Peclet number for heat and mass transfer

Peclet number for heat and mass transfer, respectively... 

The notation is the same as before, with i representing the variable dimensionless temperature within the disturbance, x representing composition variable. The reaction is first order and the Peclet numbers for heat and mass transfer are assumed to be equal. xQ represents the composition in the normal region, equal to 1 - (t/S) with t and S defined as before. 

Fourier s law and the interdiffusional fluxes are considered, but the diffusion-thermo (i.e., Dufour) effect is neglected in (30-17). Since contributions from convective transport are insignificant at extremely low Peclet numbers for heat and mass transfer within the catalytic pores, the previous balances reduce to... 

Hlavacek and Hofmann also defined necessary and sufficient conditions for multiplicity, for a simplified rate law of the type Barkelew used (Eq. 11.5-c) and equality of the Peclet numbers for heat and mass transfer. The necessary and sufficient conditions for multiplicity, which have to be fulfilled simultaneously are... 

The conditions presented above have been formulated for the case that the values of the Peclet numbers for heat and mass dispersion in a bed are indentical. However, recent experimental research on axial heat dispersion in packed beds has indicated that the values of the Peclet number for heat transfer may be different from those for mass transfer (48). Fortunately, the aforementioned conditions are still valid, however, the critical values of B and Pe as well as the bounds Dan,in and Da x are dependent on the ratio q = PeH/PeM. From the theoretical results may be inferred that for highly exothermic reactions multiple steady states may... 

GP 9] [R 16[ The extent of external transport limits was made in an approximate manner as for the internal transport limits (see above), as literature data on heat and mass transfer coefficients at low Peclet numbers are lacking [78]. Using a Pick s law analysis, negligible concentration differences from the bulk to the catalyst sur-... 

Another important practical difference between the heat and mass transfer problems is the magnitude of the Prandtl number and the Schmidt numbers. In the present chapter, these parameters appear in only the relationship between the Peclet number and the Reynolds number. However, we shall see in Chap. 11 that this is not always true. In any case, the magnitude of the Schmidt number is typically larger than the magnitude of the Peclet number. For liquids, typical values of the Schmidt number are... 

Gnielinski, V., Equations for the Calculation of Heat and Mass Transfer during Flow through Stationary Spherical Packings at Moderate and High Peclet Numbers, Int. Chem. Eng. 21, 378-383 (1981). 

Naturally, there are two more Peclet numbers defined for the transverse direction dispersions. In these ranges of Reynolds number, the Peclet number for transverse mass transfer is 11, but the Peclet number for transverse heat transfer is not well agreed upon (121, 122). None of these dispersions numbers is known in the metal screen bed. A special problem is created in the monolith where transverse dispersion of mass must be zero, and the parallel dispersion of mass can be estimated by the Taylor axial dispersion theory (123). The dispersion of heat would depend principally on the properties of the monolith substrate. Often, these Peclet numbers for individual pellets are replaced by the Bodenstein numbers for the entire bed... 

Peclet Number, Pe dimensionless number appearing in enthalpy or species mass conservation equations (defined for heat transfer and mass transfer, respectively). It is interpreted again as the ratio of the convective transport to the molecular transport and is defined as... 

Radial dispersion of mass and heat in fixed bed gas-solid catalytic reactors is usually expressed by radial Peclet number for mass and heat transport. In many cases radial dispersion is negligible if the reactor is adiabatic because there is then no driving force for long range gradients to exist in the radial direction. For non-adiabatic reactors, the heat transfer coeflScient at the wall between the reaction mixture and the cooling medium needs also to be specified. 

Table 12.3 Peclet numbers for mass and heat transfer...

Table 8.2 Peclet Numbers for Mass and Heat Transfer...

Here x is the extent of the reaction (or scaled concentration of the reagent B), X2 is the normalized temperature of the complex liquid-solid medium, Pei and Pc2 are the Peclet numbers for mass and heat transport, Le is the Lewis number, is the longitudinal spatial coordinate. Da is the Damkohler number, 7 is the normalized activation energy of the reaction, /) is the transverse residence time of fluid in the reactor determined by the rate of cross-flow, b is the adiabatic temperature rise for the empty reactor (without packing), / iv is the surface heat transfer coefficient, and X2w the temperature of the reactor walls [22],... 

The Peclet numbers are useful for estimating the relative contributions of convection and diffusion to mass and heat transfer. If Pe is large (>10), convection dominates, and a plug-flow model may be appropriate for simple reactor computations. When Pe is small (<<1), diffusion dominates, and the system behaves like a well-stirred reactor. Thus, Pe may be used to estimate whether downstream impurities can diffuse into the deposition zone. 

The pore diffusivity used in this analysis was determined by the Renkin equation4, the axial dispersion coefficient calculated by assuming a constant Peclet number of 0.2, and the mass transfer coefficient from the bulk to the particle surface calculated by the correlation of Wakao and Kaguei. The product of the heat capacity and density of the solid phase was taken to be the same as that used by Raghavan and Ruthven17. The density of the fluid phase was assumed to be that of pure C02 and was calculated from data provided by the Dionix Corporation in their AI-450 SFC software. Constant pressure heat capacities for the mobile phase were also assumed to be that of pure C02 and were taken from Brunner3. 

In Chap. 9, we considered the solution of this equation in the limit Re 1, where the velocity distribution could be approximated by means of solutions of the creeping-flow equations. When Pe 1, we found that the fluid was heated (or cooled) significantly in only a very thin thermal boundary layer of 0(Pe l/3) in thickness, immediately adjacent to the surface of a no-slip body, or () Pe l/2) in thickness if the surface were a slip surface with finite interfacial velocities. We may recall that the governing convection di ffusion equation for mass transfer of a single solute in a solvent takes the same form as (111) except that 6 now stands for a dimensionless solute concentration, and the Peclet number is now the product of Reynolds number and Schmidt number,... 

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