Моя профессиональная капьепа

Download 1,05 Mb. bet 4/4 Sana 18.02.2022 Hajmi 1,05 Mb. #452506 Turi Сборник

Bog'liq
Научно

	a CIO”7 m2/s)	T (K)	a (10 " 7 m2/s)	T 00	a (10“s m2/s)	T (K)
a (10“8 m2/$)
295.44	1.193	295.56	1.068	295.53	9.843	295.34	9.856
300.34	1.215	300.25	1.072	300.42	9.812	300.41	9.776
305.15	1,219	305.20	1.090	305.13	9.741	305.29	9.771
310.06	1.229	309.99	1.107	309.87	9.710	310.03	9.711
314.74	1.248	314.84	1.108	314.72	9.682	314.82	9.614
319.62	1.272	319.64	1.125	319.95	9.593	319.77	9,581
324.54	1.284	324.49	1.137	324.38	9.581	324.54	9.567
329.31	1.290	329.92	1.145	329.79	9.528	329.41	9.520
334.02	1.312	333.92	1.146	334.10	9.450	334.24	9.421

which are caused by deviations from one - dimensional heat conduction, and cancel these errors from the measured thermal diffusivity value. The relaxation time of the first-order diffracted intensity r and the modulus q of the grating vector can be determined to accuracies of about 1 % and _+0.55%, respectively. Hence, the accuracy of the measurements of thermal diffusivity is estimated to be about -t-1.5% [9, 11, 12]. As shown in Table 1, the thermal diffusivity of aqueous solutions of methanol tends to in-crease with increasing temperatures when the weight frac-tion of water in the solutions is greater than that of methanol . For solutions with 60% and 80% methanol, thermal diffusivity a decreases with increasingly higher temperature . The temperature dependence of the thermal diffusivity of aqueous solutions of methanol on the weight fraction of methanol can be explained with the fact that the thermal diffusivity of pure methanol decreases with increasing temperatures . In comparison, thermal diffusiv-ity of water has a tendency to increase in the temperature range 295 - 335 K when temperature T increases [13].

As there have been no experimental data on the ther-mal diffusivity of aqueous solutions of methanol reported up to now, we found the density and the specific heat capacity data available in [15, 16] and calculated the thermal conductivity of aqueous solutions of methanol using the thermal diffusivity data in Table 1. F r o m Figs. 6 and 7, the derived thermal conductivity values show very good agreement with the experimental results of [2, 15]. The deviations of the derived thermal conductivity values from the data in [2, 15] are within + 3%.
PRACTICAL SIGNIFICANCE/USEFULNESS
For many technical processes, knowledge of the thermal conductivity or thermal diffusivity of liquids is highly im-portant. However, few exact experimental data for these properties are available because of difficulties of conven-tional measurement techniques such as heat losses and we get the values of the coefficients c o and c 1 for the aqueous solutions of methanol by the method of least squares and show them with their variances, the statistical deviations, and correlation coefficients of the fits in Table 2.
w* c„ (10 ⁷ m²/s) c, (10 ¹⁰m²/s-K) a (%) r

100% 2.030 ± 0.061^b -3.487 ± 0.194^b ±0.73^b 0.989^b
Table2. Results for the Least-Squares Fit of Thermal Diffusivity of Aqueous Solutions of Methanol as a Function of Temperature


Figure 6. Thermal conductivity X of aqueous solutions of methanol at 295 K as a function of weight percent w_t of methanol.


Figure 7. Thermal conductivity X of aqueous solutions of methanol at 313 K as a function of weight percent w_t of methanol.
The convective and radiative contributions to the heat transfer in the sample. Photon correlation spectroscopy (PCS, dy-namic Rayleigh scattering) can be used to measure the thermal diffusivity of transparent, pure liquids and their binary mixtures, avoiding all the problems of conventional measurement techniques. However, it was found that sub-stances like water and aqueous solutions, whose Landau - Placzek ratio is very large, cannot be investigated by PCS because of a large Brillouin contribution [7, 17]. The laser-induced thermal grating technique can be used for accurate determination of the thermal diffusivity of liquids. Using the relationship X = apc_p, the thermal conductivity can be calculated, provided the values for p und Cp are available.

Compared with other optical meth-ods, for example, PCS, this technique has the advantage that it can be applied to all transparent or semitranspar-ent liquids and liquid mixtures. In particular, its applica-tion to high-temperature molten salts and anisotropic materials (e.g., flowing polymer melts) is most promising. In the measurement, only a very small sample volume is necessary (a few cubic millimeters), and the measuring time is very short (a few milliseconds). Because of the small temperature rise (AT < 0.2 K) in the sample during the measurements and the very short measuring time, the influence of convective heat transfer is negligible. Moreover, this measurement technique produces abso-lute values without calibration procedures. Hence, the laser-induced thermal grating technique is suitable for accurate, rapid determination of the thermal diffusivity of liquids over an extended temperature range.

CONCLUSIONS
The thermal diffusivity of aqueous solutions of methanol has been measured at atmospheric pressure and in an extended range of temperature from 295 to 335 K. The measurements were carried out using a laser-induced thermal grating technique, which is an absolute method and can be applied to all liquids and their mixtures. The derived thermal conductivity values from the measured thermal diffusivity, the density, and the available specific heat capacity data show very good agreement, within _+3%, with previous experimental results.
NOMENCLATURE a thermal diffusivity, m²/ s amplitude of the diffracted signal, V c₀ coefficient, dimensionless c_± coefficient, dimensionless C p isobaric specific heat, //( к g • K)
C background of the signal, V d sample thickness, m
I_± intensity of the first-order diffracted beam, W / m² n refractive index, dimensionless q modulus of the grating vector, m - 1 r correlation coefficient, dimensionless t time, s t_h heating pulse duration, s T temperature, K V voltage, V W_± weight percentage, %
X coordinate direction, m
Greek Symbols
Д n ( t ) modulation of refractive index, dimensionless
Д T ( t ) amplitude of the transient periodic temperature field, K
AX distance between the two peaks of the diffracted intensity distributions, m
At sample time, s
в intersection angle, deg
6_S diffraction angle, deg A grating constant, m
Л thermal conductivity, W / ( m * K)
A_h wavelength of heating laser beam, m A_p wavelength of probing laser beam, m p density, к g / m³ о statistical deviation, % т relaxation time, s

_m maximum phase variation of the grating, dimensionless
REFERENCES

1. 
   Wakeham, W. A., Nagashima, A., and Sengers, J. V,, Experimen-tal Thermodynamics, Vol. III, Measurement of the Transport Prop-erties of Fluids, Blackwell, Oxford, UK, 1991.
   
2. 
   Assael, M. J., Charitidou, E., and Wakeham, W. A., Absolute Measurements of the Thermal Conductivity of Mixtures of Alco-hols with Water, Int. J. Thermophys. 10(4), 793-803, 1989.
   
3. 
   Eichler, H. J., Salje, G., and Stahl, H., Thermal Diffusion Mea-surements Using Spatially Periodic Temperature Distributions Induced by Laser Light, J. AppL Phys. 4(12), 5383-5388, 1973.
   
4. 
   Pohl, D. W., Schwarz, S. E., and Irniger, V., Forced Rayleigh Scattering, Phys. Rev. Left. 31(1), 32-35, 1973.
   
5. 
   Urbach, W., Hervet, H., and Rondelez, F., Thermal Diffusivity Measurements in Nematic and Smectic Phases by Forced Rayleigh Light Scattering, Mol. Cryst. Liq. Cryst. 46, 209-221, 1978.
   
6. 
   Nagasaka, Y., Hatakeyama, T., Okuda, M., and Nagashima, A., Measurement of Thermal Diffusivity of Liquids by the Forced Rayleigh Scattering Method: Theory and Experiment, Rev. Sci. lnstrum. 59(7), 1156-1168, 1988.
   
7. 
   Wu, G., Fiebig, M., and Wang, J., Determination of the Thermal Diffusivity of Liquids by Laser Induced Thermal Grating, Fluid Phase Equil. 88, 239-249, 1993.
   
8. 
   Eichler, H. J., Giinter, P., and Pohl, D. W., Laser-lnduced Dy-namic Gratings, Springer-Verlag, Berlin, 1986.
   
9. 
   Wang, J., Messung der Temperaturleitfdhigkeit yon Fliissigkeiten mittels laserinduzierter thermischer Gitter Fortschritt-Berichte VDI, VDI-Verlag, Diisseldorf, 1995.
   
10. 
    Brunner, W., and Junge, K., Lasertechnik, Eine Einfuhrung, 4th ed., VEB Fachbuchverlag, Leipzig, 1989.
    
11. 
    Wang, J., Fiebig, M., and Wu, G., Numerical Simulation and Error Analysis for Thermal Diffusivity Measurements Using Laser Induced Thermal Grating Technique, Int. J. Thermophys. 17(2), 329-349, 1996.
    
12. 
    Wang, J., and Fiebig, M., Measurement of Thermal Diffusivity of Aqueous Solutions of Alcohols by a Laser Induced Thermal Grating Technique, Int. J. Thermophys. 16(6), 1353-1361, 1995.
    
13. 
    VDI-Gesellschaft Verfahrenstechnik und Chemieingeneurwesen (GVC), VDl-grdrmeatlas VDl-Verlag, Diisseldorf, I991.
    
14. 
    Wang, J., and Fiebig. M., Bestimmung der Temperaturleit-f~ihigkeit von Toluol und Methanol mittels laserinduzierter ther-mischer Gitter, Heat Mass Transfer 31, 83-87, 1995.
    
15. 
    Blanke, W., Thermophysikalische Stoffgr6ssen, Springer-Verlag, Berlin,
    

1989.

16. 
    Perry, R. H., and Green, D., Perry's Chemical Engineers' Hand-book, 6th ed., McGraw-Hill, New York, 1984.
    
17. 
    Hinz, B., Simonsohn, G., Hendrix, M., Wu, G., and Leipertz, A., The Superposition of Rayleigh and Brillouin Radiation in Photon-Correlation Spectroscopy of Liquids, J. Mod. Opt. 34(8), 1093-1106, 1987.
    

Download 1,05 Mb.

Do'stlaringiz bilan baham: