Thermal diffusivity anisotropic

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]. 

Brenner Edwards (1993) have examined mixed systems of materials of the same thermal diffusivity but differing thermal conductivity, emphasizing that the resultant effective diffusivity of the mixed system on the macroscale is not a constant scalar diffusivity but rather an anisotropic tensor diffusivity. This point is illustrated by the simple example of a laminated material, composed of alternating layers of equal diffusivity air a and liquid metal m of thicknesses and / , which extends to infinity in all three spatial directions. Applying the formulas for parallel and series conductivities, the effective diffusivity in the direction parallel to the strata is just a = a., = a . In the limit where > k, the relation for the effective diffusivity in the direction perpendicular to the strata reduces to (Brenner c Edwards 1993)... 

Ota, N. Agard, D. A., Intramolecular signaling pathways revealed by modeling anisotropic thermal diffusion. J. Mol. Biol. 2005, 351, 345-354. 

For transient wave mixings, the detailed calculations for the three-dimensional thermal grating buildup and temperature distribution and dissipation are obviously very complex, and are further complicated by the anisotropic thermal diffusion constants of the liquid crystals, as well as the enclosing glass slides. In the simplest case where the thermal grating is reducible to a one-dimensional problem [14] (e.g., the case of very small grating constant A compared to the cell thickness /), the thermal decay time constants for heat dissipation along and per-... 

Borca-Tasciuc, T, Mazumder, M., Son, Y., Pal, S. K., Schadler, L. S., Ajayan, P. M. (2007), Anisotropic thermal diffusivity characterization of aligned carbon nanotube-polymer composites. Journal of Nanoscience and Nanotechnology, 7,1581-8. 

Contributions of second order in the "nonsphericity arising from one even and one odd basis function anisotropic in the angular momentum (in the notation of reference 30, W[Q]and for thermal conductivity, diffusion and thermal diffusion, and [Q]and [W]for the shear viscosity) are included. SEE denotes Senftleben-Beenakker effect. 

Eq. 2.18) and Ohm s law for electrical conduction (where the electrical conductivity is also always positive, according to Exercise 2.1 s solution). However, this is not necessarily the case for the cross-effect tensors /3 and 7. For example, in mass diffusion in a thermal gradient, the heat of transport can be either positive or negative the direction of the atom flux in a temperature gradient can then be in either direction. The anisotropic equivalent to the heat of transport relates the direction of the mass diffusion to the direction of the temperature gradient. There is no physical requirement that these quantities could not be in reversed directions, and indeed, sometimes they are. 

As indicated above, much interest exists in dynamic behavior of thin aligned layers of nematic liquid crystals. It is not surprising to find, therefore, that measurement of the anisotropy of transport properties has been the objective of many studies of thermotropic systems. The literature on anisotropic thermal conductivity in nematic liquid crystals has been reviewed recently by Rajan and Picot (12). Among the studies of anisotropic diffusion are those of Yun and Fredrickson (13), Bline... 

Here, Ds and Dd are the coefficients representing the Soret and Dufour effects, respectively, Du is the self-diffusion coefficient, and Dik is the diffusion coefficient between components / and k. Equations (7.149) and (7.150) may be nonlinear because of, for example, reference frame differences, an anisotropic medium for heat and mass transfer, and temperature- and concentration-dependent thermal conductivity and diffusion coefficients. 

Diffusion is the random movement of a particle because of an exchange of thermal energy with its environment. Membrane lipids and proteins participate in highly anisotropic translational and rotational diffusion motion. Translational diffusion in the plane of the membrane is described by the mean square lateral displacement after a time At (r ) = TD At. Lipid lateral diffusion coefficients in fluid phase bilayers are typically in the range Dj 10 to 10 cm /s (3). 

---