Coefficient of thermal diffusion

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. 

Here, the coefficient Dk is defined as the barycentric coefficients of thermal diffusion. Due to... 

The thermal diffusion coefficients appearing in equations (18) and (19) in general may be positive or negative and depend on pressure, temperature, and concentrations. It is almost always found that the dimensionless ratio Dj J(pDij) is less than for all pairs of gaseous species i and), which implies that thermal diffusion usually is negligible in comparison with the ordinary concentration-gradient diffusion. The complicated expressions for the coefficients of thermal diffusion will therefore be omitted here the reader is referred to [5] and [9] for theoretical results and for useful empirical formulas. 

The temperature depends on both time, f, and position, x. The coefficient of thermal diffusion is... 

Due to the low permeability of shales, the coefficient of thermal diffusivity is at least a few orders of magnitude greater than the coefficient of fluid diffusivity. Hence, heat transfer in the formation will be dominated by diffusion, and convective transfer by fluid flow may be ignored. Since the coefficient of thermal expansion of pore fluid is much larger (in the order of 100 times) than the coefficient of rock solid, temperature change will result in a change in pore pressure. 

Summarizing, we should note that the methods presented in the present section can be applied without any modifications to heat exchange problems, because temperature distribution is described by an equation similar to the diffusion equation. The boundary conditions are also formulated in a similar way. One only has to replace D by the coefficient of thermal diffusivity, and the number Peo - by Pej-. The corresponding boundary layer is known as the thermal layer. Detailed solutions of heat conductivity problems can be found in [6]. 

The cross flow —(Li /r )Vr is usually written as —niD VT, in which Dt is the coefficient of thermal diffusion, so that the flow of matter is proportional to n. The ratio of the thermal diffusion coefficient to the ordinary diffusion coefficient is the Soret coefficient. 

The coefficient of thermal conductivity k usually varies with T in quite a complicated way (see below) and at 1K it may be larger or smaller than it is at 300 K, depending on the material. The coefficient of thermal diffusion, given by ... 

Thermal Diffusivity. For systems not in a temperature equilibrium or steady state, the coefficient of thermal diffusivity a(T) = XJ C p) m /s determines the time-space correlation of temperature. At low temperatures, ie, <40 K, a(T) becomes very large because the specific heat C falls more than the thermal conductivity X. The diffusivity is plotted in Figure 6 for amorphous epoxy resins and 98% crystalline HDPE (14). 

The value of the coefficient of thermal diffusivity a was set as the coefficient of diffusion D. As bovmdary conditions, the temperature of the body and the shell were set to 21 K and 0 K respectively. Thus, saturated resin at a partial pressure of 21 % of Oxygen (21 K) and no Oxygen (0 K) in the surroiuiding atmosphere were assumed. The traction of Oxygen remaining in the resin in regard to the initial value at a certain time was calculated as the average temperature of all nodes divided by 21 K. 

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