Free-molecular gas conduction

A further substitution of Eqs. (7.15) and (7.17) into Eq. (7.11) yields an expression for the free molecular gas conduction between two concentric cylinders or spheres in terms of the measurable quantities, namely. 

The task of estimating the heat inleak to a vacuum-insulated line involves many considerations. As a basis, a designer must first complete the free molecular gas conduction calculation between the long coaxial cylinders separated by a vacuum using Eq. (7.18). For practical purposes, however, the value obtained using this relation is only a small part of the heat inleak since... 

As the pressure increases from low values, the pressure-dependent term in the denominator of Eq. (101) becomes significant, and the heat transfer is reduced from what is predicted from the free molecular flow heat transfer equation. Physically, this reduction in heat flow is a result of gas-gas collisions interfering with direct energy transfer between the gas molecules and the surfaces. If we use the heat conductivity parameters for water vapor and assume that the energy accommodation coefficient is unity, (aA0/X)dP — 150 I d cm- Thus, at a typical pressure for freeze drying of 0.1 torr, this term is unity at d 0.7 mm. Thus, gas-gas collisions reduce free molecular flow heat transfer by at least a factor of 2 for surfaces separated by less than 1 mm. Most heat transfer processes in freeze drying involve separation distances of at least a few tenths of a millimeter, so transition flow heat transfer is the most important mode of heat transfer through the gas. 

The ficos peak is ascribed to an interface plasmon. Assuming that the aluminium conduction electrons are well described by a free-electron gas, the interface plasmon frequency is related to the relative dielectric constant e of the molecular film through the relation ... 

Kinetic theory, non-equilibrium statistical mechanics and non-equilibrium molecular dynamics (NEMD) have proved to be useful in estimating both straight and cross-coefficients such as thermal conductivity, viscosity and electrical conductivity. In a typical case, cross-coefficient in case of electro-osmosis has also been estimated by NEMD. Experimental data on thermo-electric power has been analysed in terms of free electron gas theory and non-equilibrium thermodynamic theory [9]. It is found that phenomenological coefficients are temperature dependent. Free electron gas theory has been used for estimating the coefficients in homogeneous conductors and thermo-couples. 

From kinetic theory it can be shown that, in general, larger gas molecules have a lower thermal conductivity. The influence of molecular weight of the gas on the thermal conductivi of fibrous insulations has been adequately covered by Wilson for standard temperatures and pressures and by Verschoor and Greebler for low pressures. However, this technique is limited to an improvement in conductivity approximately equivalent to the difference in free gas conductivity between the high molecular weight gas and air. This paper evaluates an alternate technique for improving the thermal performance of fibrous insulation, i.e., the partial removal (evacuation) of the environmental air. 

When free molecular conduction is present in a vacuum insulation system, the remaining gas molecules travel uninhibited between the warm and cold surfaces. To determine whether the free molecular conduction is significant in such a system requires comparing the distance between the two... 

In these equations x and y denote independent spatial coordinates T, the temperature Tib, the mass fraction of the species p, the pressure u and v the tangential and the transverse components of the velocity, respectively p, the mass density Wk, the molecular weight of the species W, the mean molecular weight of the mixture R, the universal gas constant A, the thermal conductivity of the mixture Cp, the constant pressure heat capacity of the mixture Cp, the constant pressure heat capacity of the species Wk, the molar rate of production of the k species per unit volume hk, the speciflc enthalpy of the species p the viscosity of the mixture and the diffusion velocity of the A species in the y direction. The free stream tangential and transverse velocities at the edge of the boundaiy layer are given by = ax and Vg = —ay, respectively, where a is the strain rate. The strain rate is a measure of the stretch in the flame due to the imposed flow. The form of the chemical production rates and the diffusion velocities can be found in (7-8). 

This radicals do not escape from the surface (this is indicated by a semiconductor microdetector located near the adsorbent surface) undergoing chemisorption on the same semiconductor adsorbent Him. Thus, they caused a decrease in the electric conductivity of the adsorbent sensor, similarly to the case where free radicals arrived to the film surface from the outside (for example, from the gas phase). Note that in these cases, the role of semiconductor oxide films is twofold. First, they play a part of adsorbents, and photoprocesses occur on their surfaces. Second, they are used as sensors of the active particles produced on the same surface through photolysis of the adsorbed molecular layer. 

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