The iterative transformation method and length estimation for tubular flow reactors

摘要

In this note we apply an iterative transformation method in order to find the numerical solution and, more important, to provide the numerical evidence of the existence and uniqueness for the free boundary value problem describing the optimal length determination for tabular flow reactors. The main idea is to introduce in the mathematical model a nonphysical parameter and then require partial invariance under an extended stretching group. The solution of the original problem can be obtained by requiring that the parameter transforms in the unity. Finally we report numerical results that show the existence and uniqueness of the solution and give us an approximation to the free boundary value involved.