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Solution of reaction and heat flow problems by nonlinear estimation
Author(s) -
Surkan A. J.,
Wu C. L.
Publication year - 1968
Publication title -
the canadian journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.404
H-Index - 67
eISSN - 1939-019X
pISSN - 0008-4034
DOI - 10.1002/cjce.5450460403
Subject(s) - nonlinear system , mathematics , residual , nonlinear regression , measure (data warehouse) , nonlinear programming , mathematical optimization , regression analysis , algorithm , computer science , statistics , physics , quantum mechanics , database
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.