Verification and validation of an advanced model of heat and mass transfer in the protective clothing
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Abstract
The paper presents verification and validation of an advanced numerical model of heat and moisture transfer in the multilayer protective clothing and in components of the experimental stand subjected to either high surroundings temperature or high radiative heat flux emitted by hot objects. The developed model included conductiveradiative heat transfer in the hygroscopic porous fabrics and air gaps as well as conductive heat transfer in components of the stand. Additionally, water vapour diffusion in the pores and air spaces as well as phase transition of the bound water in the fabric fibres (sorption and desorption) were accounted for. All optical phenomena at internal or external walls were modelled and the thermal radiation was treated in the rigorous way, i.e., semitransparent absorbing, emitting and scattering fabrics with the nongrey properties were assumed. The air was treated as transparent. Complex energy and mass balances as well as optical conditions at internal or external interfaces were formulated in order to find values of temperatures, vapour densities and radiation intensities at these interfaces. The obtained highly nonlinear coupled system of discrete equations was solved by the Finite Volume based inhouse iterative algorithm. The developed model passed discretisation convergence tests and was successfully verified against the results obtained applying commercial software for simplified cases. Then validation was carried out using experimental measurements collected during exposure of the protective clothing to high radiative heat flux emitted by the IR lamp. Satisfactory agreement of simulated and measured temporal variation of temperature at external and internal surfaces of the multilayer clothing was attained.
1 Introduction
Firefighters, soldiers, motor sportsmen and workers during their duties may be exposed to either high ambient temperature or high heat fluxes coming from hot external objects, e.g., flame or hot bodies. They may also came into direct contact with hot surfaces. Therefore, they wear special personal protective garments, which play dual role. Firstly, the protective garments maintain comfortable conditions during regular activities of people. Secondly, they protect the workers from getting severe burn injuries or minimize harmful thermal effects during the emergency situations. The regular activates are more likely and usually occur continuously. The later events are less likely and occur for a very short time, usually until the person escape from the scene.
Typical protective clothing consists of several (three or four) textile layers, e.g., the outer shell, moisture barrier, thermal insulation and lining. Each of these fabric has different thermophysical and optical properties and performs different role. The outer shell, which is the most external layer, is responsible for protection against short thermal and mechanical hazards. The penetration of either cold or hot water or other liquids is prevented by the moisture barrier. The thermal insulation secures from the increase of temperature at the inner side of the clothing during short or longterm heat exposures. The comfort of exploitation of the garments is ensured by the lining. Moreover, the fabrics may be separated by thin air gaps. The widest air gap is usually present between the inner clothing surface and the skin.
The protective clothing is considered as a porous, multicomponent and multiphase structure in which all basic heat transfer modes, i.e., conduction, convection and thermal radiation are present. In the garments the heat is conducted through the fibres in the fabric and motionless air in the pores and gaps. The forced convection in the garments is usually associated with a movement of the person and related variation of the size of the air space between the skin and inner clothing surface. Sometimes it can be induced by either direct contact of the clothing with a flame or a blast of the external air. The fabrics are also semitransparent and nongrey media which interact with thermal radiation. The radiative heat flux which is emitted by the external radiation heat source, e.g., flame or hot body is attenuated by absorption and scattering in the volume of the fabrics before reaching the skin. In the protective clothing all these heat transfer modes mentioned above are strongly coupled and nonlinear as well as dependent on both thermophysical and optical properties of fabrics as well as the structure of textile layers. Moreover, during wearing of the protective clothing the moisture transport should be also considered. The water content in the clothing system may come from the surroundings or from the human body due to sweating and epidermal water loss. Therefore, the heat transfer phenomena in the protective garments are accompanied by the diffusion and convection of water vapour in the textile layers and air gaps as well as by sorption and desorption of a moisture in the fabric fibres and phase transition of water at the skin surface. The moisture in a complex way affects energy transfer as well as thermophysical and optical properties of the fabrics, e.g., presence of the moisture increases the effective thermal conductivity and specific heat of fabrics. What is more, in the emergency situation thermochemical reactions in the fibres and changes in the fabric structure as well as in their effective optical and thermophysical properties may also appear as a results of substantial increase of the clothing temperature. The above description shows that the heat and mass transport phenomena in the multilayer protective clothing are very complex and their modelling is challenging.
The problem of mathematical and numerical modelling of transport phenomena in the protective garments was undertaken many times [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]. However, the complex nature of heat and mass transfer phenomena in the multilayer protective clothing resulted in many simplifications which were introduced into proposed heat and mass transfer models. Therefore, development of thermal models of the protective garments should be accompanied by carefully credibility analysis. In other words the obtained results should be verified against benchmark solutions and validated against experimental data. The first significant onedimensional thermal model of a single flameresistant fabric layer for heating period under high heat flux conditions was developed and validated by Torvi and Dale [1]. The model was farther extended to account for multilayer nature of the protective clothing and presence of a cooling period after thermal exposition by Torvi and Threlfall [2]. Both models dealt with conductiveradiative heat transfer in the fabric and across the air space between the fabric and test sensor which measured temperature on the skin side. Heat conduction in the sensor was also included. The absorption of thermal radiation in the fabric was modelled applying the simplified Beer’s law based model. Moreover, thermochemical reactions in the textile layers, which affected fabric thermal properties, were accounted for. The Finite Element Method was used to solve the resulting governing equations. The temperature variation predicted by applying the developed numerical models [1, 2] and Stroll seconddegree burn criterion [1] were compared with those determined experimentally. Very good agreement of the obtained results was found. In the next paper Mell and Lawson [3] developed conductiveradiative heat transfer model in a clothing assembly composed of several fabrics separated by the thin air gaps. They accounted for radiative heat transfer in this multilayer clothing in a simplified way using twostep approach. In the first step the textile layers were assumed semitransparent and the Beer’s law based model was applied with averaged optical properties of fabrics obtained by integrating their wavelength dependent values. Then in the second step the air gaps were assumed transparent and limited by infinitely thin textile layers (planes) which absorbed, transmitted and reflected thermal radiation. The credibility analysis of the model was based on the verification, using solution of the simplified analytical problem, and on the validation using measurements carried out for the threelayer protective turnout coat. Accuracy of the model was found very well. Subsequently, Song et al. [4] developed a numerical thermal model to predict the skin burn injury resulting from heat transfer through a singlelayer protective garment worn by an instrumented manikin submitted to laboratorycontrolled flash fire exposures. The model dealt with conductive and radiative heat transfer in a similar manner to models described in [1, 2, 3]. Moreover, the model accounted for characteristics of the experimentally simulated flash fire generated in the test chamber, the heatinduced variation in the fabric thermophysical properties and the air gap between the garment and the manikin. The model was validated using an instrumented manikin fire test system. The first onedimensional model, which accounted for conjugated conductive and radiative heat transfer accompanied by the moisture transport in the multilayer firefighter protective garment during the flash fire exposure and subsequent cooling process, was developed by Chitrphiromsri and Kuznetsov [5] and then validated by Song et al. [6]. They treated the fabrics as a multicomponent hydroscopic porous structure which consisted of the solid fibres, bound water and the mixture of dry air and water vapour. Radiative heat transfer was modelled in a simplified way with Beer’s law based model similarly as in the previous papers [1, 2, 3]. The validation of the developed model was based on the experimental results obtained for different fabric systems (i.e., from one through two to multilayer ones) and for different system configurations (i.e., without and with an air gap between the garment and the sensor). Good matching between model predictions and experimental measurements was found. Subsequently, Ghazy and Bergstrom [7, 8] developed a thermal model of the protective gear composed of a singlelayer fire resistant fabric [7] and of three fabric layers separated by two air gaps [8]. They dealt in a more sophisticated way with the air gap between the fabric and the sensor (skin simulant) than in the previous models [1, 2, 3, 4, 5, 6]. Namely, the simplified Beer’s law based model was used to account for absorption of the incident thermal radiation in the semitransparent textile layers while the radiative transfer equation was solved in the air gaps with the fixed value of absorption coefficient. The model for a single fabric layer was validated by applying data from the thermal protective performance tests. Numerically calculated variation of the temperature of the sensor (skin simulant) during both the exposure and cool down periods closely followed the experimental observations. The next model of a coupled heat and moisture transfer during combined drying and pyrolysis process of the wet fabrics was developed and validated by Zhu and Li [9]. The drying process was described by the onestep chemical reaction. Moreover, the model included heatinduced changes in the fabric thermophysical properties following from the pyrolysis. The model was validated using experimental data from modified radiant protective performance tests of a single cotton fabric. The comparison showed that predictions of mass loss rates, temperature profiles in the charring fabric and skin simulant as well as the required time to the second degree skin burn were in reasonably good agreement with the experimental results. Another thermal model dealing with the flameresistant fabric which shielded the cylinder simulating human limb and exposed to convective and radiative heat fluxes from a fire was proposed by Zhu et al. [10]. The model was based on the model developed in [1] and accounted for heat induced changes in the fabric and dry air thermophysical properties. The results of simulations were validated by experimental tests. The calculated temperature variations at the front and back side of fabric and at the skin simulant were compared with experimentally measured distributions for the single textile layer. Satisfactory accuracy of the predictions was found. An integrated numerical simulator, which combined one and threedimensional modelling and enabled both the estimation of burn injuries originating from fire disasters as well as the assessment of the quality of the protective clothing, was reported by Jiang et al. [11]. The onedimensional inhouse model accounted for radiativeconductive heat transfer in the clothing and human skin simulant, while threedimensional model, which was implemented in the generalpurpose computational fluid dynamics software, allowed to determine fluid flow and heat transfer in an in situ fire event. Both models were coupled in a doubleway. The predicted temperature distributions in the clothing, heat fluxes on the skin simulant surface and the burn degrees agreed reasonably well with the experimental data conducted by applying the fullscale benchmark aperture. Recently, Fu et al. [12] modelled onedimensional heat and moisture transport in the multilayer protective garment with the air gaps exposed to low levels of thermal radiation emitted in the surroundings. The proposed model accounted for absorption of thermal radiation by the water vapour which was presented in the pores of the fabrics and in the air gaps. Numerical results compared well with the experimental ones. In the latest paper Udayraj et al. [13] proposed a realistic and detailed threedimensional transient numerical model of fluid motion and heat transfer through the air gap between the fabric and test sensor. The model accounted for coupled conduction, convection and radiation in the system. The effect of the horizontal and vertical air gap orientations as well as the dynamic variation of air gap size on the sensor temperature and heat flux, thermal protection ability and fluid flow patterns in the gap were analysed. The heat transfer in the clothing was not accounted for. Prediction of the model were compared with the available experimental results for various air gaps and the agreement with the obtained results was found satisfactory. The model was then coupled with the Pennes bioheat transfer model in the human skin and influence of the air gap width and orientations as well as heterogeneous air gap on the skin burn were investigated [14].
Recently, a new onedimensional model of heat and moisture transfer in the multilayer protective garments exposed to high radiative heat flux emitted by the external heat source was proposed by Łapka et al. [15, 16, 17]. The developed model in a detailed and rigorous way accounted for thermal radiation which was emitted by the external heat source, penetrated the fabrics and air gaps and was absorbed by the human skin or skin simulating material. The semitransparent porous and hygroscopic textile layers were assumed nongrey and absorbing, emitting and scattering thermal radiation. Additionally, the model accounted for optical phenomena, i.e., either reflection and transmission or absorption, emission, reflection and transmission of thermal radiation at interfaces separating different layers of the clothing. Moreover, complex energy and moisture balances as well as optical conditions at the internal or external interfaces were formulated in order to account for exact values of temperatures, vapour densities and radiation intensities at these interfaces. The proposed model was then applied to study influence of different heat transfer modes on temperature distribution in the protective clothing and skin [18], compare different bioheat transfer models used in the assessment of burns injuries [19] and evaluate the human skin surface temperature in the protective clothingskin system based on the protective clothingskin imitating material results [20]. Although, the model predictions were reasonable, its accuracy has been not validated. Only simplified verification was carried out [21]. Therefore, a wide verification and validation analyses of the developed model are carried out in this paper. The three step credibility analysis of the model is proposed. In the first step the influence of spatial, time, angular and wavelength discretization levels on the solution convergence were investigated. Then in the second step the model predictions for several simplified cases were compared with the results obtained by applying the commercial software. Finally, in the last step the results obtained using the developed model were compared with the experimental data obtained during the exposure of the multilayer protective clothing to high radiative heat flux emitted by the IR lamp.
2 Mathematical formulation
2.1 Heat and mass transfer in the fabrics and air gaps as well as heat transfer in the plate
The respective symbols in Eqs. (1)–(4) denote: c_{ p } – specific heat at constant pressure, D_{ ef } – effective mass diffusivity, k_{ ef } – effective thermal conductivity, q_{ r } – radiative heat flux, T – temperature, Δh_{ abs } – heat of desorption, Δh_{ vap } – heat of vaporization, ε – volume fraction, ρ – density and (ρc)_{ ef } – effective heat capacity. The sum of volume fractions satisfied the following constraint: ε_{ bw }+ε_{ f }+ε_{ g } = 1 or ε_{ g } = ε_{ a }+ε_{ v } = 1 in the fabrics or in the air gaps, respectively. In the equations above the subscripts: a, bw, f, g, p, w, and v correspond to: dry air, bound water, dry fabric, moist air, plate, liquid water and water vapour, respectively. The relation for the mass rate of transition of moisture from the bounded to gaseous states in the fabric layers was assumed as: \( {\dot{m}}_{v bw}={D}_f{\uprho}_f/{d}_f^2\left({R}_{f, eq}{R}_f\right) \), where: d_{ f } was the average fibre diameter, D_{ f } – effective diffusivity of bound water in the solid phase (fibres), R_{ f } – fibre regain and R_{f,eq} – equilibrium fibre regain. More details related to calculations of effective properties and other quantities in Eqs. (1)–(4) can be found in [5, 6, 15, 16, 17].
2.2 Radiative heat transfer
2.3 Boundary, interface and initial conditions

The left external surface (see Fig. 1):

For the transparent interface

For the semitransparent interface:

The interface between the fabric layers and air gaps or between two fabric layers if there is no air gap (where: L and R denote the left and right side of the interface, respectively):

For the transparent interface:

For the semitransparent interface:

The internal surface of the plate (where: L denotes the left side of the interface, i.e., either the air in the gap or the fabric):

The right external surface of the plate:
In the above equations subscripts and superscripts: a, c, e, f, h, i, in, p, s, w, L and R denote the air, cooling water, surroundings, fabric, hot gases or source of thermal radiation, interface, incident, internal surface of the plate, external surface of the plate, clothing external surface, left and right side of the interface, respectively, while E_{ b } is the blackbody emissive power [22], h and h_{ m } – convective heat and mass transfer coefficients, respectively, n – refractive index, q – heat flux, r – hemispherical surface reflectivity [22, 25, 26] (for transparent interface r was found by averaging the Fresnel reflectivity over the hemisphere), respectively, t – hemispherical surface transmissivity and ε – surface emissivity.
The unknown interface temperatures: T_{ w }, T_{ i }, T_{ p } and T_{ s } as well as water vapour densities: ρ_{v,w}, ρ_{v,i} and ρ_{v,p} were calculated from Eqs. (6), (12), (18) and (22) as well as Eqs. (7), (13) and (19), respectively. The boundary conditions at the external and internal interfaces for the radiative transfer equation, Eq. (5), were given by either Eqs. (8), (14a, 14b) and (20) or (10), (16a, 16b) and (20). The Eqs. (8) and (14a, 14b) assumed diffusive reflection and transmission of the incident radiation due to different values of refractive index on both sides of interfaces, while Eqs. (10) and (16a, 16b) emission and diffusive reflection and transmission of the incident radiation. For more details see [24, 25, 26]. Initial conditions for Eqs. (1)–(4) corresponded to the steady state distributions of temperature, volume fraction of the bound water and water vapour density in the whole system which was in contact only with the surroundings at temperature T_{ e } and relative humidity ϕ_{ e }.
3 Numerical solutions
4 Data for simulations
4.1 Model setup for verification analyses
Thicknesses [mm] of the fabrics and air gaps – verification analyses
I layer  I gap  II layer  II gap  III layer  III gap 

0.56  0.1  0.73  0.1  1.66  6.35 
Thermophysical properties of fabrics – verification analyses (R_{f,ϕ=0.65} – fibre regain at ϕ = 0.65, τ – tortuosity factor, other quantities explained in the text)
I layer  II layer  III layer  

ρ_{ f } [kg/m^{3}]  1384.0  1295.0  1380.0 
c_{ f } [J/kg/K]  1420.0  1325.0  1200.0 
k_{ f } [W/m/K]  0.179  0.144.0  0.130 
ε _{ f }  0.334  0.186  0.115 
R _{f,ϕ=0.65}  0.084  0.038  0.045 
τ _{ f }  1.5  1.25  1.0 
D_{ f } [m^{2}/s]  6.0⋅10^{−14}  6.0⋅10^{−14}  6.0⋅10^{−14} 
d_{ f } [m]  1.6⋅10^{−5}  1.6⋅10^{−5}  1.6⋅10^{−5} 
Optical properties of the grey fabrics – verification analyses
K_{e,f} [1/m]  n _{ f }  

I layer  8223.6  1.19 
II layer  6308.4  1.11 
III layer  2774.2  1.07 
Optical properties of the nongrey fabric – verification analyses
λ_{1} [μm]  λ_{2} [μm]  K_{a,λ,f} [1/m]  K_{s,λ,f} [1/m] 

0  1.0  1386.3  0.0 
1.0  2.5  2772.6  0.0 
2.5  5.0  5991.5  0.0 
5.0  ∞  opaque  0.0 
4.2 Model setup for validation analysis
Thicknesses [mm] of the fabrics and air gaps – validation analysis
I layer (aramid fibres)  I gap  II layer (Polyurethane laminated Kevlar®)  II gap  III layer (aramid fibres)  III layer (viscose)  III gap 

0.54  0.1  1.13  0.1  1.72  0.39  0.45 
Thermophysical properties of fabrics – validation analysis
I layer  II layer  III layer  IV layer  

ρ_{ f } [kg/m^{3}]  1340.0  1356.0  1340.0  1435.0 
c_{ f } [J/kg/K]  1172.36  1536.26  1797.68  2017.12 
k_{ f } [W/m/K]  0.04  0.117  0.08  0.39 
ε _{ f }  0.2965  0.0924  0.0681  0.2258 
R _{f,ϕ=0.65}  0.04  0.045  0.04  0.075 
τ _{ f }  1.50  1.25  1.0  1.0 
D_{ f } [m^{2}/s]  6.0⋅10^{−14}  6.0⋅10^{−14}  6.0⋅10^{−14}  6.0⋅10^{−14} 
d_{ f } [m]  1.6⋅10^{−5}  1.6⋅10^{−5}  1.6⋅10^{−5}  1.6⋅10^{−5} 
Nongrey optical properties – validation analysis
λ_{1} [μm]  λ_{2} [μm]  T _{λ,f}  K_{e,λ,f} [1/m]  n _{λ,f} 

I layer  
0  0.4  –  opaque  1.24 
0.4  0.7  0.450  416.2  
0.7  2.5  0.225  973.6  
2.5  5.0  0.023  2825.5  
5.0  ∞  –  opaque  
II layer  
0  0.4  –  opaque  1.06 
0.4  0.7  0.610  81.0  
0.7  2.5  0.305  348.4  
2.5  5.0  0.031  1233.3  
5.0  ∞  –  opaque  
III layer  
0  0.4  –  opaque  1.05 
0.4  0.7  0.578  67.5  
0.7  2.5  0.289  242.5  
2.5  5.0  0.029  823.9  
5.0  ∞  –  opaque  
IV layer  
0  0.4  –  opaque  1.15 
0.4  0.7  0.636  191.0  
0.7  2.5  0.318  962.9  
2.5  5.0  0.032  3527.0  
5.0  ∞  –  opaque 
4.3 Default discretization levels

Spatial: each fabric layer and air gap as well as the plate were divided into N_{ l } = 25 elements.

Angular: the polar and azimuthal angles were divided into N_{ θ }×N_{ φ } = 2×4 control angles.

Time: the time step was kept at Δt = 0.05 s.

Wavelength: discretisation depends on assumed number of bands and varied from case to case.
5 Results of simulations
5.1 Verification
5.1.1 Influence of discretization levels
In the first step of verification of the developed model the influence of spatial, time, angular and wavelength discretization levels on the obtained results were investigated, i.e., discretisation convergence tests were carried out. Simulations were performed for the multilayer protective clothing presented in Fig. 1 (three fabric layers and three air gaps) and for three values of the incident radiative heat flux equal to q_{ total } = 20, 40 and 80 kW/m^{2} as well as for three exposure times equal to t_{ e } = 10, 20 and 30 s. Other material properties and parameters assumed during the simulations were described in the section 4.1.
Next studies were performed for the various time steps. Three values were considered: Δt = 0.025, 0.05 and 0.1 s. It was found that decreasing or increasing of the time step had negligible effect on the results obtained, e.g., relative differences between temperature distributions calculated for two different time steps were below 0.1% for all analysed cases.
Subsequently influence of the angular discretization levels were studied. Four divisions of the polar and azimuthal angles were considered: N_{ θ }×N_{ φ } = 2×4, 4×4, 4×8 and 8×8. It was observed that increasing polar angle discretization from N_{ θ } = 2 to 4 and from 4 to 8 had minor effect on relative differences between temperature distributions in the clothing obtained for two different polar angle divisions, but changing the azimuthal angle division from N_{ φ } = 4 to 8 resulted in the greatest relative difference reaching up to 4% between temperature distributions calculated for two different azimuthal angle discretizations. This effect is related to rise in accuracy of calculations of thermal radiation with increasing of the angular discretization level. For the larger number of discrete direction the ray effect is reduced.
Finally influence of the number of radiation bands considered was studied. Simulations were performed for the number of bands equal to: N_{ b } = 1, 4 and 8. Each band had the same constant optical properties which were defined in Table 3. It was found that the number of bands did not affect the obtained results.
5.1.2 Conductiveradiative heat transfer in the single and multilayer clothing system
The next comparison was performed for a system which consisted of the multilayer protective clothing (three fabric layers separated by the thin air gaps), the wide air space and the aluminium plate – see Fig. 1. The boundary conditions at the outer clothing surface and at the internal surfaces between fabric layers and air gaps were assumed the same as in the previous simulation. The clothing configuration and thermophysical data assumed during simulations were given in Tables 2 and 3. Additionally, the fabrics were treated as the nongrey with the same values of optical properties in each layer (Table 4) and with wavelength independent refractive index (Table 3). Other parameters were defined in section 4.1. Again very good agreement between the results from the present numerical simulator and from the commercial code can be noticed in Figs. 5b and 6b. This time the relative difference between the results from the inhouse and commercial software were below 2%. Moreover, the peaks of temperature in the multilayer clothing were observed during the cooling period, but the source of them was the same as in the previous cases. These peaks were higher than for the single clothing layer due to higher thermal resistance to heat flow for the multilayer clothing than for the single fabric.
5.2 Validation

Improper estimation of thermophysical and optical properties of the clothing layers as the nongrey optical properties were not measured but instead were evaluated using the Bamford and Boydell’s method [33].

Large number of input material parameters of the model. Some of them were difficult to estimate and were assumed arbitrary basing on the available literature data.

Neglecting of some phenomena, e.g., heat convection in the porous clothing or chemical reaction in the fabrics which may lead to changes in the fabric properties and structure.

Neglecting temperature variation of thermophysical and optical properties of the fabrics.
Another source of differences between the simulated and measured temperatures may be incorrect assessment of the initial and boundary conditions. The performed experiments were not typical validation experiments [34]. Therefore, the initial and boundary conditions were not strictly controlled during them.
6 Conclusions
The paper presents credibility analysis of the novel advanced numerical simulator of heat and mass transfer in the multilayer protective clothing and in the elements of the experimental stand subjected to either high temperature environment or high incident radiative heat flux emitted by hot objects. The developed numerical model accounted for conjugated conductive and radiative heat transfer in the hygroscopic and nongrey porous fabrics and in the transparent air filling the gaps as well as conductive heat transfer in the opaque components of the stand. Moreover, diffusion of the water vapour in the pores and air spaces as well as phase transition of the bound water in the fabric fibres (sorption and desorption) were included. Complex energy and mass balance as well as optical conditions between the clothing layers were formulated in order to find the values of temperature, vapour density and radiation intensity at these interfaces. The obtained highly nonlinear coupled system of discrete equations was solve by the inhouse iterative numerical algorithm which was based on the Finite Volume Method. Additionally, the unknown temperatures at the external and internal interfaces were calculated using the NewtonRaphson Method, while the Band Model accounted for spectral optical properties.
Subsequently, the correctness and accuracy of the results predicted by the developed model were assessed. At first influence of the spatial, time, angular and wavelength discretization levels on the obtained solutions were investigated. No problems were detected. Despite different discretization levels the results obtained were close to each other. Then, the part of the solver responsible for calculations of transient conductive and radiative heat transfer in the fabrics with the nongrey optical properties and other elements of the system was verified. In these simulations moisture transport was neglected. Two clothing configurations, i.e., the single and multilayer were studied. Afterwards the results obtained were compared with the ANSYS Fluent predictions and very good agreement was observed. Finally the simulated and measured temporal variation of temperature at the outer and inner surfaces of the multilayer protective clothing were compared. The presented numerical model predicted the increase in temperature during the heating period quite well. Greater discrepancies were observed during the cooling stage for which the model underestimates the temperature variation at the outer and inner surfaces. The source of these differences may be related to, e.g., improper estimation of thermophysical and optical properties of the clothing layers, neglecting of some phenomena and drawbacks in validation character of the carried experiments. Having in mind that the developed model requires large number of input parameters the matching of the predicted and measured results seems satisfactory.
Notes
Acknowledgments
This work was supported by the National Centre for Research and Development (Poland) under Grant No. O ROB/0011/03/001 and by the Faculty of Power and Aeronautical Engineering of Warsaw University of Technology in the framework of statutory activity.
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