2-Maxwell-两相导热率比例0.5比204.docx
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1、Izmir Composites Science and Technology 63 (2003) 113117 Thermal conductivity of particle lled polyethylene composite materials . Dilek Kumlutas a,*, Ismail H. Tavmana, M. Turhan C obanb aDokuz Eylul University, Mechanical Engineering Department, Bornova, . 35100, Turkey bTUBITAK Marmara Research C
2、ent., Energy Syst. Environmental Res. Inst., Gebze, Turkey Received 17 January 2002; received in revised form 28 August 2002; accepted 28 August 2002 Abstract In this study, the e ective thermal conductivity of aluminum lled high-density polyethylene composites is investigated numeri- cally as a fun
3、ction of ller concentration. The obtained values are compared with experimental results and the existing theoretical and empirical models. The thermal conductivity is measured by a modied hot-wire technique. For numerical study, the e ective thermal conductivity of particle-lled composite was calcul
4、ated numerically using the micro structural images of them. By identi- fying each pixel with a nite di erence equation and accompanying appropriate image processing, the e ective thermal conductivity of composite material is determined numerically. As a result of this study, numerical results, exper
5、imental values and all the models are close to each other at low particle content. For particle content greater than 10%, the e ective thermal conductivity is expo- nentially formed. All the models fail to predict thermal conductivity in this region. But, numerical results give satisfactory values i
6、n the whole range of aluminum particle content. # 2002 Elsevier Science Ltd. All rights reserved. Keywords: Composite material; Thermal conductivity; Image processing; Finite di erence 1. Introduction Knowing physical properties of the composite mate- rials has gained signicant importance in the des
7、ign of new systems. For many materials applications, infor- mation is needed on their thermal properties. Deter- mining the thermal conductivity of composite materials is crucial in a number of industrial processes. The tem- perature elds in composite materials cannot be deter- mined unless the ther
8、mal conductivities of the media are known. Despite the importance of this material prop- erty and the considerable number of studies that have been carried out, the determination of e ective thermal conductivity of a composite material is partially under- stood. The e ective thermal conductivity of
9、a composite material is a complex function of their geometry, the thermal conductivity of the di erent phases, distribution within the medium, and contact between the particles. * Corresponding author. Tel.: +90-232-3883138-121; fax: +90- 232-3887868. E-mail address: dilex.kumlutasdeu.edu.tr (D. Kum
10、lutas ). Numerous theoretical and experimental approaches have been developed to determine the precise value of this parameter. Maxwell 1 studied the e ective thermal conductivity of heterogeneous materials. By solving Laplaces equa- tion, he determined the e ective conductivity of a ran- dom suspen
11、sion of spheres within a continuous medium. The model developed by Maxwell 1 assumes that the particles are su ciently far apart that the potential around each sphere will not be inuenced by the presence of other particles. Russell 2 developed one of the early model systems using the electrical anal
12、ogy, assuming that the discrete phase is isolated cubes of the same size dispersed in the matrix material and that the isothermal lines are planes. Based on Tsaos 3 prob- abilistic model, Cheng and Vachon 4 assumed a para- bolic distribution of the discontinuous phase. Lewis and Nielsen 5 derived a
13、semi-theoretical model by a modi- cation of the Halpin-Tsai equation 6,7 to include the e ect of the shape of the particles and the orientation or type of packing for a two-phase system. Baschirow and Selenew 8 developed the equation for the case when 0266-3538/02/$ - see front matter # 2002 Elsevie
14、r Science Ltd. All rights reserved. PII : S0 266 -3 538 (0 2)001 94 -X 114 D. Kumlutas et al. / Composites Science and Technology 63 (2003) 113117 2 m the particles are spherical and the two phases are iso- tropic. In real composite material, the isothermal sur- and for series conduction model: 1 1
15、faces present a very complex shape and cannot be analytically determined. The models used to calculate thermal conductivities are thus highly simplied models kc km kf of the real media. Veyret et al. 9 characterized con- ductive heat transfer through composite, granular, or In the case of geometric
16、mean model, the e ective thermal conductivity of the composite is given by: brous materials by using the nite element method. 1 Terada et al. 10 generated the nite element model by identifying each pixel with a nite element and accom- panying appropriate image processing. Deissler and Boegli 11 carr
17、ied out the numerical studies. They pro- posed a solution to Laplaces equation for a cubic array of spheres presenting a single point of contact. Deiss- lers 11 works were extended by Wakao and Kato 12 for a cubic or orthorhombic array of uniform spheres in contact. Shonnard and Whitaker 13 have inv
18、estigated the inuence of contacts on two-dimensional models. They have developed a global equation with an integral method for heat transfer in the medium. In this study, the e ective thermal conductivity of aluminum lled high-density polyethylene composites is investigated numerically as a function
19、 of ller con- centration. The obtained values are compared with experimental results and the existing theoretical and empirical models. kc kf :km 3 Tsao 3 derived an equation relating the two phase solid mixture thermal conductivity to the conductivity of the individual components and to two paramet
20、ers which describe the spatial distribution of the two pha- ses. By assuming a parabolic distribution of the dis- continuous phase in the continuous phase (Fig. 1), Cheng and Vachon 4 obtained a solution to Tsaos 3 model that did not require knowledge of additional parameters. The constants of this
21、parabolic distribution were determined by analysis and presented as a function of the discontinuous phase volume fraction. Thus, the equivalent thermal conductivity of the two phase solid mixture was derived in terms of the distribution func- tion, and the thermal conductivity of the constituents.:
22、For, kf km The e ective thermal conductivity of high-density 1 1 polyethylene containing particulate llers is obtained kc pCk k k Bk k numerically at several ller concentrations. A numerical approach was used to determine the e ective thermal conductivity of particle composites in this study. The f
23、m m f B m 4 e ective thermal conductivity of the material was determined using the Laplace equation, as were the ln pkm Bkf km 2 pC k f k m B 1 B k temperature and ux elds within the control volume. A nite di erence method was used in this study. Calcu- lation is carried out on two-dimensional geome
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