation (9)). The values of the coefficients, adjusted R 2 and SEE of Equation (9) for the whole body and local body parts are listed in Table 6. The adjusted R 2 is above 0.935.
where h c,front is the convective heat transfer coefficient under a frontal wind at an air speed of 0.5 m/s in W/(m 2 K), and w d represents the wind direction, calculated as the ratio between the wind angle and 180 • , e.g. for a 45 • wind, w d is 0.25 (45/180 = 0.25). Since a very limited selection of values for h c under various wind directions is available in the literature, Equation (9) was validated against only the measured data of de Dear et al. [12] for a standing thermal manikin. Exemplary validation results for the whole body are shown in Fig. 13.

Whole human body
According to the findings in Fig. 8, both v a and TI have a positive influence on h c at the body surface, and the influence of v a on h c becomes stronger with an increment in TI. In addition, consistent with the findings of another CFD study [22], the variation in the overall h c caused by the change in TI at higher air speed is greater than at lower air speed. The slope of the air speed within the range 1.5-2.5 m/s is approximately zero, indicating a stable influence of TI. To explain this phenomenon, the Archimedes number (Ar) representing the proportions of forced and natural convection in the mixed flow was checked. It was found that when the air speed was above 1.65 m/s, the Ar was smaller than 1, meaning that the mode of airflow was predominantly forced convection. This is consistent with the finding by Danielsson [36] that mixed-mode convection prevails in the airflow at air speeds of between 0.2 and 1.5 m/s, and when the air speed exceeds 1.5 m/s, forced convection dominates. It is therefore reasonable to observe a change in the influence of TI on h c when the air speed is below 1.5 m/s (air flow dominated by natural convection) and a more stable influence when the air speed is between Fig. 10. Simulated h c at the surface of the human body for five wind directions.

Table 4
Change in h c for different wind directions in relation to the front wind at an air speed of 2.5 m/s (where the minus symbol means that h c is lower than that for a frontal wind).

Individual body segments
The greater absolute value of h c for the chest, hand and lower arm than for the back is related to the frontal wind direction and the large effective projected area of these sectors with respect to the wind. It is consistent with the findings of other researchers [12,37] who also reported higher values of h c for the limbs, chest and peripheral segments than at the back under a frontal wind.
The influence of TI varies with air speed. At the lowest investigated air speed of 0.5 m/s, TI has the least influence on h c at the foot (less than 8%), followed by the hand (less than 20%). This is related to the composition of the airflow; at an air speed of 0.5 m/s, according to the Ar, natural convection predominates in the airflow. The foot and hand are also the places in which natural convection due to gravity starts and the airflow is laminar, which means that changes in TI do not have a promising influence on h c at these points.
As the air speed increases, the change in the local h c caused by the increment in TI reaches a steady level, with forced convection dominating the airflow. Finally, TI is found to have a stronger influence on h c for body parts with a larger projected area, such as the chest (which is totally oriented towards the wind), where the influence remains around 51%, than for body parts with smaller projected areas, such as the leeward segment of the back (which is totally sheltered from the wind) and the pelvis (half sheltered from the wind). These discrepancies among the individual body surfaces can be attributed to many factors, including the orientation of the body part against the direction of the blowing air, the buoyancy of the air, and the positional relationships between body segments. This reveals the significance of mentioning the airflow condition in the room as concrete as possible while showing the results of convective heat transfer.

Whole human body
According to the findings in Fig. 10, the influence of wind direction on the overall value of h c becomes stronger with air speed, and the convective heat is lost more easily when the human body is facing the wind rather than laterally exposed to the wind. This can be explained by the greatly reduced area facing a side wind. As shown in Fig. 9, the left half of the body is aerodynamically shielded under a side wind, resulting in a h c that is 33% lower than that for the right half of the body (Fig. 11). This contradicts the results reported by de Dear et al. [12], where the measured h c under a side wind was only 4% lower than under a frontal wind at an air speed of 2 m/s. It can be partially explained by the difference in the geometrical shape of the manikin (a female manikin with breasts was used by de Dear et al. and a male manikin in the present study) and the vague description of the environmental setup in the measurement. However, this finding is consistent with that of Luo et al. [38], who used the same manikin (Newton). In their study, the lateral movement of the manikin on a trolley (causing a uniform relative air movement between the manikin and the environment) led to a convective heat loss that was 10% lower than forward movement.

Individual body segments
The reason why a change in the wind direction has only a slight influence (<10%) on h c at the top (head) and bottom (foot) parts is that they are not shielded by other body segments under any wind direction. However, the side and diagonal winds have resulted in an asymmetrical distribution of h c over the head. This is related to the sphere-like shape of head that the left side of it is shielded from the asymmetrical wind.
The influence of change in wind direction on the h c at limbs and hand segments cannot be ignored for the side wind. As shown in Fig. 9(a), the inner sides of the right limbs and hand are shielded from the right side wind, and the left limbs and hand are shielded from the moving air by the right half of the body. In other words, the wind contact area of the limbs and hand is greatly reduced under a side wind compared with the other wind directions, which causes a great decrease in h c of 15%-27%. As for the chest and back segments, they are rather flat, oval shapes, and are almost completely shielded from back and front winds, respectively. We therefore see the expected variation (>20%) in h c under back and front winds for the chest and back, respectively.
For the cylindrical pelvis segment, the lower h c under side and diagonal winds is due to the position of the lower arm and hand, which block winds blowing laterally or diagonally towards the human body, resulting in lower air flow in the proximity of the inferior part of pelvis. This has indicated a different finding can be presented if the position or posture of the human body is changed. For example, if the human body is in a seated posture with its arms horizontally positioned, wind from side is not likely to cause any influence on the h c at the pelvis compared with a frontal wind. Fig. 12(a) shows that for a TI of 5%, the simulated correlation in this study is within the range of previous correlations. It is closest to the correlation reported by de Dear et al. when the air speed is below 1.0 m/ s, and closest to the correlation of Ichihara et al. when the air speed is above 1.0 m/s. The increasing discrepancy between the correlation in this study and that of de Dear et al. [12] is partly because the equation For a TI higher than 5%, discrepancies of up to 4.5 W/(m 2 K) can be observed from Fig. 12(c); however, this value is much smaller than that at an air speed of 2.5 m/s (a discrepancy of 15.3 W/(m 2 K)) in Fig. 12(a), where a larger selection of experimental results was compared. Further validation against other experimental datasets may help address the rationality of Equation (8) for TI greater than 5%. In addition, the discrepancy between the six correlations with an identical TI of 5% in Fig. 12(a) is even larger than between the two correlations from this study with different TI of 5% and 40% (4.05-15.31 W/(m 2 K) and 2.59-10.86 W/(m 2 K), respectively). This indicates that the airflow conditions in different labs can be substantially different, despite the reported values of average air speed and TI being identical. It also emphasizes the necessity of measuring and reporting the airflow conditions in detail when presenting results on heat loss under forced convection.

Validation of correlation between h c , v a and wind direction
According to Fig. 13, Equation (9) gave good predictions for h c at a low air speed of 0.5 m/s, except under a back wind where h c was overestimated by 21% (1.3 W/(m 2 K)). As we found in the current study that the airflow condition influences h c more strongly at higher air speeds, the acceptable estimation error (lower than 5%) calculated using Equation (9) for an air speed of under 0.5 m/s is magnified (above 10%) when the air speed exceeds 2.0 m/s.

Conclusions
A numerical human body-environment interface model for the study of heat transfer under windy conditions was developed. It was validated against measurements in a climatic chamber with a thermal manikin under the same environmental conditions (RMSD for v a of below 0.4 m/ s, for h t below 3.4 W/(m 2 K)). Using the validated numerical model, the three parameters of air speed (0.5-2.5 m/s), TI (5%-40%) and wind direction (0 • -180 • ), were investigated in terms of their influence on the h c at the surface of the human body. It was found that: (1) Both the air speed and TI have an influence on h c , with the air speed showing a stronger influence. The influence of TI remains at a steady level when the air speed exceeds 1.5 m/s and forced convection becomes predominant; for example, the rate of change in the overall h c caused by an increase in TI from 5% to 40% remains at 42%. (2) The wind direction does not have any influence on the convective heat transfer from the entire body surface at a low air speed of 0.5 m/s, but becomes an influential parameter as the air speed increases. At an air speed of 2.5 m/s, a side (90 • ) wind causes an asymmetrical distribution in h c over the whole body surface, resulting in an overall h c that is 18% lower than for front (0 • ), diagonal (45 • and 135 • ) and back (180 • ) winds. Locally, the wind direction shows only a slight influence on the head and feet. For the limbs, hands and trunk, a side wind gives a value of h c that is 15%-26% lower than the front, diagonal and back winds. and v a and wind direction. Further validation studies are likely to improve these equations, which can be used in combination with human thermoregulation models to predict human thermal comfort in built environments.

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.