Dimensionless number Lewis

The dimensionless number Le is called the Lewis number (m Russian literature it is called the Luikov number). The Lewis number incorporates the specific heat capacity of humid air pCp (J/m C), the diffusion factor of water vapor in... 

It seems like we need one more dimensionless number to represent the relative magnitudes of heat and mass diffusion in the thermal and concentration boundary layers. That is the Lewis number, defined as (Fig. 14-41)... 

Define and interpret the following dimensionless numbers Schmidt, Prandtl, and Lewis. 

Anonymous (1964). Rouse, Hunter. Who s who in engineering 9 1595. Lewis New York. Rouse, H. (1934). On the use of dimensionless numbers. Civil Engineering 4(11) 563-568. Rouse, H. (1937). Modem conceptions of the mechanics of fluid turbulence. Trans. ASCE 102 463-543. 

Lewis number A dimensionless number, Le, used in heat and mass transfer that characterizes a particular substance as the ratio of the thermal diffusivity, a, to the molecular diffusivity, D ... 

The dimensionless parameter Dpc / is called the Lewis number, which is the ratio of the diffusion coefficient of a gas through the mixture divided by the thermal diffusion coefficient of the gas mixture. 

These are dimensionless groups, and h/KCp is referred to as the Lewis number. 

The dimensionless Lewis number measures the ratio of the heat capacitance term and... 

S/m and fl/ x = Biot numbers for mass and heat transfer 4 and 4 x = Thiele modulus Le = Lewis number A0 i = dimensionless adiabatic temperature rise t) = effectiveness factor kg =mass transfer coefficient (ms-1) Rp = radius of catalyst pellet (m) Da = effective diffusion coefficient (ms-2) r =rate of reaction (molm-3s-1) C —concentration of reactant (molm-3) ... 

The mass diffusivity Dt], the thermal diffusivity a = k/pCp, and the momentum diffusivity or kinematic viscosity v = fi/p, all have dimensions of (length)2/time, and are called the transport coefficients. The ratios of these quantities yield the dimensionless groups of the Prandtl number, Pr, the Schmidt number, Sc, and the Lewis number, Le... 

Pick diffusivity for species i relative to mixture molecular mean-free-path (we assume Rp /) latent heat of fuel vaporization (per g) interparticle separation dimensionless interparticle separation, L/Rp Lewis number (mass/heat diflFusivity ratio) individual particle gasification rate fuel particle number density total number of particles in cloud total pressure... 

Example 3.6 In the energy equation (3.119) for a binary mixture consisting of water vapour and air at 100 °C estimate the magnitude of the individual terms. Chemical reactions are excluded. The specific heat capacity of the water vapour is cpA = 1.8477 kJ/kgK, and that of the air cpB = 1.00258 kJ/kgK. In addition the Lewis number is Le = a/D = 1. Introducing the dimensionless quantities which will be used for the derivation of the energy equation for the boundary layer for pure substances, gives... 

Sinee in the DPF the gas flows through a solid bed, with a non-Arrhenius reaction rate given by k = koTQxp —E/RT), we redefine, for the DPF, the following parameters the charaeteristic reaction time tr d (such that Td = tjty d) the eharacteristic time for thermal convection tc,d (such that the cooling parameter 3 = tr /tc ), the dimensionless adiabatic temperature rise Bd, and the Lewis number. Led, s the ratio of the total heat capaeity of the soot bed to that of the substrate wall. Z = w/w is the dimensionless soot layer thickness, and 6 is the dimensionless temperature, defined earlier. 

A third dimensionless group, the Lewis number, is formed by dividing the thermal by the mass diffusivity ... 

In Table 3.5.2 values are given for a third dimensionless fluid parameter, which is the ratio of the Schmidt number to the Prandtl number. This parameter, Lewis number, is defined by... 

Lewis number Le) - A dimensionless quantity used in fluid mechanics, defined by Le = a/D, where a is thermal diffusivity and D is diffusion coefficient. [2]... 

Gutman chose the reaction enthalpy of solvent with the reference aeeeptor (antimony pentachloride) to quantify Lewis-donor properties. The donor number, DN, is a dimensionless parameter obtained from negative values of reaction enthalpy. The data obtained from electrochemical and NMR studies were combined into one scale in whieh data... 

Here v and d represent dimensionless convection velocity and dimensionless thermal dif-fusivity, resp. (axial mass dispersion is neglected) B is dimensionless reaction enthalpy. Da is the Damkohler number and Le is the Lewis number. We have avoided the conventional introduction of the Peclet number since we would like to examine the effects of convection and thermal diffusion separately. Otherwise, the scaling of the variables and definitions of the dimensionless quantities are conventional, see e.g. (Nekhamkina et al. (2000)). 

Solutions of the complete transient equations, containing an additional dimensionless parameter, the Lewis number Lw = XJpsCpsDeA, are much more complex. Lee and Luss [1971] have shown for some cases that Lw > 1 (an author s definition of the Lewis number must be carefully checked, because sometimes the reciprocal of Lw is used) can lead to limit cycles and other complex behavior. However, Ray [1972] estimates that for this to occur, considering reasonable values of p and A, the critical value for Lw would have to exceed 5, if not 10. Such high values are not likely at all. For NHs-synthesis Lw = 2.6 X 10 and for ethylene hydrogenation Lw =0.11. 

The Lewis number is a dimensionless group composed of four parameters fluid density (p), fluid heat capacity (Cp), molecular diffusivity (D), and fluid thermal conductivity (k). 

The third dimensionless group, formed by dividing the thermal by the mass diffusivity, is the Lewis number, Le = a/Z) = Sc/Pr, and it plays an important part in problems of simultaneous heat and mass transfer, as will be developed later. 

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