The Information Obtained from Model Solutions

the dependent variable u, which is typically a concentration or a mass related to the system, is seen to be a function of time f, distance z, or another mass or concentration v plus a set of specific parameters pertinent to the system. 

The first of these represents the special case where distance 2 becomes the dependent variable and time the independent variable. Solutions of this form arise, for example, in systems involving reacting particles, where particle radius is now the dependent variable, which varies with time. The matiie-matical expression that results has been given by Equation 2.9. The second. Equation 2.16e, is a multidimensional one and arises from a PDE. Some solutions to such PDE models appear in Qiapter 3, and the models themselves are taken up in Illustration 2.6 and Illustration 2.7. 

We first note that in addition to u either t or z may be the unknowns being sought. This is in fact the most common occurrence. We may wish, for example, to determine the time or distance necessary to affect a prescribed concentration change. Designing a scrubber, i.e., calculating its height z, falls in the latter categories. 

Next in importance as an unknown are the parameters, which we can accommodate in the following broad categories  

Transport coefficients, such as diffusivities, film coefficients, overall mass transfer coefficients, and permeabilities 

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