Lewis relation

Lewis-Randall rule Lewis relation Lewmet 55 Lexan... 

A closer look at the Lewis relation requires an examination of the heat- and mass-transfer mechanisms active in the entire path from the hquid—vapor interface into the bulk of the vapor phase. Such an examination yields the conclusion that, in order for the Lewis relation to hold, eddy diffusivities for heat- and mass-transfer must be equal, as must the thermal and mass diffusivities themselves. This equahty may be expected for simple monatomic and diatomic gases and vapors. Air having small concentrations of water vapor fits these criteria closely. 

For the air—water system, the Lewis relation shows that r = 1. Under these conditions, the two parenthetical terms on the right-hand side of equation 33 ate enthalpies, and equation 33 becomes the design equation for humidification operations ... 

The last expression of equation 42 is obtained by applying the Lewis relation, Cf = h jky. If the differentials of equation 42 are replaced by finite differences, the following obtains ... 

Equation 12.105 is often referred to as the Lewis Relation. It provides an approximate method for evaluating a mass transfer coefficient if the heat transfer coefficient is known. The assumption that the turbulent eddies can penetrate right up to the surface is justified however only in special circumstances and the problem is considered further in the next section. 

Equation 12.112 is the form of the Lewis Relation which is applicable to mass transfer with bulk flow. 

Equation 12.121 is a modified form of the Lewis Relation, which takes into account the resistance to heat and mass transfer in the laminar sub-layer. 

In Chapter 12 it is shown that when the Schmidt and Prandtl numbers for a mixture of gas and vapour are approximately equal to unity, the Lewis relation applies, or ... 

If the Lewis relation (equation 13.11) is applied, it is possible to obtain workable equations in terms of enthalpy instead of temperature and humidity. Thus, writing h(, as hops, from equation 13.42 ... 

Some workers have attempted to base the design of humidifiers on the overall heat transfer coefficient between the liquid and gas phases. This treatment is not satisfactory since the quantities of heat transferred through the liquid and through the gas are not the same, as some of the heat is utilised in effecting evaporation at the interface. In fact, at the bottom of a tall tower, the transfer of heat in both the liquid and the gas phases may be towards the interface, as already indicated. A further objection to the use of overall coefficients is that the Lewis relation may be applied only to the heat and mass transfer coefficients in the gas phase. 

Calculations involving to systems where the Lewis relation is not applicable are very much more complicated because the adiabatic saturation temperature and the wet-bulb temperature do not coincide. Thus the significance of the adiabatic cooling lines on the psychrometric chart is very much restricted. They no longer represent the changes which take place in a gas as it is humidified by contact with liquid initially at the adiabatic saturation temperature of the gas, but simply give the compositions of all gases with the same adiabatic saturation temperature. 

Flgure10.23 Sialyl Lewis -related selectin inhibitorandfluorogenicscreening compound for transketolase prepared using enzymatic aldolization, and multienzymatic oxidation-aldolization strategy for the synthesis of bicyclic higher carbon sugars. 

What role does the Lewis relation (Equation 3.69) play on the psychrometric chart (Figure 2.5) ... 

For the air-water system at ordinary conditions, the Lewis relation states the following ... 

The Taylor-Prandtl modification to heat and mass transfer is discussed in Section 12.8.3 resulting in the modified Lewis relation ... 

The discussion of the Reynolds analogy is presented in Section 12.8 and consideration of mass transfer in Sections 12.8.2 and 12.8.3 leads to the modified Lewis relation which... 

Lewis related the parachor of hydrocarbons to the critical temperature Tc and the abs. boiling point Tb by the equations ... 

PSYCHROMETRIC LINE AND LEWIS RELATION. For a given wet-bulb temperature, Eq. (23.19) can be plotted on the humidity chart as a straight line having a slope of —hylMJCyX and intersecting the 100 percent line at T . This line is called the psychrometric line. When both a psychromctric line, from Eq. (23.19), and an adiabatic-saturation line, from Eq. (23.11), are plotted for the same point on the 100 percent curve, the relation between the lines depends on the relative magnitudes of and hyIMjJCy. 

Equation (23.21) is known as the Lewis relation. When this relation holds, the psychrometric line and the adiabatic-saturation line becomes essentially the same. In Fig. 23.2 for air-water, therefore, the same line may be used for both. 

Note that since the Lewis relation is used in their derivation, Eqs. (23.36),... 

It has been observed that for the system air-water vapor at near-ambient conditions, Le = 1.0 (Treybal, 1980). This observation, called the Lewis rela -tion, has profound implications in humidification operations, as will be seen later. Based on the Lewis relation, estimate the diffusivity of water vapor in air at 300 K and 1 atm. Compare your result with the value predicted by the Wilke-Lee equation. For air at 300 K and 1 atm C = 1.01 kJ/kg-K, k = 0.0262 W/m-K, x = 1.846 x 10-5 kg/m-s, and p = 1.18 kg/m3. 

Notice the similarities between equations (8-10) and (8-15). The adiabatic saturation temperature, Tm, would be identical to the wet-bulb temperature, Tw, if CS1 = hG/kr For the system air-water, these are nearly equal at moderate humidities that is, hG/ky/Cs 1. This is called the Lewis relation (Lewis, 1922). It must be emphasized that this is not the case for most other systems. Not only does the Lewis relation lead to the near equality of the wet-bulb and adiabatic saturation temperatures in the case of air-water mixtures, but also to other important simplifications to be developed later. 

When cooling water with air in an adiabatic process, the Lewis relation applies reasonably well and equation (8-28) can be simplified. Assuming a thoroughly irrigated tower packing, aH = aM = ah, and application of the Lewis relation, the left-hand side of equation (8-28) can be written as... 

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