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Finite volume solution of heat and moisture transfer through three-dimensional textile materials. (English) Zbl 1365.76156

Summary: This paper focuses on the numerical study of heat and moisture transfer in three-dimensional clothing assemblies, based on a multi-component and multiphase flow model, which includes heat/moisture convection and conduction/diffusion as well as phase change (in the form of the condensation/evaporation and vapor absorption by fiber). A class of flux type boundary conditions is used for the clothing assemblies. To maintain physical conservations, a splitting semi-implicit finite volume method on a structured hexahedron mesh is proposed for solving the system of nonlinear convection-diffusion-reaction equations, in which the calculation of liquid water content absorbed by fiber is decoupled from the rest of the computation. Four types of clothing assemblies are investigated and comparisons with experimental measurements are also presented.

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage
80A20 Heat and mass transfer, heat flow (MSC2010)
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
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[1] Berning T. Three-dimensional computational analysis of transport phenomena and PEM fuel cell. Ph.D thesis, Canada: University of Victoria; 2002.; Berning T. Three-dimensional computational analysis of transport phenomena and PEM fuel cell. Ph.D thesis, Canada: University of Victoria; 2002.
[2] Canuto, C.; Cimolina, F., A sweating model for the internal ventilation of a motorcycle helmet, Comput Fluids, 43, 29-37 (2011) · Zbl 1452.76006
[3] Fan, J.; Luo, Z.; Li, Y., Heat and moisture transfer with sorption and condensation in porous clothing assemblies and numerical simulation, Int J Heat Mass Transfer, 43, 2989-3000 (2000) · Zbl 0969.76085
[4] Farnworth, B., A numerical model of the combined diffusion of heat and water vapor through clothing, Text Res J, 56, 653-665 (1986)
[5] Foss, W. R.; Bronkhorst, C. A.; Bennett, K. A., Simultaneous heat and moisture transport in paper sheets during moisture sorption from humid air, Int J Heat Mass Transfer, 46, 2875-2886 (2002) · Zbl 1049.76622
[6] Henrique, G.; Santos, D.; Mendes, N., Combined heat, air and moisture (HAM) transfer model for porous building materials, J Build Phys, 32, 203-220 (2009)
[7] Hang, X.; Li, J.; Yuan, G., Assistant mesh difference method for parabolic equations on distorted meshes with large aspect ratio, Chinese J Comput Phys, 24, 268-276 (2007)
[8] Li, B.; Sun, W.; Wang, Y., Global existence of weak solution to the heat and moisture transport system in fibrous porous media, J Diff Equat, 249, 2618-2642 (2010) · Zbl 1207.35181
[9] Li, B.; Sun, W., The global existence of weak solution for nonisothermal multicomponent flow in porous textile media, SIAM J Math Anal, 42, 3076-3102 (2010) · Zbl 1277.76106
[10] Ogniewicz, Y.; Tien, C. L., Analysis of condensation in porous insulation, J Heat Mass Transfer, 24, 421-429 (1981) · Zbl 0461.76087
[11] Henry, P. S.H., Diffusion in absorbing media, Proc Roy Soc, 171A, 215-241 (1939) · Zbl 0023.42102
[12] Li, Y.; Zhu, Q., Simultaneous heat and moisture transfer with moisture sorption, condensation, and capillary liquid diffusion in porous textiles, Text Res J, 73, 515-524 (2003)
[13] Fan, J.; Cheng, X.; Wen, X.; Sun, W., 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 (2004)
[14] Huang, H.; Ye, C.; Sun, W., Moisture transport in fibrous clothing assemblies, J Eng Math, 61, 35-54 (2008) · Zbl 1138.76063
[15] Ye, C.; Huang, H.; Fan, J.; Sun, W., Numerical study of heat and moisture transfer in textile materials by a finite volume method, Commun Comput Phys, 4, 929-948 (2008) · Zbl 1364.76122
[16] Ye, C.; Li, B.; Sun, W., Quasi-steady state and steady state models for heat and moisture transport in textile assemblies, Proc Roy Soc Lond Ser A, 466, 2875-2896 (2010) · Zbl 1211.76125
[17] Le, C. V.; Ly, N. G.; Postle, R., Heat and moisture transfer in textile assemblies, Text Res J, 65, 203-212 (1995)
[18] Cheng, A.; Wang, Hong, An error estimate on a Galerkin method for modeling heat and moisture transfer in fibrous insulation, Numer Meth PDEs, 24, 504-517 (2008) · Zbl 1132.76031
[19] Sun W, Sun Z. Finite difference methods for a nonlinear and strongly coupled heat and moisture transport system in textile materials, Numer Math, 2011 (published online).; Sun W, Sun Z. Finite difference methods for a nonlinear and strongly coupled heat and moisture transport system in textile materials, Numer Math, 2011 (published online). · Zbl 1332.76034
[20] Li, D. Y.; Shui, H. S.; Tang, M. J., On the difference scheme of 2-D parabolic equation for non-rectangle mesh, J Numer Methods Comput Appl, 1, 217-224 (1980)
[21] Huang W, Kappen AM. A study of cell-center finite volume methods for diffusion equations. Mathematics research report, 98-10-01, University of Kansas, Lawrence KS66045.; Huang W, Kappen AM. A study of cell-center finite volume methods for diffusion equations. Mathematics research report, 98-10-01, University of Kansas, Lawrence KS66045.
[22] Aavatsmark, I., An introduction to multipoint flux approximations for quadrilateral grids, Comput Geosci, 6, 405-432 (2002) · Zbl 1094.76550
[23] Kershaw, D. S., Differencing of the diffusion equation in lagrangian hydrodynamic codes, J Comput Phys, 39, 375-395 (1981) · Zbl 0467.76080
[24] Morel, J. E.; Dendy, J. E.; Hall, J. M.; White, S., A cell-centered lagrangian-mesh diffusion differencing scheme, J Comput Phys, 103, 286-299 (1992) · Zbl 0763.76052
[25] Fatenejad, M.; Moses, G. A., Extension of Kershaw diffusion scheme to hexahedral meshes, J Comput Phys, 227, 2187-2194 (2008) · Zbl 1136.65080
[26] Fan, J.; Cheng, X.; Chen, Y. S., An experimental investigation of moisture absorption and condensation in fibrous insulations under low temperature, Exp Therm Fluid Sci, 27, 723-729 (2002)
[27] Taylor, R.; Krishna, R., Multicomponent mass transfer (1993), John Wiley & Sons Inc.: John Wiley & Sons Inc. New York
[28] Ye C. Mathematical modeling and numerical simulation of heat and moisture transfer in textile assemblies. Ph.D. Thesis, Hong Kong (PR China): City University of Hong Kong; 2010.; Ye C. Mathematical modeling and numerical simulation of heat and moisture transfer in textile assemblies. Ph.D. Thesis, Hong Kong (PR China): City University of Hong Kong; 2010.
[29] Jones, F. E., Evaporation of water (1992), Lewis Publishers Inc.: Lewis Publishers Inc. Michigan, p. 25-43
[30] van der Vorst, H. A., Iterative Krylov methods for large linear systems (2003), Cambridge University Press: Cambridge University Press Cambridge · Zbl 1023.65027
[31] Saad, Y., Iterative methods for sparse linear systems (1996), PWS Publishing Company: PWS Publishing Company Boston · Zbl 1002.65042
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