A rational approximation of the effectiveness factor

A fast, approximate method of calculating the effectiveness factor for arbitrary rate expressions is presented. The method does not require any iterative or interpolative calculations. It utilizes the well known asymptotic behavior for small and large Thiele moduli to derive a rational function which gives an approximation valid for all Thiele moduli.

The approximation converges to the proper asymptotic values for small and large Thiele moduli and gives only small errors for intermediate values of 0. The method fails in the range in which either steep slopes or multiplicity exist in the η(ф) graph.