By Guy B. Marin
The cross-fertilization of physico-chemical and mathematical principles has a protracted historic culture. This quantity of Advances in Chemical Engineering is nearly thoroughly devoted to a convention on ''Mathematics in Chemical Kinetics and Engineering'' (MaCKiE-2007) which was once held in Houston in February 2007, bringing jointly approximately forty mathematicians, chemists, and chemical engineers from ten international locations to debate the appliance and improvement of mathematical instruments of their respective fields.* Updates and informs the reader at the most up-to-date examine findings utilizing unique reports* Written by way of major specialists and students* reports and analyses advancements within the box
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Additional info for Advances in Chemical Engineering: Mathematics in Chemical Kinetics and Engineering
Effective Dispersion Equations for Reactive Flows with Dominant Pe´clet and Damkohler Numbers 25 In each of the cases we will solve the full physical problem numerically. Its section average will be compared with the solution the proposed effective 1D model with Taylor’s dispersion. Finally, if one makes the unjustified hypothesis that the average of a product is equal to the product of averages, averaging over sections gives a 1D model which we call the ‘‘simple mean’’. We will make a comparison with the solution of that problem as well.
Both the time step and the grid size are kept constant and satisfying the Courant Friedrichs Lewy (CFL) condition to ensure the stability of the calculations. g. Quarteroni and Valli, 1994, Chapter 14). We call this method SlopeLimit. A similar procedure is considered for the upscaled, 1D problems, obtained either by our approach or by taking the simple mean. It is refined in the situations when we have explicit formulas for the solution, using the direct numerical evaluation of the error function erf.
In our approach, the concept of ensemble of equilibrium subsystems introduced in our earlier chapters (see in detail Lazman and Yablonskii, 1991) was used as a very efficient tool of mathematical analysis and physico-chemical understanding. The equilibrium subsystem is such a system that corresponds to the following assumption: (nÀ1) steps are considered to be under equilibrium conditions, one step is limiting, where n is a number of steps. In fact, the concept of ‘‘equilibrium subsystems’’ is a generalization of the concept of ‘‘equilibrium step’’, which is well known in chemical kinetics.