Solution of reaction and heat flow problems by nonlinear estimation

Abstract

Before the advent of nonlinear optimization algorithms, the solution of chemical reaction or heat transfer equations was attempted primarily by trial and error or linear approximation methods. In the method illustrated by the two examples in this paper, any set of nonlinear equations for a chemical or physical process are replaced by a single equation. The variables of interest are in the resulting functional equation treated as parameters whose optimum values are determined by a nonlinear estimation technique. These values are considered as nonlinear regression coefficients which are simultaneously adjusted by an optimization algorithm. The method gives an estimate of the standard deviation in the determination of the value of each variable and provides information concerning the errors associated with their interaction or pairwise correlations. Validity of the results is confirmed by comparison with solutions independently obtained through a matrix technique developed by Wu 1. For each of the examples the magnitude of computed residual is provided as a measure of the precision of the solution set. The general method is applicable to a very wide class of physical and chemical problems described by one or more nonlinear equations. Copyright © 1968 Canadian Society for Chemical Engineering