Application of the Quasi-Regular Cooling Regime Method to Experimental Determination of the Thermophysical Parameters of Textile Materials

We have experimentally established that the surface temperature of vertically positioned flat samples, made from textile materials and previously uniformly heated to temperatures in the range 60°-80°C, under natural convection conditions varies with time according to a single law defined by two constants m and μ, respectively having the meaning of cooling rate and the change in cooling rate. The parameters m and μ of the cooling curve depend on the geometric and thermophysical characteristics of the test materials. We give a theoretical explanation for the time dependence of the cooling curve, based on solution of the nonlinear thermal conductivity problem. Based on the constructed theory, we find the correlation between the parameters of the cooling curve and the thermophysical characteristics of textile material. We propose an analytical method for using the values of the constants of the cooling curve to determine the thermophysical constants of textile materials. We show that the overall accuracy in the determination of the thermophysical constants of materials from the cooling curve is mainly limited by the measurements of the geometric characteristics of the samples, and is within 5% of the values of the thermophysical constants. We have conducted experimental studies to determine the thermal conductivity coefficient for needlepunched nonwoven fiber material as a function of the thermophysical parameters of its constituent components. The studies allowed us to find a quantitative correlation between the composition of the nonwoven material and its thermal insulation properties.

Appendix

Quasi-regular cooling regime theory is based on the assumption that there is a continuous transition of the system from one configuration of the temperature field, corresponding to the regular cooling regime with a given Biot number, to another one with a new value of the Biot number, as occurs in the conventional adiabatic approximation in the dynamics for any process. It is physically obvious that regardless of the initial temperature distribution in the system, a cooling regime is rather rapidly established corresponding to nonlinear boundary conditions, for which the configuration of the temperature field does not depend on the initial conditions and is determined only by the parameters Bi and b. To what extent the cooling curve has a shape close to that which is obtained for the condition that the quasi-regular cooling regime occurs, can be determined only by numerical integration of the system of equations describing the process of cooling the system, and thus the range of application of the quasi-regular cooling regime theory can be found.

Fig. 8 shows the numerical solutions of the system of equations describing the time dependence of the temperature during cooling of a previously uniformly heated sample [11]. In order to present the calculation results as a dimensionless temperature, we used the quantity θ = u/t ₀, where t ₀ is the ambient temperature. With no loss in generality, we can assume that t ₀ is equal to 20°C.

Fig. 8

Results of numerical calculations for cooling curve: 1) b ₀ = 0.17; 2) b ₀ = 0.34.

We give two graphs for the time dependence of the dimensionless surface temperature of a flat layer for two values of the parameter b. For convenience in comparing the results of the numerical calculations, instead of the parameters Bi and b we chose the parameters Bi _m and b ₀. The first parameter gives the value of the Biot number at the time the cooling process begins at temperature θ_m, equal to the initial temperature of the heated sample. This is the maximum possible temperature. The second parameter determines the rate of decrease in the Biot number as the temperature decreases. The relationship between these parameters is defined by the simple formulas

$$ \mathrm{B}{\mathrm{i}}_m=\overline{\mathrm{Bi}}\left(1+b{\theta}_m\right),{b}_0=\frac{b}{1+{\theta}_mb}. $$

The curves were calculated for Bim = 1.7 and the two values b0 = 0.17 (curve 1) and b0 = 0.34 (curve 2). The crosses indicate the calculation results for the same temperatures according to the quasi-regular regime theory. From the figure we see that if in the dimensionless time Fo = aτ/δ² = 1 the Biot number does not change by more than 50% of the initial value, the results match within 1%. For a faster rate of decrease in Bi, the calculations according to the quasi-regular regime theory are less accurate (see curves 1 and 2 in Fig. 8). The change in Bi for curve 2 is greater than 75%.

The result obtained is practically independent of the Biot number Bi. Therefore the range of application of the quasi-regular regime theory is a relatively large interval of change in the heat transfer coefficient for the sample surface with a change in temperature, for unchanged thermal conductivity coefficient of the material: up to 50% of the initial value. In the temperature interval from room temperature up to 100°C and for existing nonwoven materials, these conditions are certainly met.