Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1278622 | International Journal of Hydrogen Energy | 2012 | 5 Pages |
Transcendental equations have to be solved in order to extract surface exchange and diffusion coefficients from transient techniques. In this work, numerical evaluations of the equation βntanβn = A, frequently used for a thin plane sheet geometry, have been studied in detail. Based on the Newton–Raphson method and the characteristics of the tangent function, a fast and stable algorithm was suggested to solve this equation for all values of A, which has so far not been the case in the literature. Moreover, a numerical approach to the transcendental equation used in a spherical geometry was also brought up.
► The transcendental equation βntanβn = A has been evaluated numerically. ► The only algorithm in the literature can not handle small values of A. ► Based on the Newton–Raphson method, a fast numerical algorithm has been developed. ► A numerical approach for a spherical geometry was also briefly brought up.