INTRODUCTION
The impetus behind a polymeric composite is their ability to be tailored to
any system such as improved thermal resistance (Gao et
al., 2007). As a load is applied to the continuous phase it is then
transferred to the discontinuous, reinforcement phase. The choice and degree
of reinforcing filler (in this study, clay) can then be assigned according to
the requirements of the particular application. Superior performance and the
resulting cost savings have allowed composites to be incorporated into nearly
every aspect of our lives regarding the main environmental effects which are
related to temperature, moisture, radiation and contact with various types of
chemicals. These factors can affect the thermal and the mechanical properties
of the composites in different ways (Selzer and Friedrich,
1995, 1997).
Heat transfer by radiation in materials was investigated theoretically by Mital
et al. (1998). The heat transfer in materials was reported by Dietl
et al. (1998).
The effective conductivity Keff is defined as below (Fricke
et al., 1990):
Keff = Kcond + Kconv + Krad
Where:
Kcond 
= 
The conductivity due to conduction 
Kconv 
= 
The conductivity due to convection 
Krad 
= 
The conductivity due to radiation 
The most of researchers like Mohammadi et al. (2003)
neglect Kconv because the probability of a gas molecule movement through
the structure is minimal. In this study, only Kcond will be studied and determined.
Other researchers like Zhou and Lucas (1995) investigated
the physical mechanisms involved during the perception of composite and fabric
dampness by studying the heat and moisture transfer in the fabric and at the
fabricskin interface (Li et al., 1995; Gautier
et al., 1999), which has been performed by several apparatus such
as thermal manikins (Bhattacharyya, 1980; Mastura,
1994) or other apparatus.
The purpose of this study is to establish a mathematical equation linking the adiathermic power of a nanocoated cotton fabric to clay percentage, fabric thickness, coating and the used resin conductivity and to show how the nanocomposite coatings enhances the thermal insulation of this new hybrid fabric in conjunction with the clay percentage and the sort of resin.
MATERIALS AND METHODS
Ten grams of Tunisian clay added to 100 mL of methylene chloride (CH_{2}Cl_{2}) have been ultrasonicated for 2 h at 25°C (freq. = 28 KHz), in order to have a good dispersion of clay particles. Then the prepared clay solution was added to the resin at different loadings of clay: 5, 20, 40 and 70%.
Five sorts of resin were selected to be mixed with clay: modified DMDHEU, VinylPolyacetate (PVAv), Polyacrylate (PAC), elastic Polyurethane (PU1) and rigid Polyurethane (PU2).
Table 1: 
Adiathermic power percentage in conjunction with the clay
quantity, the deposited quantity and the sort of resin 

Mixtures PU2/70% clay and DMDHEU/70% clay failed because they
became too thick 
These different mixtures resin/clay were deposited on a cotton fabric Sergey
(about 400 g m^{2}) using a coating apparatus with rake pressure and
deposited paste regulations. The deposited quantities of the mixtures are shown
in Table 1. The polymerization of these coatings was carried
out at 150°C during 5 min (Choi et al., 2001)
and after a drying operation during 5 min permitting to water and CH_{2}Cl_{2}
to evaporate.
Then, the thermal isolation properties of the coated materials (three trials for each sample; σ = 0.0344%) were determined by measuring the adiathermic characteristics using a PASOD device for measuring the adiathermic power (Table 1).
RESULTS AND DISCUSSION
The deposited quantity of nanocomposite on the fabric (Qc) and the Adiathermic Power (AP) are shown in Table 1.
Here, we want to calculate the adiathermic power in conjunction with the clay percentage, the deposited quantity and the used resin. Thus, knowing these parameters, the adiathermic power and using some equations, can be determined, without measuring. From Table 1, interpolation equations in this form
AP% = A+B1x + B2x^{2}
where, x is the clay percentage and using the software Origin,
can be determined (Table 2).
Table 2: 
Adiathermic power percentage in conjunction with Qc: AP% =
A+B1x+B2x^{2} 

Table 3: 
Coefficients A, B1, B2 in conjunction with Qc: (A, B1, B2)
= C+D1xQc+D2xQc^{2}+D3xQc3 

The coefficients A, B1 and B2 vary from deposited quantity to another. For this reason, the coefficients have to be interpolated too, in conjunction with Qc Table 3 in this form PA% = A+B1xQc+B2xQc^{2}.
Table 4: 
Calculated and found AP of coated fabrics in conjunction with
the clay percentages, the deposited quantities and the used resin 

Model verification: In order to verify this model, some more samples have to be prepared:
The clay quantities 2.5 and 15% have been mixed with the same resins, but with different amounts, to make deposited quantities equal to 100 and 400 g m^{2}. The obtained adiathermic powers and the corresponding errors are recorded in Table 4.
The model is reliable for all resins (except the DMDHEU resin), for error <2%. The thermal resistances can be easily deduced from a simple computing of the clay percentage and the deposited quantity on the fabric without any measure. This model is no more reliable for other resins or other fabrics.
CONCLUSIONS
In this study, we have developed a method of mathematical stimulating the fabric thermal resistance. The mathematical model has proved to be effective in predicting the fabric thermal resistance, which demands a long time to be evaluated by the concise measurement of the adiathermic power. This good agreement between these values has been demonstrated by mathematical formulas linking the clay percentage, coating, nanocomposite deposited quantities and the used resin. The result of theses computations indicates that clay application in nanocomposites proved its importance because the thermal insulation properties of the fabric are really enhanced according to the clay percentage in the coating. The average of this enhancement is about 20 to 30% and this is upon the used resin, the deposited quantity and the clay percentage present in the nanocomposite.
Besides, the clay percentage is a very important parameter since the high clay
quantities in the nanocomposite generally present the better thermal resistances.
Validation of these results is only possible through direct conductivity measurements.
In this case, then, several parameters like α, β, γ and λ,
predicting the percentages of the series and parallel models in the coated fabric,
can be determined. Work is in progress to develop some theoretical model to
evaluate these findings.