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Heat and sweat transport in fibrous media with radiation

Published online by Cambridge University Press:  11 March 2014

JILU WANG  and
WEIWEI SUN
JILU WANG
Affiliation:
Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong emails: [email protected], [email protected]
WEIWEI SUN
Affiliation:
Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong emails: [email protected], [email protected]
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Abstract

The paper is concerned with heat and sweat transport in porous textile media with a non-local thermal radiation and phase change. The model, based on a combination of these classical heat transfer mechanisms (convection, conduction and radiation), is governed by a nonlinear, degenerate and strongly coupled parabolic system. The thermal radiative flow is described by a radiation transport equation and characterized by the thermal absorptivity and emissivity of fibre. A conservative boundary condition is introduced to describe the radiative heat flux interacting with environment. With the conservative boundary condition, we prove the global existence of positive/non-negative weak solutions of a nonlinear parabolic system. A typical clothing assembly with a polyester batting material sandwiched in two laminated covers is investigated numerically. Numerical results show that the contribution of radiative heat transfer is comparable with that of conduction/convection in the sweating system.

Keywords

Heat and moisture transferRadiative heat transferPorous mediaGlobal weak solution
Type
Papers
Information
European Journal of Applied Mathematics , Volume 25 , Issue 3 , June 2014 , pp. 307 - 327
Copyright
Copyright © Cambridge University Press 2014 

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References

[1]Canuto, C. & Cimolin, F. (2011) A sweating model for the internal ventilation of a motorcycle helmet. Comput. Fluids, 43, 29–37.Google Scholar
[2]Chapman, A. J. (1987) Fundamentals of Heat Transfer, Macmillan, New York, NY, pp. 463–482.Google Scholar
[3]Cheng, A. & Wang, H. (2008) An error estimate on a Galerkin method for modeling heat and moisture transfer in fibrous insulation. Numer. Methods Partial Differ. Equ. 24, 504–517.Google Scholar
[4]Choudhary, M. K., Karki, K. C. & Patankar, S. V. (2004) Mathematical modeling of heat transfer, condensation, and cappilary flow in porous insulation on a cold pipe. Int. J. Heat Mass Transfer. 47, 5629–5638.CrossRefGoogle Scholar
[5]Cimolin, F. (2006) Analysis of the Internal Ventilation for a Motorcycle Helmet, Ph.D. thesis, Politecnico di Torino, Italy.Google Scholar
[6]David, H. G. & Nordon, P. (1939) Case studies of coupled heat and moisture diffusion in wool beds. Text. Res. J. 39, 166–172.Google Scholar
[7]Davis, L. B. Jr & Birkebak, R. C. (1973) One-dimensional radiative energy transfer in thin layers of fibrous materials. J. Appl. Phys. 44, 4585–4587.Google Scholar
[8]Fan, J., Cheng, X. & Chen, Y. S. (2002) An experimental investigation of moisture absoption and condensation in fibrous insulations under low temperature. Exp. Therm. Fluid Sci. 27, 723–729.Google Scholar
[9]Fan, J., Cheng, X., Wen, X. & Sun, W. (2004) An improved model of heat and moisture transfer with phase change and mobile condensates in fibrous insulation and comparison with experimental results. Int. J. Heat Mass Transfer. 47, 2343–2352.Google Scholar
[10]Farnworth, B. (1983, Dec.) Mechanics of heat flow through clothing insulation. Text. Res. J. 53, 717–725.CrossRefGoogle Scholar
[11]Hang, X., Sun, W. & Ye, C. (2012) Finite volume solution of heat and moisture transport in three-dimensional porous fibrous materials, Comput. Fluids 57, 25–39.Google Scholar
[12]Henrique, G., Santos, D. & Mendes, N. (2009) Combined heat, air and moisture (HAM) transfer model for porous building materials J. Build. Phys. 32, 203–220.Google Scholar
[13]Hou, Y., Li, B. & Sun, W. (2013) Error estimates of splitting Galerkin methods for heat and sweat transport in textile materials SIAM J. Numer. Anal. 51, 88–111.Google Scholar
[14]Huang, H., Lin, P. & Zhou, W. (2007) Moisture transport and diffusive instability during bread baking SIAM J. Appl. Math. 68, 222–238.CrossRefGoogle Scholar
[15]Huang, H., Ye, C. & Sun, W. (2008) Moisture transport in fibrous clothing assemblies. J. Engrg. Math. 61, 35–54.Google Scholar
[16]Jones, F. E. (1992) Evaporation of Water, Lewis, Chesea, MI, pp. 25–43.Google Scholar
[17]Le, C. & Ly, N. G. (1995) Heat and mass transfer in the condensing flow of steam through an absorbing fibrous medium. Int. J. Heat Mass Transfer. 38, 81–89.Google Scholar
[18]Le, C., Ly, N. G. & Postle, R. (1995) Heat and moisture transfer in textile assemblies. Text. Res. J. 65, 203–212.Google Scholar
[19]Li, B. & Sun, W. (2010) Global existence of weak solution for non-isothermal multicomponent flow in porous textile media. SIAM Math. Anal. 42, 3076–3102.Google Scholar
[20]Li, B. & Sun, W. (2012) Global weak solution for a heat and sweat transport system in three-dimensional fibrous porous media with condensation/evaporation and absorption. SIAM J. Math. Anal. 44, 1448–1473.CrossRefGoogle Scholar
[21]Li, B. & Sun, W. (2013) Numerical analysis of heat and moisture transport with a finite difference method. Numer. Methods Partial Differ. Equ. 29, 226–250Google Scholar
[22]Li, B., Sun, W. & Wang, Y. (2010) Global existence of weak solution to the heat and moisture tansport system in fibrous media. J. Differ. Equ. 249, 2618–2642.CrossRefGoogle Scholar
[23]Li, Y. & Zhu, Q. (2003) Simultaneous heat and moisture transfer with moisture sorption, condensation, and capillary liquid diffusion in porous textiles Text. Res. J. 73, 515–524.Google Scholar
[24]Li, Y., Li, F. & Zhu, Q. (2005) Numerical simulation of virus diffusion in facemarsk during breathing cycles, Int. J. Heat Mass Transfer 48, 4229–4242.Google Scholar
[25]Nadela, E. R. (1983) Factors affecting the regulation of body temperature during exercise. J. Therm. Biol. 8, 165–169.CrossRefGoogle Scholar
[26]Ogniewicz, Y. & Tien, C. L. (1981) Analysis of condensation in porous insulation. J. Heat Mass Transfer 24, 421–429.CrossRefGoogle Scholar
[27]Smith, P. & Twizell, E. T. (1984) A transient model of thermoregulation in a clothed human. Appl. Math. Model. 8, 211–216.Google Scholar
[28]Song, G. (2002) Modeling Thermal Protection Outfits for Fire Exposures, Doctoral Dissertation, North Carolina State University, Raleigh, NC.Google Scholar
[29]Sun, W. & Sun, Z. Z. (2012) Finite difference methods for a nonlinear and strongly coupled heat and moisture transport system in textile materials. Numer. Math. 120, 153–187.CrossRefGoogle Scholar
[30]Torvi, D. A. (1997) Heat Transfer in Thin Fibrous Materials Under High Heat Flux Conditions, PhD Thesis, University of Alberta, Edmonton, Alberta, Canada.Google Scholar
[31]Wang, J. & Catton, I. (2001) Evaporation heat transfer in thin biporous media. Heat Mass Transfer 37, 275–281.CrossRefGoogle Scholar
[32]Vasserman, A. A. & Putin, B. A. (1975, November) Logarithmic density dependence of viscosity and thermal conductivity of a dense gas, Odessa Naval Engineers Institute (translated), Inzhenerno-Fizicheskii Zhurnal, 29 (5), 821–824.Google Scholar
[33]Ye, C., Li, B. & Sun, W. (2010) Quasi-steady state and steady state models of moisture transport in porous textile materials. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 466, 2875–2896.Google Scholar
[34]Ye, C. (2010) Mathematical Modeling and Numerical Simulation of Heat and Moisture Transfer in Textile Assemblies. PhD Thesis, City University of Hong Kong, Hong Kong, P. R. China.Google Scholar
[35]Zhang, Q., Li, B. & Sun, W. (2011) Heat and sweat transport through clothing assemblies with phase changes, evaporation/condensation and fibre absorption. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 467, 3469–3489.Google Scholar