Transpiration

Thermal transpiration and thermal diffusion effects have been neglected in developing the dusty gas model, and will be neglected throughout the rest of the text. The physics of these phenomena and the justification for neglecting them are discussed in some detail in Appendix I. 

Thermal transpiration and thermal diffusion will not be considered here, but it would be incorrect to assume that their influence is negligible, or even small in all circumstances. Recent results of Wong et al. [843 indi cate that they may Influence computed values of the effectiveness factor iby as much as 30. An account of thermal transpiration and thermal diffu-Ision is given in Appendix I. 

Equations (12.13) and (12.14) are themselves approximations, since in Chapter 3 we eliminated thermal transpiration and diffusion from consideration before constructing the dusty gas model flux relations. See Appendix 1. 

The phenomenon of thermal transpiration was discovered by Osborne Reynolds [82], who gave a clear and detailed description of his experiments, together with a theoretical analysis, in a long memoir read before the Royal Society in February of 1879. He experimented with porous plates of stucco, ceramic and meerschaum and, in the absence of pressure gradients, found that gas passes through the plates from the colder to the hotter side. His experimental findings were summarized in the following "laws" of thermal transpiration. 

In the second part of hla memoir Reynolds gave a theoretical account of thermal transpiration, based on the kinetic theory of gases, and was able CO account for Che above "laws", Chough he was not able to calculate Che actual value of the pressure difference required Co prevent flow over Che whole range of densities. ... 

At very low densities It Is quite easy Co give a theoretical description of thermal transpiration, alnce the classical theory of Knudsen screaming 9] can be extended to account for Che Influence of temperature gradients. For Isothermal flow through a straight capillary of circular cross-section, a well known calculation [9] gives the molar flux per unit cross-sectional area, N, In the form... 

Reynolds also discussed transpiration under the Influence of a pressure difference alone and gave an account of the phenomenon of Impulsion In a Crookes radiometer, an effect of great Interest to 19ch century scientists. 

Now in the present case i/a 1, so it follows from equation (A.1.7) that G/a 1, provided f differs significantly from zero. Thus che first term on the right hand side of (A.L.8) is a close approximation to the familiar Poisoiille flux. The second term, on the other hand, represents thermal transpiration. In particular, setting N 0, we find... 

This point was taken up by Reynolds in a letter addressed to G. G. Stokes, in the latter s capacity as Secretary of the Royal Society [83]. Reynolds pointed out that Maxwell s theory evaluated the effects of thermal transpiration only in circumstances where they were too small to be measured, and complained that Maxwell had misrepresented his own theoretical treat ment of the phenomenon. However, this incipient controversy never developed... 

It is also interesting to examine the relative importance of thermal transpiration and thermal diffusion in the two limiting cases. From equations (A. 1.12) and (A. 1.13)... 

Finally, let us return to the question of the practical importance of thermal diffusion and thermal transpiration in modeling reactive catalyst... 

For transpiration through a long capillary, on the other hand, he conclude as follows. 

Turning finally to the Interpretation of Graham s experimental resul on transpiration, the theory of viscous flow of an ideal gas through a Ion capillary gives... 

The relationship between heat transfer and the boundary layer species distribution should be emphasized. As vaporization occurs, chemical species are transported to the boundary layer and act to cool by transpiration. These gaseous products may undergo additional thermochemical reactions with the boundary-layer gas, further impacting heat transfer. Thus species concentrations are needed for accurate calculation of transport properties, as well as for calculations of convective heating and radiative transport. 

Protective Coatings. Some flame retardants function by forming a protective Hquid or char barrier. These minimize transpiration of polymer degradation products to the flame front and/or act as an insulating layer to reduce the heat transfer from the flame to the polymer. Phosphoms compounds that decompose to give phosphoric acid and intumescent systems are examples of this category (see Flame retardants, phosphorus flame retardants). 

Tables 2,3, and 4 outline many of the physical and thermodynamic properties ofpara- and normal hydrogen in the sohd, hquid, and gaseous states, respectively. Extensive tabulations of all the thermodynamic and transport properties hsted in these tables from the triple point to 3000 K and at 0.01—100 MPa (1—14,500 psi) are available (5,39). Additional properties, including accommodation coefficients, thermal diffusivity, virial coefficients, index of refraction, Joule-Thorns on coefficients, Prandti numbers, vapor pressures, infrared absorption, and heat transfer and thermal transpiration parameters are also available (5,40). Thermodynamic properties for hydrogen at 300—20,000 K and 10 Pa to 10.4 MPa (lO " -103 atm) (41) and transport properties at 1,000—30,000 K and 0.1—3.0 MPa (1—30 atm) (42) have been compiled. Enthalpy—entropy tabulations for hydrogen over the range 3—100,000 K and 0.001—101.3 MPa (0.01—1000 atm) have been made (43). Many physical properties for the other isotopes of hydrogen (deuterium and tritium) have also been compiled (44).

B. 5-26-A Graphical comparisons experiments and correlations. [E,S] For spheres. Includes transpiration effects and changing diameters. [78] [146] p.222... 

Transpiration Cooling Cooling by this method requires the coolant flow to pass through the porous wall of the blade material. The heat transfer is directly between the coolant and the hot gas. Transpiration cooling is effective at very high temperatures, since it covers the entire blade with coolant flow. This method has been used rarely due to high costs. 

The leaf structure has several important functions, three of which are photosynthesis, transpiration, and respiration (2). Photosynthesis is accomplished by chloroplasts in the leaf, which combine water and COj in the presence of sunlight to form sugars and release O2. This process is shown in Eq. (8-1). 

Transpiration is the movement of water from the root system up to the leaves and its subsequent evaporation to the atmosphere. This process moves nutrients throughout the plant and cools the plant. Respiration is a heat-producing process resulting from the oxidation of carbohydrates by O2 to form CO2 and H2O, as shown in Eq. (8-2). 

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