Heat and Mass Transfer Investigation in Fabrics: Modeling and
Experimentation

S.Quiniou1, F.Lesage 1, V.Ventenat2 and M.A.Latifi1*
1Laboratoire des Sciences du Génie Chimique, CNRS-ENSIC, 1 rue Grandville, 54001, Nancy Cedex,
France
2 Centre de recherche Décathlon, 4 bd de Mons, 59665, Villeneuve d’Ascq, France
*Corresponding author: latifi@ensic.inpl-nancy.fr


Abstract: In this paper, an investigation of heat
and mass transfer in fabrics used in the
manufacture of comfortable sportswear is
presented. It is based on a model which is
described by partial differential equations
representing the mass balance of free and
adsorbed water and vapour and the heat balance
in the fabric. The model involves several
unknown physical and transfer parameters. Two
specific experimental setups are designed in
order to determine some of these parameters.

Keywords: Heat and Mass transfer – Fabrics –
Modeling – Drying – MMT.

1. Introduction

In the design of sportswear, reliable predictive
models are needed in order to accurately
investigate the transport and transfer properties
of fabrics. These properties are especially
important in the design of comfortable
sports wear items. Moreover the models can be
used in the design of new fabrics which improve
or maximize the comfort during sports practice.
The objective of this work is to develop a fabric
model based on heat and mass transfer balance
equations where several unknown parameters are
involved. Naturally, the prediction quality of the
developed model depends on the accuracy of
determination or estimation of these parameters.
In this paper two experimental setups are
designed in order to determine some of the
unknown model parameters. In the first setup, a
piece of the fabric is placed in a room where the
temperature and relative humidity are fixed. A
controlled amount of water is initially introduced
in the fabric and its drying rate is measured with
time. The second experimental setup is based on
the use of Moisture Manager Tester (MMT)
apparatus and the objective is to determine the
lateral and longitudinal diffusions of a drop of
water placed at the fabric top surface. The
experimental results as well as the model
predictions obtained in these two experimental
setups are presented and discussed.

2. Model development

The model is developed for a fabric where
the transport and transfer of vapor, water and
heat are involved. It consists of a system of
partial differential-algebraic equations with
associated initial and boundary conditions [1].
The algebraic part of the system is mainly
constituted by a relation describing adsorption
equilibrium.
The resulting model equations contain several
unknown physical and transfer parameters. Some
of them are determined through the experiments
carried out and presented in the next section.

3. Experimental setups

3.1. Drying rate

In this experimental setup, a piece of the
fabric is placed in a room where the temperature
and relative humidity are monitored. A fixed and
known amount of water is initially introduced in
the fabric and its time-varying drying rate is
measured.
Typical measurements are presented in figure 1.
For this specific fabric, the drying rate decrease
linearly with time.
In the modeling of this experiment, we assume
that only free water in the fabric is evaporated.
We assume also that the effects of gas phase are
negligible in this process. The resulting is given
by the two following equations:

- Free water :

evap
LGLLL
LL D
t
jerer . (3.1)


Excerpt from the Proceedings of the COMSOL Users Conference 2006 Paris

- Heat balance :

evap
LGV
P hT
t
TC jlr . (3.2)
The parameters involved in this model are the
diffusion coefficient of water in liquid phase LD ,
heat conductivity l and gas/liquid mass transfer
coefficient GLk .

Figure 1. Drying rate of the considered fabric.

3.2. Moisture Manager Test

The Moisture Manager Test apparatus [2] is
used to determine the liquid spreading and
transfer rates of a fabric. Its schematic
representation is given in figure 2.



Figure 2. Schematic representation of the MMT

The principle of the method is based on the
change of the electrical resistance of the fabric
with its water content. Six concentric rings
(sensors) of different sizes are then placed on
both surfaces of the fabric. The distance between
two consecutive rings is 5 mm except the first
one which is at 1.5 mm from the centre. They
allow us to measure the spreading and transfer of
a 0.22 g drop of water during 2 minutes. More
specifically they allow to determine the water
content at different ring locations (local) and
consequently on the overall (global) surface.
The typical experimental measurements of water
content (WC) for both top and bottom surfaces
are presented in figure 3. The level and time lag
of different curves show clearly the spreading
rates of water.
In the modeling of MMT experiments, we
assume that the processes involved in the gas
phase do not play an important role and the
whole system is isothermal. The resulting model
is described by the two following equations [3]:

LSSS
S
V
SS D
t
jerer . (3.3)
LSLLL
LL D
t
jerer . (3.4)

The parameters involved in this model are the
diffusion coefficient of water in solid phase SVD ,
heat conductivity LD and gas/solid mass
transfer coefficient LSk .



Figure 3. Top and Bottom Water Content of
the considered fabric

Excerpt from the Proceedings of the COMSOL Users Conference 2006 Paris

4. Simulations with Comsol Multiphysics

4.1. Simulation

The code Comsol Multiphysics was used to
solve the model equations (3.1 – 3.2) and (3.3 –
3.4) with their associated initial and boundary
conditions. For symmetrical reasons, a 2D
geometry was used for the two models.
The variables deduced from the solution of
the two models are: the evaporated amount of
water for the model (3.1 – 3.2) and the water
contents at different rings for the model (3.3 –
3.4). The values of these variables are used in an
optimization problem in order to estimate the
unknown parameters involved in the models.

4.2. Parameter identification

It is noteworthy that the parameters LD and
LSk are identified from the MMT experiments,
whereas GLk is estimated from the drying
experiments. Of course, additional parameters,
like SVD , l , can be included in the identification
process if their values are not available.
The two optimization problem are solved under
Matlab by using the function “fminsearch”
which is a simplex method [1,3].

5. Results and discussion

Figure 4 presents experimental and
simulation results of water content for the first
ring at the top surface of the considered fabric.
It can be seen that the simulation results are quite
in good agreement with the corresponding
experimental measurements.
Similarly, figure 5 presents experimental and
simulation results of the free water weight of the
considered fabric versus time.
Here also the agreement is quite good hence
leading to good estimates of the considered
parameters.

6. Conclusions

The objective of this work is to develop a
model for a fabric where heat and mass transfer
phenomena are involved and to identify some of
the unknown parameters involved through two
specific experiments. The results obtained are
very promising but the estimation process
deserves to be improved especially for the
estimation of the diffusion of water in liquid
phase. Moreover, additional appropriate
experiments should be designed in order to
correctly estimate the parameters which have not
been explored yet.



Figure 4. Water content for the first
ring of the considered fabric.




Figure 5. Free Water Weight






Excerpt from the Proceedings of the COMSOL Users Conference 2006 Paris

7. References

1. Fichet, D., Simulation spatio-temporelle d’un
textile soumis à des transferts couplés de chaleur
et matière.
DEA – ENSIC – INPL, Nancy, France (2005)

2. Hu, J., Li,Y., Wong, A.W.S., Xu, W.,
Management Tester: A Method to Characterize
Fabric Liquid Moisture Management Properties,
Textile Research Journal (submitted).

3. Fichet, D., Lesage, F., Ventenat, V., Latifi,
M.A., Water spreading analysis on fabrics
surfaces, Proceedings of the Comsol
Multiphysics Conference, pp.199 – 204,
November 15, Paris (2005)


Excerpt from the Proceedings of the COMSOL Users Conference 2006 Paris