Numerical solution of a two-dimensional simulation on heat and mass transfer through cloth☆
Introduction
Over the last century many researchers have been interested in the subject of heat and moisture transferring through cloth. Downes and Mackay [1] and Watt [2] observed experimentally that the sorption of water vapor by wool fiber is a two-stage process: a fast Fickian diffusion with a concentration dependent diffusion coefficient and a non-Fickian diffusion that is much slower. In 1967, Nordon and David improved Henry’s model by proposing an exponential relationship. In 1992, Li and Holcombe developed a new two-stage model for coupling diffusion of moisture and heat in wool fabrics. In 2002, Wang, Li and Kowk [3], [4] integrated mathematically a fabric heat and moisture transfer model to simulate perception of fabric thermal and moisture sensations. Nishimura and Matsuo [5] presented a numerical discussion of moisture changes with time in a fiber assembly with the help of a two-dimensional model.
All these researches have established a sound scientific foundation on heat and moisture transfer in clothing. Here we introduce a heuristic two-dimensional mathematical simulation model with partial differential differential equations to simulate heat and moisture transfer through cloth.
Section snippets
Statement of problems and mathematical simulation model
The model was developed under the following assumptions:
- 1.
Volume change of the fibers due to absorbing moisture is neglected.
- 2.
The inertial force is ignored due to the relatively low velocities for liquid transfer.
- 3.
Forced convections such as the effect of a wind penetration are neglected.
- 4.
The cloth fabric is isotropic in terms of structure and thermal properties.
Let Ua(x, y, t) = Ca(x, y, t)εa,Ul = Cl(x, y, t)εl, εa + εl + εf = 1, suppose now , they are continuous functions in Ω · Ω = [0, 1] × [0, 1].
Under
Method of solution
The solution domain [x, y] ∈ [0,1] × [0.1], t > 0 are divided into intervals h1, h2 and δ in the direction of the spatial variable x, y and in the direction of time t. So xi = ih1(Ih1 = 1); yj = jh2(Jh2 = 1); t = kδ. volij is the i × jth unit volume. (Ua)ijk(xi, yj, tk) is denoted by (Ua)ijk, (Ul)ijk(xi, yj, tk) is denoted by (Ul)ijk. Second order in space finite volumes is used to discretize the diffusion operator in the vapor and liquid water diffusion equation on a uniform grid. The diffusion coefficients, Dl and D
Numerical solutions and discussion
In this section, numerical analysis and solutions to the two-dimensional model is shown. In computation, the values of the material parameters are listed as follows: τa = 0.9 (effective tortuosity of the fabric batting), εa = 0.6.
For the results shown in Fig. 1, the water concentration in the fabric thickness is reducing with time. Let x = 0, y = 0, we got the Fig. 2. From Fig. 2 we know the concentration of water vapor is linear with time. At the beginning the water concentration is 1, after 1 min the
Conclusion
A dynamic two-dimensional model of heat and moisture transfer in cloth has been established in the paper. In this model, we got the water vapor concentration and liquid water concentration with time. The change on heat and moisture transfer is shown in the simulation results. It accords with the experimental results. It is believed that the 2D new dynamic model cannot only be useful in 3D Garment CAD, but also in other scientific and engineering fields involved heat and moisture transfer in
References (9)
- et al.
Numerical simulation of moisture transmission through a fiber assembly
Textile Res. J.
(2000) - et al.
Sorption kinetics of water vapor in wool fibers
J. Polym. Sci.
(1958) Diffusion in absorbing media
Proc. Roy. Soc.
(1939)Kinetic studies of the wool-water system. Part I. The mechanisms of two-stage absorption
Textile Res. J.
(1960)- et al.
Mathematical simulation of the perception of fabric thermal and moisture sensations
Textile Res. J.
(2002)
Cited by (6)
Influence of chitosan and porosity on heat and mass transfer in chitosan-treated porous fibrous material
2012, International Journal of Heat and Mass TransferCitation Excerpt :The membranes were prepared by cast-drying method, the effects of chitosan concentration, sodium tripolyphosphate concentration and crosslinking tiome on flux and lag time were studied using central composite design. Meanwhile, the coupled heat and mass transfer in porous fibrous material is complex and a lot of researchers [14–16] have placed their emphasis on it. Li and Holcombe [17] studied the coupled diffusion of moisture and heat in wool fabrics and developed an improved mathematical simulation of it.
The skim of balance theory of 3D garment simulation
2011, Applied Mathematics and ComputationHeat transfer-A review of 2005 literature
2010, International Journal of Heat and Mass TransferHeat and moisture transfer in 3D Garment CAD
2008, Proceedings - 2008 2nd International Symposium on Intelligent Information Technology Application, IITA 2008Continuous time M/G/1 queue with multiple vacations and server close-down time
2007, Journal of Computational Information SystemsResearch on modified live-wire interaction segmentation algorithm
2007, Journal of Computational Information Systems
- ☆
This work is supported by the Foundation: National Science Fund (ID:60273063), Guangdong Natural Science Fund (ID:031538).