Diffusion of mass

The unsteady version of the convective diffusion equation is obtained just by adding a time derivative to the steady version. Equation (8.32) for the convective diffusion of mass becomes... 

It is also assumed that axial diffusion of mass, heat and momentum are negligible. The velocity profiles are assumed to be locally fully developed in length. For this simplified case the polymer concentration and secondary flows are determined by three dimensionless groups ... 

Much work has been focused on the significance of dispersion terms in the transient material and energy equations for packed bed reactors. In general, axial diffusion of mass and energy and radial diffusion of mass have been... 

The Lewis number, Le = a/D, that determine the ratio between the diffusivity of heat and the diffusivity of mass. 

This chapter uses FEMLAB to solve problems involving two- or three-dimensional flow (2D or 3D) and diffusion of mass and/or heat. Convection and diffusion of mass... 

Dh equals about 1CT7 m2 s-1 for most food components this is correct within a factor of two. For crystalline material the value tends to be higher than for a liquid, and ice even has Du x 10 6 m2 s 1 (most metals are in the range 10 5 10 4). Since the mass diffusion coefficient nearly always is < 10 9 m2 s, the diffusion of heat is at least 100 times as fast as the diffusion of mass. Nevertheless, it is still slow at distances longer than a few mm. 

Axial diffusion of mass and heat is negligible (Singh and Saraf,... 

From the foregoing discussion, it is clear that the catalyst pellet is not only the heart of the catalytic reactor but also the hardest part of the system to model accurately. The difficulties associated with the modelling of the single pellet (especially the porous pellet) is due to the uncertainties associated with the intrinsic kinetics and the precise modelling of diffusion of mass and heat inside the pellet as well as the complex interaction between these two processes. The complex tortuous structure of porous catalyst pellet adds to the complexity. Different trials to estimate the tortuosity factor (which accounts for the complex tortuous structure of the pellet) theoretically have failed to give accurate results and this factor is usually estimated experimentally. 

The dimensionless equations for the convective diffusion of mass and heat are... 

This section applies the method of lines to the equations for convective diffusion of mass and heat. It is convenient to replace r hy r = i Ar, i = 0,..., I, for coding... 

Reaction rates can be controlled by the rate of conversion of the reactants or by nonchemical rate processes such as the rate of diflusion of reactants or the rate of heat transfer. In the study of chemical kinetics we will be interested in the rates of chemical change governed by the speed of chemical processes. Any investigation of reaction rates meant for mechanistic studies must first establish that this is what we are measuring. Fortunately, it is relatively easy to check for extraneous effects before the kinetic investigation is undertaken. The effects that are most likely to cause problems involve diffusion of mass and heat in catalyst particles and mixing in the reactor. 

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