Numerical solution of a two-dimensional simulation on heat and mass transfer through cloth

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Abstract

This paper presents a mathematical model for heat and moisture transfer through cloth. A two-dimensional mathematical model, which considers complicated heat and mass transfer is developed. The coupled partial differential equations are created based on integrations of porous medium equations and heat, diffusion equations. A non-linearized implicit finite-difference method is presented to find numerical solutions of the two-dimensional simulation model. Results obtained by the present method are found to agree satisfactorily with the experimental data available in the literature.

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 Ua,Ul,TC02(Ω¯), 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 = . 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

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This work is supported by the Foundation: National Science Fund (ID:60273063), Guangdong Natural Science Fund (ID:031538).

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