Handbook of Thermal Science and Engineering pp 885-916 | Cite as

# Modeling of Heat and Moisture Transfer in Porous Textile Medium Subject to External Wind: Improving Clothing Design

## Abstract

This chapter covers convective modeling approaches of heat and moisture transfer in textile materials coupled with human thermal response models. Fabrics are highly porous and relatively thin materials consisting mainly of solid fiber, adsorbed water vapor, and gaseous mixture of water vapor and air in the void space. Fabric ventilation is induced by external wind or body motion which causes the air to penetrate the fabric and transfer heat and water vapor away from the human skin to the environment.

Convective fabric models are developed to predict local and overall clothing ensemble ventilation rates. This modeling approach is combined with segmental bio-heat model to predict human local and overall comfort in hot humid environment. The integration of clothing ventilation models with “cylindrical” segments of the clothed human body is presented showing examples of how segmental and inter-segmental ventilation, sensible heat loss, and moisture transport through clothing are used to assess the whole body comfort.

## Nomenclature

*A*_{f}Area of the fabric (m

^{2})*A*_{i}Inner node area in contact with the outer node (m

^{2})*A*_{o}Outer-node exposed surface area to air flow (m

^{2})*C*_{a}Gas concentration in the micro-climate measurement location (m

^{3}Ar /m^{3}air)- C
_{f} Fiber specific heat (J/kg K)

*C*_{in}Gas concentration in the distribution system (m

^{3}Ar /m^{3}air)*C*_{p}Specific heat of air at constant pressure (J/kg ⋅K)

*C*_{v}Specific heat of air at constant volume (J/kg ⋅K)

*D*Water vapor diffusion coefficient in air (m

^{2}/s)*e*_{f}Fabric thickness (m)

*g*Gravitational acceleration (m/s

^{2})*h*_{ad}Heat of adsorption (J/kg)

*H′*_{ci}Normalized conduction heat transfer coefficient between inner node and outer node (W/m

^{2}⋅K)*H′*_{co}Normalized convection heat transfer coefficient between outer node and air flowing through fabric (W/m

^{2}⋅K)*h*_{c( f-∞)}Heat transport coefficient from the fabric to the environment (W/m

^{2}⋅K)*h*_{c( o-air)}Heat transport coefficient from the fabric to the trapped air layer (W/m

^{2}⋅K)*h*_{c(skin -air)}Heat transport coefficient from the skin to the trapped air layer (W/m

^{2}⋅K)*h*_{fg}Heat of vaporization of water (J/kg)

*H′*_{mi}Normalized diffusion mass transfer coefficient between inner node and outer node (kg/m

^{2}⋅kPa⋅s)*H′*_{mo}Normalized mass transport coefficient between outer node and air void in the fabric (kg/m

^{2}⋅kPa⋅s)*h*_{m(f-∞)}Mass transfer coefficient between the fabric and the environment (kg/m

^{2}⋅kPa⋅s)*h*_{m( o-air)}Mass transfer coefficient between the fabric and the air (kg/m

^{2}⋅kPa⋅s)*h*_{m(skin -air)}Mass transfer coefficient between the skin and the air layer (kg/m

^{2}⋅kPa⋅s)*i*_{m}Permeability index

*k*_{a}Thermal conductivity of air (W/m⋅K)

*h*_{r}Linearized radiative heat transfer (W/m

^{2}⋅K)*L*Fabric length in z direction (m)

- \( {\dot{m}}_{aY} \)
Mass flow rate of air in radial direction (kg/m

^{2}⋅s)- \( {\dot{m}}_{a\theta} \)
Mass flow rate of air in angular direction(kg/m

^{2}⋅s)- \( {\dot{m}}_{aZ} \)
Mass flow rate of air in axial direction (kg/m

^{2}⋅s)- \( {\dot{m}}_a \)
Total ventilation rate (kg/m

^{2}⋅s)*P*_{a}Pressure of the microclimate air (kPa)

*P*_{s}Pressure at the external surface of the fabric (kPa)

*T*_{a}Temperature of the microclimate air (°C)

*T*_{amb}Ambient temperature (°C)

*T*_{skin}Skin temperature (°C)

*T*_{o}Temperature of the fabric outer layer (°C)

*T*_{v}Temperature of the fabric void layer (°C)

*Q*Heat loss (W/m

^{2})*R*Total regain in fabric (kg of adsorbed H

_{2}O/kg fiber)*R*_{D}Fabric dry resistance (m

^{2}⋅K/W unless specified in the equation per mm of thickness)*R*_{E}Fabric evaporative resistance (m

^{2}⋅kPa/W)*R*_{dynamic}The dynamic resistance for ventilation through the fabric (m

^{2}⋅K/W)*R*_{f}Fabric cylinder radius (m)

*R*_{s}Segment cylinder radius (m)

*V*Liquid movement velocity (m/s)

*V*_{∞}Velocities of the environment cross wind (m/s)

*w*Humidity ratio (kg of water/kg of air)

*Y*Air layer thickness (m)

*z*Coordinate in vertical direction (m)

## Greek Symbols

*α*Fabric air permeability (m

^{3}/m^{2}⋅s)*β*The volumetric thermal expansion (°C

^{−1})*μ*Viscosity of air (N·s/m

^{2})*θ*Angular coordinate

- ε
Porosity of fabric

*ρ*_{a}Density of air (kg/m

^{3})

## Subscripts

*a*Conditions of air in the annulus

- fabric
Fabric

*o*Fabric outer node

- void
Fabric void node

- skin
Conditions at the skin surface

- ∞
Environment condition

## References

- Alarabi M, El-Shaarawi MAI, Khamis K (1987) Natural convection in uniformly heated vertical annuli. Int J Heat Mass Tran 30(7):1381–1389CrossRefGoogle Scholar
- American Society for Testing and Materials (1965) ASTM D-39-49. ASTM D39-65 Method of test for construction characteristics of woven fabricsGoogle Scholar
- American Society for Testing and Materials (1983) ASTM D737-75, Standard test method for air permeability of textile fabrics, (IBR) approved 1983Google Scholar
- American Society for Testing and Materials (1985) ASTM D1518: Standard test method for thermal resistance of batting systems using a hot plateGoogle Scholar
- American Society for Testing and Materials, ASTM D737-96 (2012) Air permeability. Standard test method for air permeability of textile fabrics
**,**ASTM OrganizationGoogle Scholar - American Society of Heating, Refrigerating and Air-Conditioning Engineers (2005) ASHRAE handbook of fundamentals. ASHRAE, AtlantaGoogle Scholar
- Anil Lal S, Kumar A (2012) Numerical prediction of natural convection in a vertical annulus closed at top and opened at bottom. Heat Tran Eng 33(15):70–83Google Scholar
- Anil Lal S, Reji C (2009) Numerical prediction of natural convection in vented cavities using restricted domain approach. Int J Heat Mass Transf 52:724–734CrossRefGoogle Scholar
- Chan YL, Tien CL (1985) A numerical study of two dimensional laminar natural convection in shallow open cavities. Int J Heat Mass Transf 28:603–612CrossRefGoogle Scholar
- Chatterjee PK (1985) Absorbency. Elsevier Science Publishing Company, AmsterdamGoogle Scholar
- Danielson U (1993) Convection coefficients in clothing air layers. Doctoral thesis, The Royal Institute of technology, StockholmGoogle Scholar
- Evangellos B, Vrachopoulos M, Koukou M, Margaris D, Filios A, Mavrommatis S (2007) Study of the natural convection phenomena inside a wall solar chimney with one wall adiabatic and one wall under a heat flux. App Therm Eng 27:226–234Google Scholar
- Farnworth B (1986) A numerical model of combined diffusion of heat and water vapor through clothing. Text Res J 56:653–655CrossRefGoogle Scholar
- Fourt L, Hollies NRS (1970) Clothing: comfort and function. Martin Dekker, New YorkGoogle Scholar
- Gagge AP (1973) A two node model of human temperature regulation in FORTRAN. In: Parker JF, West VR (eds) Bioastronautics data, 2nd edn. NASA, Washington, DCGoogle Scholar
- Ghaddar N, Ghali K, Harathani J (2005) Modulated air layer heat and moisture transport by ventilation and diffusion from clothing with open aperture. ASME Heat Transf J 127(3):287–297CrossRefGoogle Scholar
- Ghaddar N, Ghali K, Jreije B (2008) Ventilation of wind-permeable clothed cylinder subject to periodic swinging motion: modeling and experimentation. J Heat Transf 130:1107–2020CrossRefGoogle Scholar
- Ghaddar N, Ghali K, Othmani M, Holmer I, Kuklane K (2010) Experimental and theoretical study of ventilation and heat loss from clothed vertical isothermally-heated cylinder in uniform flow field. J Appl Mech 77(3):1–8CrossRefGoogle Scholar
- Ghali K, Ghaddar N, Bizri M (2011) The influence of wind on outdoor thermal comfort in the city of Beirut: a theoretical and field study. Int J HVAC R res 17(5):813–828Google Scholar
- Ghali K, Ghaddar N, Jones B (2002a) Empirical evaluation of convective heat and moisture transport coefficients in porous cotton medium. J Heat Transf 124(3):530–537CrossRefGoogle Scholar
- Ghali K, Ghaddar N, Jones B (2002b) Multi-layer three-node model of convective transport within cotton fibrous medium. J Porous Media 5(1):17–31CrossRefGoogle Scholar
- Ghali K, Ghaddar N, Jones B (2002c) Modeling of heat and moisture transport by periodic ventilation of thin cotton fibrous media. Int J Heat Mass Transf 45(18):3703–3714CrossRefGoogle Scholar
- Ghali K, Jones B, Tracy J (1994) Experimental techniques for measuring parameters describing wetting and wicking in fabrics. Text Res J 64:106–111CrossRefGoogle Scholar
- Ghali K, Jones B, Tracy J (1995) Modeling heat and mass transfer in fabrics. Int J Heat Mass Transf 38:13–21CrossRefGoogle Scholar
- Ghali K, Othmani M, Jreije B, Ghaddar N (2009) Simplified heat transport model of wind permeable clothed cylinder subject to swinging motion. Text Res J 79:1043–1055CrossRefGoogle Scholar
- Harnett PR, Mehta PN (1984) A survey and comparison of laboratory test methods for measuring wicking. Text Res J 54(7):471–478CrossRefGoogle Scholar
- Havenith G, Heus R, Lotens WA (1990) Resultant clothing insulation: a function of body movement, posture, wind clothing fit and ensemble thickness. Ergonomics 33(1):67–84CrossRefGoogle Scholar
- Havenith G, Holmér I, Parsons KC, Den Hartog E, Malchaire J (2000) Calculation of dynamic heat and vapor resistance. Environ Ergon 10:125–128Google Scholar
- Henry HPS (1939) Diffusion in absorbing media. Proc R Soc 171A:215CrossRefGoogle Scholar
- Ismail N, Ghaddar N, Ghali K (2014) Predicting segmental and overall ventilation of ensembles using an integrated bio-heat and clothed cylinder ventilation models. Text Res J 84:2198–2213CrossRefGoogle Scholar
- Ismail N, Ghaddar N, Ghali K (2016) Theoretical and experimental estimation of inter-segmental clothing ventilation and impact on human segmental heat losses. In: Proceedings of ASME IMECE2015-50255E, Houston, Nov 2015Google Scholar
- Ismail N, Ghaddar N, Ghali K (2016) Effect of inter-segmental air exchanges on local and overall clothing ventilation. Text Res J 86(4):423–439CrossRefGoogle Scholar
- ISO 11092 (EN31092) (1993) Textiles-physiological effects - Measurement of thermal and water-vapor resistance under steady-state conditions (sweating guarded-hotplate test)Google Scholar
- ISO 7730 (2005) Ergonomics of the thermal environment - Analytical determination and interpretation of thermal comfort using calculation of the PMV and PPD indices and local thermal comfort criteriaGoogle Scholar
- Jones BW, Ogawa Y (1993) Transient interaction between the human and the thermal environment. ASHRAE Trans 98(1):189–195Google Scholar
- Ke Y, Havenith G, Li J, Li X (2013) A new experimental study of influence of fabric permeability, clothing sizes, openings and wind on regional ventilation rates. Fibers Polym 14:1906–1911CrossRefGoogle Scholar
- Ke Y, Havenith G, Zhang X, Li X, Li J (2014) Effects of wind and clothing apertures on local clothing ventilation rates and thermal insulation. Text Res J 84:941–952CrossRefGoogle Scholar
- Kind RJ, Jenkins JM, Seddigh F (1991) Experimental investigation of heat transfer through wind-permeable clothing. Cold Reg Sci Technol 20:39–49CrossRefGoogle Scholar
- Leong JC, Lai FC (2006) Natural convection in a concentric annulus with a porous sleeve. Int J Heat Mass Transf 49:3016–3027CrossRefGoogle Scholar
- Li Y, Holcombe BV (1992) A two-stage sorption model of the coupled diffusion of moisture and heat in wool fabrics. Text Res J 62(4):211–217CrossRefGoogle Scholar
- Lotens W (1993) Heat transfer from humans wearing clothing, doctoral thesis. TNO Institute for Perception, SoesterbergGoogle Scholar
- Massey BS (1989) Chapter 6. In: Mechanics of fluids, 6th edn. Springer, New YorkGoogle Scholar
- McCullough EA, Jones BW, Huck J (1985) A comprehensive data base for estimating clothing insulation. ASHRAE Trans 91:29–47Google Scholar
- McCullough EA, Jones BW, Tamura T (1989) A data base for determining the evaporative resistance of clothing. ASHRAE Trans 95(2):316–328Google Scholar
- Minkowycz WJ, Haji-Shikh A, Vafai K (1999) On departure from local thermal equilibrium in porous media due to a rapidly changing heat source: the sparrow number. Int J Heat Mass Transf 42:3373–3385CrossRefGoogle Scholar
- Mohanty AK, Dubey MR (1996) Buoyancy induced flow and heat transfer through a vertical annulus. Int J Heat Mass Transf 39(10):2087–2093CrossRefGoogle Scholar
- Morton WE, Hearle LW (1975) Physical properties of textile fibers. Heinemann, LondonGoogle Scholar
- Nordon P, David HG (1967) Coupled diffusion of moisture and heat in hygroscopic textile materials. Int J Heat Mass Transf 10(7):853–866CrossRefGoogle Scholar
- Othmani M, Ghaddar N, Ghali K (2008) An angular multi-segmented human bio-heat model to assess local segment comfort in transient and asymmetric radiative environment. Int J Heat Mass Transf 51(23–24):5522–5533CrossRefGoogle Scholar
- Patankar SV (1980) Numerical heat transfer and heat flow. Hemisphere Publishing Corporation, McGraw Hill Book Company, New YorkzbMATHGoogle Scholar
- Rees WH (1941) The transmission of heat through textile fabrics. J Text Inst 32:149–165CrossRefGoogle Scholar
- Sobera MP, Kleijn CR, Brasser P, Van den Akker HEA (2003) Convective heat and mass transfer to a cylinder sheathed by a porous layer. AICHE J 49:3018–3028CrossRefGoogle Scholar
- Song G (2007) Clothing air gap layers and thermal protective performance in single layer garment. J Ind Text 36(3):193–204CrossRefGoogle Scholar
- Woodcock A (1962) Moisture transfer in textile systems, part I. Text Res J 32:628–633CrossRefGoogle Scholar
- Zamora B, Hernandez J (2011) Influence of upstream conduction on the thermally optimum spacing of isothermal, natural convection-cooled vertical plate arrays. Int Comm Heat Mass Transf 28(2):201–210CrossRefGoogle Scholar
- Zhang H (2003) Human thermal sensation and comfort in transient and non-uniform thermal environments. PhD thesis, University of California, BerkeleyGoogle Scholar
- Zhang Y, Zhao R (2007) Effect of local exposure on human responses. Build Environ 42:2737–2745CrossRefGoogle Scholar