Thermal diffusivity composites

Thermal imaging is sensitive to iafrared radiation that detects temperature changes over the surface of a part when heat has been appHed. Thermal diffusion ia a soHd is affected by variatioa ia composition or by the preseace of cracks, voids, delamiaatioas, etc the effects are detected by surface temperature changes. Defects cannot be detected if their depth below the surface is more than two to three times their diameter. Nondestmctive testing has been primarily used for composites and analysis of adhesive bonds or welds. Several studies are documented ia the Hterature (322—327). 

The foremnner of the modern methods of asphalt fractionation was first described in 1916 (50) and the procedure was later modified by use of fuller s earth (attapulgite [1337-76-4]) to remove the resinous components (51). Further modifications and preferences led to the development of a variety of fractionation methods (52—58). Thus, because of the nature and varieties of fractions possible and the large number of precipitants or adsorbents, a great number of methods can be devised to determine the composition of asphalts (5,6,44,45). Fractions have also been separated by thermal diffusion (59), by dialysis (60), by electrolytic methods (61), and by repeated solvent fractionations (62,63). 

In our treatment of directional solidification above, only one diffusion field was treated explicitly, namely the compositional diffusion. If a simple material grows dendritically (thermal diffusion) one may worry about small amounts of impurities. This was reconsidered [132], confirming a qualitative previous result [133] that impurities may increase the dendritic growth rate. Recently some direct simulation results have been obtained with two coupled diffusion fields, one for heat and one for matter, but due to long computing times they are not yet in the state of standard applications [120,134]. 

If temperature gradients are small, Cr may be regarded as effectively constant. Furthermore, Kart is a function of composition, being approximately proportional to the product x, Xr. It is therefore useful to work in terms of the thermal diffusion factor a, where ... 

Though these may provide a standard for screening production quality, they are merely representative. The flexural properties will be a consistent test of the many possible mechanical property testing modalities. Other areas of physical properties that are important to the success of a composite dental restorative are radiopacity, polymerization shrinkage and thermal interactions, e.g., thermal expansion and thermal diffusivity. 

An additional thermal property of interest is thermal diffusivity. The dental pulp sensory system is extremely sensitive to changes in temperature. These sensory inputs are interpreted only as pain. Metallic restorations of deep carious lesions of the tooth frequently need to have a low thermal conductor placed beneath them to avoid causing pulpal pain. The thermal diffusivity of composite varies from approximately that of tooth structure (0.183 mm2/s) to twice that value [204, 254], Metallic restorations of concern have diffusivities at least an... 

Before developing the necessary equations to predict the temperature within a composite part, it is enlightening to consider the thermal diffusion problem in polymer matrix composites. Thermal diffusivity is defined as... 

As the thickness of the laminate increases, the strength of this thermal spike and the degree of thermal lag during heat-up increases. Figure 8.8 shows the results for a 62.5-mm (500 ply) laminate of the same material. Now the center-line temperature never reaches the autoclave temperature during the first dwell, and the thermal spike during the second dwell is nearly 135°C. The thermal spike is directly related to the release of internal heat during cure. The thermal lag is a manifestation of the low thermal diffusivity of polymer matrix composites. 

Equation (56) states that the effect of a thermal gradient on the material transport bears a reciprocal relationship to the effect of a composition gradient upon the thermal transport. Examples of Land L are the coefficient of thermal diffusion (S19) and the coefficient of the Dufour effect (D6). The Onsager reciprocity relationships (Dl, 01, 02) are based upon certain linear approximations that have a firm physical foundation only when close to equilibrium. For this reason it is possible that under circumstances in which unusually high potential gradients are encountered the coupling between mutually related effects may be somewhat more complicated than that indicated by Eq. (56). Hirschfelder (BIO, HI) discussed many aspects of these cross linkings of transport phenomena. 

The large fluctuations in temperature and composition likely to be encountered in turbulence (B6) opens the possibility that the influence of these coupling effects may be even more pronounced than under the steady conditions rather close to equilibrium where Eq. (56) is strictly applicable. For this reason there exists the possibility that outside the laminar boundary layer the mutual interaction of material and thermal transfer upon the over-all transport behavior may be somewhat different from that indicated in Eq. (56). The foregoing thoughts are primarily suppositions but appear to be supported by some as yet unpublished experimental work on thermal diffusion in turbulent flow. Jeener and Thomaes (J3) have recently made some measurements on thermal diffusion in liquids. Drickamer and co-workers (G2, R4, R5, T2) studied such behavior in gases and in the critical region. 

Various forms of diffusion coefficients are used to establish the proportionality between the gradients and the mass flux. Details on determination of the diffusion coefficients and thermal diffusion coefficients is found in Chapter 12. Here, however, it is appropriate to summarize a few salient aspects. In the case of ordinary diffusion (proportional to concentration gradients), the ordinary multicomponent diffusion coefficients Dkj must be determined from the binary diffusion coefficients T>,kj. The binary diffusion coefficients for each species pair, which may be determined from kinetic theory or by measurement, are essentially independent of the species composition field. Calculation of the ordinary multicomponent diffusion coefficients requires the computation of the inverse or a matrix that depends on the binary diffusion coefficients and the species mole fractions (Chapter 12). Thus, while the binary diffusion coefficients are independent of the species field, it is important to note that ordinary multicomponent diffusion coefficients depend on the concentration field. Computing a flow field therefore requires that the Dkj be evaluated locally and temporally as the solution evolves. 

Figure 19.14. Construction and performance of thermal diffusion columns, (a) Basic construction of a thermal diffusion cell, (b) Action in a thermogravitationai column, (c) A commercial column with 10 takeoff points at 6 in. intervals the mean dia of the annulus is 16 mm, width 0.3 mm, volume 22.5 mL (Jones and Brown, 1960). (d) Concentration gradients in the separation of cis and trans isomers of 1,2-dimethylcyclohexane (Jones and Brown, 1960). (e) Terminal compositions as a function of charge composition of mixtures of cetane and cumene time 48 hr, 50°C hot wall, 29°C cold wall (Jones and Brown, 1960).

These equations contain a number of assumptions. First of all, they are a result of a dilute gas approximation in which binary diffusion coefficients, which may be assumed independent of composition, are used. Secondly, thermal diffusion has been neglected although this assumption should be verified for the system under investigation. It appears that the flux due to thermal diffusion could be a substantial fraction of the ordinary diffusion flux for some systems (F6). 

Thermal diffusivity a and thermal conductivity l strongly depend on the composition (Fig. 27). Materials containing a high residual a content show a very low thermal diffusivity (88 vol% a a = 5 mm2 s-1) whereas the same composition after complete a// transformation has 13 mm2 s-1 at RT. ass ceramics also show low thermal diffusivity (Fig. 27). The intrinsic anisotropic thermal diffusivity inside the individual grains is without connection with the macroscopic diffusivity, as a consequence of the dispersion of grain orientations in the ceramics [375]. 

The diffusion, thermal diffusion, and Soret coefficients of this system are shown in Fig. 8. Samples of two different off-critical compositions (c = 0.3 and c = 0.9) were prepared. The temperature was set to a value of a few degrees above the bin-odal. Hence, the sample was entirely within the homogeneous phase and one would expect that heating could only drive the blend further into the stable one-phase region. 

A modified Cahn-Hilliard (CH) model [114] is used for the theoretical analysis of the impact of thermal diffusion on phase separation by taking into account an inhomogeneous temperature distribution, which couples to a concentration variation via the Soret effect. The Flory-Huggins model is used for the free energy of binary polymer-mixtures. The composition is naturally measured in terms of volume fraction 0 of a component A, which can be related to the weight fraction c by... 

Russell, L.M., Donaldson, K.Y., Hasselman, D.P.H., Corbin, N.D. Petrovic, J.J. and Rhodes, J.F. Effect of vapor-liquid-solid and vapor-solid silicon carbide whiskers on the effective thermal diffusivity/conductivity of silicon nitride matrix composites , J. Am. Ceram. Soc., 74[4] (1991) 874-877. 

Keywords Metal-hydride composite materials Thermal diffusivity Thermal conductivity ... 

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