A correlation method of computational results. Application to absorption enhancement factor and catalyst effectiveness factor.:APPLICATION TO ABSORPTION ENHANCEMENT FACTOR AND CATALYST EFFECTIVENESS FACTOR
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To correlate a large number of computational results into a compact analytical equation, an improved method is proposed for technical problems which have the two asymptotes y(0)→1 and y(∞)→x. When an analytical solution g(x) for a simple system is obtained, solutions of a family of similar problems can be approximated by the equation y=G(xj))1/j (A)in which a parameter j is determined so that Eq. (A) agrees with the exact value at x=1, thus j=logg(1))/logy(1)A recently proposed method of Churchill, Usagi and Ozoe is a special case of Eq. (A) with g(x)= 1+x. The validity of the proposed method is confirmed in an application to simultaneous diffusion-reaction problems for various systems. It is interpreted that Eq. (A) describes a family of figures "similarly transformed" from an original g(x) with a similitude ratio 1/j on a logarithmic scale. A method of rough but simple estimation of j is also discussed.
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