STUDY OF THERMAL DIFFUSIVITY IN HEAT-INSULATING MATERIALS

Transcription

1 STUDY OF THERMAL DIFFUSIVITY IN HEAT-INSULATING MATERIALS PAVLA ŠTEFKOVÁ, OLDŘICH ZMEŠKAL Institute of Physical and Applied Cheistry, Faculty of Cheistry, Brno University of Technology, Purkyňova 118, 6100 Brno, Czech Republic, eail: Introduction The building industry is using odern aterials that are usually extreely porous to iprove the theral insulation properties. The perforance of these aterials depends on their therophysical properties. This paper discusses the heat transport properties in glass wool fibers easured by pulse transient ethod and deals with the use of new data evaluation ethod 1. The ethod results fro generalized relations that were designed for study of physical properties of fractal structures. As it is shown these relations are in a good agreeent with the equations used for the description of tie responses of teperature for the pulse input of supplied heat 3, 4, 5. Theral paraeters (specific heat, theral diffusivity and theral conductivity) calculated are corresponding for both ethods. Theory The dependence of fractal structures (characterized by the fractal diension D in E- diension space) teperature on the distance fro heat source h T and on the tie t was deterined 1 using the theory of the space-tie fractal field T Q = ( E D)/ cpρ (4π a t) h exp, (1) 4a t where Q is the total heat transferred to the body fro the heat source with the theral conductivity λ = c ρ a. This relation 3, 4, 5 is applicable for fractal diensions D = 0, 1, p and topological diension E = 3, see Fig. 1.

2 Fig. 1 Heat flow geoetry for a) plane-parallel, b) cylindrical and c) spherical coordinates Euclidean space. Fro this equation the theral diffusivity at the axial tie can be deterined h h a = =, () t f ( E D) t a where f a is a coefficient that characterizes the deforation of the theral field 5. This coefficient is equal to one for the ideal plane source (E = 3, D = ). The axiu teperature of the response for Dirac theral pulse is obtained by introducing of the theral diffusivity () in the ter (1) T = p D E exp ρ Q c E D h π ( E D)/. (3) It is possible to definite the coefficient f a (fractal diension D respectively) for every point of the experiental dependence ln( T T ) f a = E D =, ln( t t ) + ( t t 1) ln( T T ) f a = E D = respectively. (4) ln( t t ) + ( t t 1) The relations on the left side are used for the teperature increase; the relations on the right side are used for the teperature decrease. The value of the coefficient f a could be also affected by the geoetry of saple 5 or by the finite pulse width 6, too. When the value f a is known it is feasible to deterine the paraeters of the studied theral syste.

3 Experiental The Therophysical Transient Tester 1.0 was used for easuring of the responses to the pulse heat. It was developed at the Institute of Physics, Slovak Acadey of Science 6. Theral responses fro Slovak Acadey were used for the data evaluation. The easured saple was round shaped with diaeter R = 0,03. Its density was ρ = 77,9 kg. 3 for its thickness h = 0,0075, the theral conductivity was λ = 0,054 W..K 1. Results The Fig. represents the typical tie responses of teperature for the pulse of input power. The coefficient f a of the fractal heat source for every point of the experiental dependence was calculated using the Eq. (4). The fractal heat source characterizes the distribution of the teperature in the specien in specific tie. Fro the Fig. 3 it is evident that for very short tie there is the value of the fractal diension D and therefore, the plane heat source is fored. The value of the fractal diension decreases with increasing tie value since the heat disperses into the space. Fro the tie τ 1 16 s (the intersection of tangents of the curves) the fractal diension is getting settled to the value D 0,15. The spatial distribution of the teperature in the saple does not change yet in this area. It is possible to deterine the coefficient of the heat source f a0 = 1 and the diffusivity of the specien 7 1 a s fro the extrapolated value of the fractal diension to the tie t = 0 s. This value is identical to value deterined by the Institute of Physic, Slovak Acadey of Sciences, Bratislava.

4 Fig. Theral response of the saple easured by the pulse transient ethod. Fro the descending characteristic we can again deterine, by using (4) for each point of experiental dependence of easured teperature on tie, coefficient f a, fractal diension D of the fractal source of cold presented by specien surface. Fro Fig. 3b it is evident that there are not any cold spots over the surface of specien for tie intervals close to the axiu. With rising tie the value of fractal diension of decreasing teperature is saller again until the value D. This is a fractal diension of the specien surface.

5 Fig. 3 Fractal diension of the heat distribution in the specien fro a) increased and fro b) decreased part of characteristics. Conclusion In this article, the results of theral responses to the pulse of supplied heat evaluations are discussed. To interpret the outcoes, the siplified heat conductivity odel is used 1. The odel is based on expectations 3. Results show the iage of heat distribution in the specien, in various tie intervals after the heat supply fro the source. These evaluations could be used for ore accurate deterination of the theral paraeters of studied atters. References 1. Zeškal O., Buchníček M., Nežádal M., Štefková P., Capoušek R.: Therophysics 003: Theral Properties of Fractal Structure Materials, Kočovce, Zeškal O., Nežádal M., Buchníček M.: Field and Potential of fractal Cantorian structures and El Naschie's infinite theory. Chaos, Solitons & Fractals 004; 19: Carslaw H. S., Jaeger J. C.: Conduction of Heat in Solids. Clarendon Press London 1959, 496 pp. 4. Krepaský J.: Measureent of Therophysical Quantities. VEDA, Bratislava 1969, 87 pp. 5. Kubičár L.: Pulse Method of Measuring Basic Therophysical Paraeters. VEDA, Bratislava and Elsevier Nederland 1990, 344 pp. 6. Boháč V., Kubičár Ľ., Vretenár V.: TEMPMEKO 004, 9th International Syposiu on Teperature and Theral Measureents in Industry and Science: Methodology of paraeter estiation of pulse transient ethod and the use of PMMA as standard reference aterial, Cavtat - Dubrovnik Croatia, 5 June, 004.