Thin gas

Next we consider the heat flux associated with this gas. The derivative d/ds in Eq. (10.28) is the gradient in the direction of the propagation of radiation. In terms of a cartesian coordinate, say x, noting from (Kg. 10.2) that 

This result may be rearranged with the help of Eq, (10.30) to give 

Finally, noting that /o is independent of the solid angle and that7r/o(V) = , Eq. (10.32) may be reduced to 

So far, we have considered one extreme case corresponding to the negligible decay of e x(-SiS which led us to the thin-gas limit. We proreed now to the other extreme case corresponding to the rapid decay of g-W-1 ). 

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Fukui, S., and Kaneko, R., Analysis of Uitra-Thin Gas Fiim Lubrication Based on Linearized Boltzmann Equation First Report—Derivation of a Generalized Lubrication Equation In-ciuding Thermai Creep Fiow," ASME J. Tribal., Voi. 110, 1988,pp.253-262. 

The last category is the pressure-driven gas flows, which are typical in micro gas fluidic and micro heat transfer systems. Because the channel diameter or width in micro gas fluidic systems is in the scale of sub-micrometer or less, ultra-thin gas lubrication theory plays an important role in... 

Huang, P., Niu, R. J., and Hu, H. H., A New Numerical Method to Solve Modified Reynolds Equation for Magnetic [31] Head/Disk Working in Ultra Thin Gas Films, Sci. China,... 

Wu, J. K. and Chen, H. X., Operator Splitting Method to Calculate Pressure of Ultra-Thin Gas Film of Magnetic Head/ Disk," Tribology, Vol. 23, No. 5, 2003, pp. 402-405 (in Chinese). 

Vaivars G., Kleperis J., Zubkans J., Vitins G., Liberts G., Lusis A., Application of sol-gel and laser evaporation methods to obtain thin gas sensitive films, Proc. 8th International Conference on Solid-State Sensors and Actuators and Eurosensors IX, 1995, pp. 870-873. 

The concentration of gases such as C02, NH3, S02 andN02 in aqueous solutions can be measured with an electrode consisting of a glass electrode/reference electrode pair inside a plastic tube which is sealed with a thin gas-permeable membrane and containing an appropriate electrolyte solution (Figure 6.5). 

On the other hand, it has been argued that the resistance to heat transfer is effectively within a thin gas film enveloping the catalyst particle [10]. Thus, for the whole practical range of heat transfer coefficients and thermal conductivities, the catalyst particle may be considered to be at a uniform temperature. Any temperature increases arising from the exothermic nature of a reaction would therefore be across the fluid film rather than in the pellet interior. 

McGreavy and THORNTON(23) have developed an alternative approach to the problem of identifying such regions of unique and multiple solutions in packed bed reactors. Recognising that the resistance to heat transfer is probably due to a thin gas film surrounding the particle, but that the resistance to mass transfer is within the porous solid, they solved the mass and heat balance equations for a pellet with modified boundary conditions. Thus the heat balance for the pellet represented by equation 3.24 was replaced by ... 

In a well-fluidized gas-solid system, the bulk of the bed can be approximated to be isothermal and hence to have negligible thermal resistance. This approximation indicates that the thermal resistance limiting the rate of heat transfer between the bed and the heating surface lies within a narrow gas layer at the heating surface. The film model for the fluidized bed heat transfer assumes that the heat is transferred only by conduction through the thin gas film or gas boundary layer adjacent to the heating surface. The effect of particles is to erode the film and reduce its resistive effect, as shown by Fig. 12.3. The heat transfer coefficient in the film model can be expressed as... 

Figure 2.2. (a) Model spectra from optically thin gas of solar abundance with temperatures... 

To obtain the large capacities required for B battery eliminator circuits, we must use very large plates or a very thin dielectric. The electrolytic condenser, on account of its extremely thin gas-film dielectric, has an enormous capacity when only small plates are used. C. I. Zimmermon found that the thickness of the film is between 1/50,000 and 1/500,000 of an inch, depending upon the formation-voltage. The dielectric constant of the film is about 10, so that a capacity of to j4-mfd. per square inch of electrode surface is easily obtained. 

Glass vent tube 2. Thermocouple to measure the or the temperature of an oxidatively-heating substance 3. Thermocouple to measure the 7, , 4. Gas inlet 5. Gas outlet 6. Safety valve 7. Bellows 8. Draft cell in which a reference material or a gas-permeable oxidatively-heating substance is charged 9. Thin gas-penneable silica fiber sheet 10. Heating wire 11. Glass wool. 

The three kinds of open cells, i.e., the open-cup, the draft and the touch-flow cell, are, however, the same to the effect that each has the ground-glass joint at the upper end. A difference in the three is only that the thin gas-permeable silica fiber sheet, which is used to support a reference material, or a gas-permeable oxidatively-heating substance, tested on the bottom of the draft cell, is not used in both the open-cup cell and the touch-flow cell. ... 

The touch-flow cell is, however, not fit to measure the heat generation data required to ealeulate the T for a gastight oxidatively-heating substance. For further details, refer to Subsection 4.2.2. Whenever the draft cell, which has a hole at the base, is used, it is required to place a thin gas-permeable silica fiber sheet on the bottom of the cell in order to support a reference material or a gas-permeable oxidatively-heating substance, before either of them is charged in the cell (refer to Subsection 7.4.1, etc.). 

After a thin gas-permeable silica fiber sheet has been placed on the bottom of a draft cell, i.e., the cell with which the sample cell is prepared, a definite quantity of a moisture-containing gas-permeable oxidatively-heating substance, the volume of which is about 2 cm, is charged in the cell. The glass jig mentioned in a footnote in Section 7.3 is used at this time to provide a thin vertical hole at the center of the substance charged in the cell in order to facilitate the insertion of the thermocouple into the substance. 

In the determination of a constant mean beam length sm we first will consider the limiting case of an optically thin gas with kq = kGL0 —> 0. The spectral radiation flow emitted from a volume element of the gas in all directions is, according to (5.181),... 

It is not weakened as it passes through the optically thin gas. Therefore, the radiation flow emitted from the entire gas volume is... 

An optically thin gas hemisphere of radius R = sm causes, according to (5.200), the spectral... 

The mean beam length has to be determined for the calculation of G and oq. Its limit for an optically thin gas is... 

Here the units of c are parts-per-million-meter (ppm-m) and the units of k(X) are l/[ppm-m]. Additionally, for optically thin gas layers, the gas transmission can be approximated as... 

Figure 10.11 Radiant heat flux for thin gas, thick gas, and for any optical thickness.

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