History effects coefficient

The effective diffusivity depends on the statistical distribution of the pore transport coefficients W j. The derivation shows that the semi-empirical volume-averaging method can only be regarded as an approximation to a more complex dynamic behavior which depends non-locally on the history of the system. Under certain circumstances the long-time (t —> oo) diffusivity will not depend on t (for further details, see [191]). In such a case, the usual Pick diffusion scenario applies. The derivation presented above can, with minor revisions, be applied to the problem of flow in porous media. When considering the heat conduction problem, however, some new aspects have to be taken into accoimt, as heat is transported not only inside the pore space, but also inside the solid phase. 

In a supersonic gas flow, the convective heat transfer coefficient is not only a function of the Reynolds and Prandtl numbers, but also depends on the droplet surface temperature and the Mach number (compressibility of gas). 154 156 However, the effects of the surface temperature and the Mach number may be substantially eliminated if all properties are evaluated at a film temperature defined in Ref. 623. Thus, the convective heat transfer coefficient may still be estimated using the experimental correlation proposed by Ranz and Marshall 505 with appropriate modifications to account for various effects such as turbulence,[587] droplet oscillation and distortion,[5851 and droplet vaporization and mass transfer. 555 It has been demonstrated 1561 that using the modified Newton s law of cooling and evaluating the heat transfer coefficient at the film temperature allow numerical calculations of droplet cooling and solidification histories in both subsonic and supersonic gas flows in the spray. 

Drops accelerated by an air stream may split, as described in Chapter 12. For drops which do not split, measured drag coefficients are larger than for rigid spheres under steady-state conditions (R2). The difference is probably associated more with shape deformations than with the history and added mass effects discussed above. For micron-size drops where there is no significant deformation, trajectories may be calculated using steady-state drag coefficients (SI). 

Thermal Expansion. Most manufacturers literature (87,119,136—138) quotes a linear expansion coefficient within the 0—300°C range of 5.4 x 10"7 to 5.6 x 10 7 /°C. The effect of thermal history on low temperature expansion of Homosil (Heraeus Schott Quarzschmelze GmbH) and Osram s vitreous silicas is shown in Figure 4. The 1000, 1300, and 1720°C curves are for samples that were held at these temperatures until equilibrium density was achieved and then quenched in water. The effect of temperature on linear expansion of vitreous silica is compared with that of typical soda—lime and borosilicate glasses in Figure 5. The low thermal expansion of vitreous silica is the main reason that it has a high thermal shock resistance compared to other glasses. 

The variation in the measured electron mobilities from sample to sample in sintered materials (also observed by Hahn, ref. 24), may be due to any of several effects. The most probable reason for this variation in the well-sintered samples studied is a difference in history the individual samples are obtained with different numbers of conduction electrons per cm. frozen in in the necks. That is, the different history has allowed different amounts of oxygen to be adsorbed on the surface. Thus the concentration of electrons in the grain, as measured by the Hall coefficient, will have little relation to the concentration of electrons in the neck, as measured by the conductivity, and the mobility, obtained from the product of the Hall coefficient and the conductivity, will be neither the true mobility nor constant from sample to sample. The different samples may also end up with varying geometry of their necks, according to their previous treatment. 

A second historical line which, is of paramount importance to the present understanding of solid state processes is concerned with electronic particles (defects) rather than with atomic particles (defects). Let us therefore sketch briefly the, history of semiconductors [see H. J, Welker (1979)]. Although, the term semiconductor was coined in 1911 [J. KOnigsberger, J, Weiss (1911)], the thermoelectric effect had already been discovered almost one century earlier [T. J. Seebeck (1822)], It was found that PbS and ZnSb exhibited temperature-dependent thermopowers, and from todays state of knowledge use had been made of n-type and p-type semiconductors. Faraday and Hittorf found negative temperature coefficients for the electrical conductivities of AgzS and Se. In 1873, the decrease in the resistance of Se when irradiated by visible light was reported [W. Smith (1873) L. Sale (1873)]. It was also... 

However, for nonspherical particles, rotational Brownian motion effects already arise at 0(0). In the case of ellipsoidal particles, such calculations have a long history, dating back to early polymer-solution rheologists such as Simha and Kirkwood. Some of the history of early incorrect attempts to include such rotary Brownian effects is documented by Haber and Brenner (1984) in a paper addressed to calculating the 0(0) coefficient and normal stress coefficients for general triaxiai ellipsoidal particles in the case where the rotary Brownian motion is dominant over the shear (small rotary Peclet numbers)—a problem first resolved by Rallison (1978). 

Moreover the electrodiffusion potential gradient is likely to cause electroosmotic transfer of the solution, whose local content is not in equilibrium with that of the counterions [5]. In this case, as it is pointed out in Ref. 5, the ion mobility and concentration depend on the prior history of the process which can bring about non-Fickian diffusion. The application of Nemst-Planck equations to the real system may require inclusion of additional terms that account for the effect of activity coefficient gradients which may be important in IE with zeolites [4,5]. 

Further, the erosion law factor K, defined in equation (4), regulates the age distribution of eroded material relative to the age structure of the crust. Thus for a given crust mass v. time curve, the three parameters E, R and K fully describe the crust formation and erosion history. In the present modelling E was varied between 0.2 and 1, R from 0.3 to 0.7, and K from 1.5 to 3.5. The approach used and the effective partition coefficients, as well as initial (meteori-tic) concentrations of the trace species are the same as those used by Kramers Tolstikhin (1997) and Nagler Kramers (1998). 

The properties which determine heat transfer through a deposit layer of given thickness are thermal conductivity, emissivity, and absorptivity. These properties vary with deposit temperature, thermal history, and chemical composition. Parametric studies and calculations for existing boilers were carried out to show the sensitivity of overall furnace performance, local temperature, and heat flux distributions to these properties in large p.f. fired furnaces. The property values used cover the range of recent experimental studies. Calculations for actual boilers were carried out with a comprehensive 3-D Monte Carlo type heat transfer model. Some predictions are compared to full-scale boiler measurements. The calculations show that the effective conduction coefficient (k/As)eff of wall deposits strongly influences furnace exit temperatures. 

The complete concentration time history is shown in Figure 6.5. The composition trajectories do not compare all that favorably with the experimental data of Krishna et al. (1985). The actual observed equilibration paths and the predictions of the linearized equations are more highly curved (see Fig. 5.3). It must also be pointed out that the effective volumetric mass transfer coefficients should take on equal values (cf. discussion in Section... 

The effective P may be determined with the electron beam apparatus. When the sample (slab geometry) is thick enough to absorb all of the incident electrons, a compressive stress wave propagates from the irradiated region into the sample bulk. A transducer, located just beyond the deposition depth, may be used to record the stress pulse. Alternatively, the displacement or velocity of the rear surface of sample may be observed optically and used to infer the initial pressure distribution from the experimentally measured stress history. Knowledge of the energy-deposition profile then permits the determination of the Gruneisen coefficient. 

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