NUMERICAL INVESTIGATION OF HEAT TRANSFER IN GARMENT AIR GAP

and insisted that the heat ﬂ ux was deviated to a lower level if neglect convection. Abstract: This article aimed to study the characteristics and mechanisms of 3D heat transfer through clothing involving the air gap. A three-dimensional fi nite volume method is used to obtain the coupled conductive, convective, and radiative heat transfer in a body-air-cloth microclimate system. The fl ow contours and characteristics of temperature, heat fl ux, and velocity have been obtained. The reason for the high fl ux and temperature regions was analyzed. Computational results show that the coupled effect of the air gap and the airfl ow between the skin and garment strongly infl uences the temperature and heat fl ux distribution. There are several high-temperature regions on the clothing and high heat fl ux regions on the body skin because the conductive heat fl ux can cross through the narrow air gap and reach the cloth surface easily. The high-speed cooling airfl ow brings about high forced convective heat fl ux, which will result in the temperature increase on the upper cloth surface. The radiative heat fl ux has a strong correlation with the temperature gradient between the body and clothing. But its proportion in the total heat fl ux is relatively small.


Introduction
Thermal comfort is one of the important factors that meet customer's needs nowadays. The development of textile science and thermal control technology gives the chance to study the thermal comfort of clothing accurately. The garment system is constructed by clothing, air gap, and body skin [1]. Under ordinary temperature, thermal comfort can be achieved from the microclimate in this system with reasonable importation and interaction of conductive, convective radiative heat transfer, as shown in Figure 1 (T skin >T cloth >0K).
Some experimental studies are available in the literature where thermal comfort performance of 3D body was analyzed under different types of exposures [2,3]. The bench top test was widely used to study heat transfer between the body and clothing either 2D or 3D [4-6]. However, the air gap was considered to be equally everywhere because the bench was considered to be fl at [2,7]. Santos [8] used a computational fl uid dynamics (CFD) approach to perform numerical studies of fl uid fl ow and heat transfer across cylindrical clothing microclimates with different values of microclimate thickness and argued that the increase of microclimate thickness can decrease the convective heat fl uxes rapidly. Some scholars discussed a few fi nite volume method (FVM) models of heat transfer in the microclimate under the assumption of constant thermophysical properties of the fabric and constant convection in the air gaps [4,6]. Ghazy [9] used the FVM method to solve the radiative transfer equations and energy equations and analyzed the effect of the dynamic air gap on heat transfer through the air gap. Udayraj [10] studied the heat transfer through air gaps by the CFD model, which considered conduction, convection, and radiation, and insisted that the heat fl ux was deviated to a lower level if neglect convection.

Abstract:
This article aimed to study the characteristics and mechanisms of 3D heat transfer through clothing involving the air gap. A three-dimensional fi nite volume method is used to obtain the coupled conductive, convective, and radiative heat transfer in a body-air-cloth microclimate system. The fl ow contours and characteristics of temperature, heat fl ux, and velocity have been obtained. The reason for the high fl ux and temperature regions was analyzed. Computational results show that the coupled effect of the air gap and the airfl ow between the skin and garment strongly infl uences the temperature and heat fl ux distribution. There are several high-temperature regions on the clothing and high heat fl ux regions on the body skin because the conductive heat fl ux can cross through the narrow air gap and reach the cloth surface easily. The high-speed cooling airfl ow brings about high forced convective heat fl ux, which will result in the temperature increase on the upper cloth surface. The radiative heat fl ux has a strong correlation with the temperature gradient between the body and clothing. But its proportion in the total heat fl ux is relatively small.

Keywords:
Garment, air gap, heat transfer, conduction and convection, numerical simulation As mentioned above, not enough work has been done on analyzing the heat transfer mechanism of the real 3D human body. The present study thus employs an FVM to develop a test method for determining the conduction, convection, and radiation heat fl ux between 3D body and clothing. The distributions of temperature on clothing surface and heat fl ux on the body surface are discussed. The relationship between heat fl ux and air gap distance, as well as airfl ow properties are analyzed.

Physical model
In the present work, heat transfer through clothing involving air gap is analyzed and temperature distribution on clothing surface is predicted. A standard female body and a type of fi tting apparel are chosen here. The surface of the female body is established by the CLO 3D virtual try-on programs. Then, the girth feature curves were extracted by adding distance ease to the editable feature curves of the initial 3D mannequin [11]. Basic dimensions of body and clothing are given in Table 1.

Mesh generation
The unstructured grids are generated with fi ne mesh near walls by the commercial mesh generation software ICEM-CFD 17.0. For the symmetry of the human body, only half-geometry meshes are generated in this study to reduce computation load and improve precision. 3D garment and mesh are shown in Figure 2.

Landmarks and ease allowance measurement
This study focused on the distance ease in the horizontal direction, and four characteristic landmarks (Figure 3(a)) were selected to measure the distance ease and airfl ow contours. The virtual model of a clothed mannequin was simulated by commercial software Geomagic Qualify to obtain the 3D air gap distance, namely distance ease (Figure 3(b)). The distance ease is below 5 mm at the location of the shoulder, right side bust, side waist, and side thigh. The ease allowance value is between 5 mm and 15 mm at the chest, waist, and abdomen.

Coupled
Reynolds-averaged Navier-Stokes (RANS) equations [12] with radiative transfer equations (RTE) were   where p I is the equivalent emission of the particles, is the equivalent absorption coeffi cient and scattering coeffi cient. They can be expressed as: N is the number density of the i particulate species, i N i N i is the number density of the i particulate species, is its emissivity, temperature, diameter, projected area, and scattering factor. In this article, the radiation absorption coeffi cient is set to 0.0001 for air medium.

Solution procedure
To get the numerical solution for the heat transfer in air gap, some variable conditions, such as initial and boundary conditions, are needed. Owing to the complexity of heat transfer in air gap, some assumptions are adopted to simplify the numerical model. The fl ow inside air gap can be characterized as turbulent, weakly hem, natural convection due to buoyancy and heat radiation due to temperature gradient compressible fl ow containing forced convection due to the airfl ow from the clothing. The airfl ow within the fabric occurs in a laminar regime with low velocity. The buoyancy effects are considered because of natural convection heat transfer. The air bulk density is set used to simulate heat transfer and fl uid fl ow in a cloth-air-skin system. Three-dimensional continuity, momentum, and energy equations with the realizable k-ɛ model [13,14] in tensor forms were considered for modeling heat transfer and fl uid fl ow in the air gap. The divergence of the radiative heat fl ux can be obtained using: (1) where I b is the blackbody intensity, is defi ned as: (2) G is the irradiation, is expressed as: ( 3) The solid angle Ω and radiation intensity I obtained by solving radiative transfer equations. The particles absorbing, emitting, and scattering are considered by the discrete ordinate radiation model (DORM).
The radiative transfer equations (RTE), used to calculate the radiation heat fl ux inside the air gap, are solved using the DORM, which is expressed as [15]: (4)

Validation of numerical methods
The numerical method is validated fi rst against the available results [8,18,19] for a 2D horizontal impermeable cylinder, namely, human limb, with an external environment of 283K. The cylindrical clothing microclimates between the limb and the cloth surface are investigated. Figure 4(a) and (b) shows the present results for heat transfer Nusselt number and dimensionless tangential velocity variation along the skin, respectively, compared against the public works. The present method is found to be well in agreement with the available results and is satisfactory to carry out the following investigation.

Temperature on the cloth surface
The temperature contours under the condition of conduction, convection, and radiation are shown in Figure 5. As can be seen, the temperature distribution looks uneven all over the surface. The locations of the shoulder, upper chest, back chest, lower bust, and lower hem of cloth surface are the highest temperature regions.
To analyze the temperature quantitatively, temperature distributions near chest (y = 69 cm), bust (y = 58 cm), waist (y = 42 cm), and hip girth (y = 22 cm) are exhibited with the distance ease in Figure 6. As is shown, the temperature was increased with the ease allowance decrease. The temperature of the cloth was overall higher at the chest and bust girth (Figure 6(a) and (b)), and lower at the waist and hip ( Figure  6(c) and (d)). This is partly because the conduction heat fl ux can cross through the narrow ease and reaches the cloth surface easily. However, the temperature increases nonlinearly with increasing ease distance. The most signifi cant changes are noticeable between X = 0.05 m and 0.07 m at chest and between X = 0.09 m and 0.11 m at bust because of the hightemperature results from high-speed cooling airfl ow, as we will explain in Chapter 4.4. This is a new and interesting observation of the present study.
to 1.29 kg/m 3 . Gravity is considered to be acting in a vertically downward direction. The gravitational acceleration vector is −9.81 m/s 2 . The mesh independence test was carried out with three different mesh scales, namely, 1.1 million for coarse mesh, 1.6 million for moderate, and 2.2 million for a refi ned mesh. The refi ned mesh was selected because of its accuracy to evolve the following calculations [16].
The freestream airfl ow was applied to the inlet, which is specifi ed as a standard atmosphere with T air = 283.15K and v air = 0.5 m/s, the gases emissivity is set to 0.02. The outlet properties are extrapolated from inner cells. The body skin and inner fabric are considered as diffuse surfaces, with the emissivity of 0.98 and 0.95 [8,17] ] (Table 2).  noted that all the heat fl ux curves present wavelike appearance both on the front and backside of the body (Figure 8). The smaller distance ease leads to the higher heat fl ux on the whole, further confi rming the infl uence of distance ease on the heat fl ux. It is also important to note here that the relationship between distance and heat fl ux is a little complex; the heat fl ux curve raises to a high level when the ease curve decreases especially at the location of X = 0.00 m to 0.02 m and X = 0.10m to 0.12 m. However, the heat fl ux curve does not keep pace with the distance ease curve (Figure 8(b) and (d)). Therefore, the total heat fl ux is affected by air gap distance, and the airfl ow between the body and clothing should be considered at the same time.

Heat fl ux on the body skin
The total heat transfer and radiative heat fl ux are shown in Figure 7. Predictably, the air gap between the skin and the garment strongly infl uences the airfl ow and heat transfer in this region. The area around the neck, waist, and under the bust is the high heat fl ux regions (HFRs) where the lost total heat fl ux is above 1400 W/m 2 (Figure 7 (a)). This phenomenon mainly results from narrow distance ease. Interestingly, the total heat fl ux under the bust is also very high, for which the distance ease is wide enough. The circumference around the thigh has the maximum heat loss of more than 3200W/m 2 . These phenomena might result from air-forced convection, which is taken by the infl ow of cooling air from the skirt's hemline. Compared with Figure 7(a), the high radiative HFR (Figure  7(b)) is very different from that of total heat fl ux. The radiative heat fl ux on the cloth surface is relatively small about 150W/m 2 on the area of middle bust, waist, and abandon. If considered Figure 6 and Figure 7(b) together, we will fi nd that the high cloth surface temperature regions in Figure 6 are similar to low radiative heat transfer regions in Figure 7(b) to some extent. This is because the radiative exchange between the body and clothing depends on the distance between them and the temperature difference. The lower radiation heat transfer across air gap occurs due to the lower temperature gradient.
To analyze the heat transfer distribution quantitatively, heat fl ux curves at different cross-sections were obtained. It is to be  2. The temperature of the clothing was overall higher at the chest and bust girth due to the conduction heat fl ux, which can cross through the narrow ease and reach the cloth surface easily. The high-speed cool airfl ow brings about high forced convective heat transfer and then results in the temperature increase on the cloth surface.
3. The radiative heat fl ux is just a small part of total heat fl ux and has a strong correlation with the temperature gradient between the body and clothing.

Flow in the air gap
To understand the physical reason behind heat fl ux and air gap width, another important factor of air velocity was considered. Based on airfl ow velocity obtained from the CFD analysis for the space of body and cloth, the stream traces are shown in Figure 9(a). As can be seen, the air velocity is relatively small between the double legs because of the wide space. The air velocity increases to a high level around the waist, bust, and chest because of narrow ease distance. The 3D velocity contours distribution between the body and clothing are shown in Figure 9(b). As shown, the high speed appears on the upper chest, bust, and waist with the Mach number of more than 0.02.
If considered Figures 6 and 8 together, we will fi nd that the peak value of temperature partly results from the high-speed cooling airfl ow. The comparison of high-velocity region (HVR) and HFR are shown in Table 3. These distributions are helpful to understand the infl uence of forced convection.

Summary and conclusions
This article aimed to investigate the 3D heat transfer of the bodyair-cloth system, coupled conduction, convection, and radiation models. The microclimate characteristics of temperature, heat fl ux, and velocity contours were discussed in the present work.
The following are some of the major observations derived from the study: