A new approach to the sensitivity analysis of large computational models is presented. The basis for the method is the well-known Green’s function technique. By working with the same differential equations as the conventional direct method, this new approach reduces the number of differential equations to be solved and replaces them by a set of integrals. Altogether, there is only one set of differential equations in the Green’s function method, regardless of the number of system parameters m. Sensitivity coefficients of all orders are expressed in integral form and evaluated in a recursive manner. Since evaluating well-behaved integrals is usually much easier than solving stiff differential equations, substantial savings can be achieved by the method when the number of system parameters is large. It is estimated that if only linear sensitivity coefficients are desired, then the Green’s function method could be advantageous for the case m≳n, where n is the number of dependent variables. However, if both linear and higher order sensitivity coefficients are to be computed, the method could be competitive with other approaches even when m<n. A numerical calculation on a simple linear system is presented to provide a brief illustration of the method.

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A numerical procedure is presented for implementing the Green’s function method of sensitivity analysis in chemical kinetics. The procedure is applied to three sets of chemical reactions: the Chapman mechanism for ozone kinetics, a mechanism for methane combustion and a model for formaldehyde oxidation in the presence of carbon monoxide. Whenever possible, comparisons with alternative methods of sensitivity analysis are made. It is shown that carefully analyzed sensitivity profiles can be used in conjunction with experiments and/or models to obtain useful information about chemical kinetic behavior. By using methods from multivariable calculus an entire family of sensitivity coefficients may be derived from the elementary sensitivities obtained by solving differential equations. Each elementary or derived sensitivity coefficient has a unique physical interpretation in terms of an experiment or modeling calculation. A simple nonlinear interpolation formula is suggested for easily estimating higher-order sensitivity information. Finally the overall computational efficacy of the Green’s function method of sensitivity analysis is assessed.

Kinetic modeling calculations on the H2–O2 system have been carried out with an extensive reaction set to probe the vicinity of the three explosion limits. Sensitivity analysis is used throughout this investigation to study system behavior, in particular, to elucidate mechanistic details. The concentrations and sensitivity profiles are discussed in light of the appropriate experimental results and existing theories of hydrogen combustion. The results indicate the present model to be useful over a wide pressure–temperature range. The reaction set is also used to probe the sensitivities for an experimental study designed to measure the rate constant of an important elementary reaction, H+O2+M→HO2+M, involved in this system. The versatility of the reaction set is also demonstrated by a study of a related chemical reaction, the decomposition of hydrogen peroxide. Finally, prospects for utilizing the methods and results of this study to examine other complex kinetic schemes are discussed.

Injection molding of foamed components typically uses chemical blowing agents (CBAs) or physical blowing agents (PBAs) to produce a cellular or microcellular structure. A CBA can be easily and directly mixed with plastic pellets and fed into the molding machine through the hopper while a generally finer, microcellular structure can be realized using PBAs. The PBA route is accomplished by injecting more environmentally benign gases into the machine barrel to form a single‐phase polymer–gas solution that subsequently foams during molding. This article proposes a new foam injection molding technology that enables the ease of processing of the CBA method with the foaming characteristics of a PBA, but in a cost‐effective fashion. In this article, the manufacturing method and theoretical background for producing plastic pellets loaded with carbon dioxide as well as the resulting part characteristics are described. Using the proposed technique, lightweight injection molded parts with a cellular structure, good dimensional stability, and a good surface quality can be produced. POLYM. ENG. SCI., 2011. © 2011 Society of Plastics Engineers