Author(s)

Dan Gabriel Cacuci

Department of Mechanical Engineering, University of South Carolina, Columbia, SC, USA.

This work illustrates the application of the 1^st-CASAM to a paradigm heat transport model which admits exact closed-form solutions. The closed-form expressions obtained in this work for the sensitivities of the temperature distributions within the model to the model’s parameters, internal interfaces and external boundaries can be used to benchmark commercial and production software packages for simulating heat transport. The 1^st-CASAM highlights the novel finding that response sensitivities to the imprecisely known domain boundaries and interfaces can arise both from the definition of the system’s response as well as from the equations, interfaces and boundary conditions that characterize the model and its imprecisely known domain. By enabling, in premiere, the exact computations of sensitivities to interface and boundary parameters and conditions, the 1^st-CASAM enables the quantification of the effects of manufacturing tolerances on the responses of physical and engineering systems.

First-Order Comprehensive Adjoint Sensitivity Analysis Methodology (1^st-CASAM), Response Sensitivities for Coupled Systems Involving Imprecisely Known Interfaces, Parameters, And Boundaries, Coupled Heat Conduction and Convection

Cacuci, D.G. (2020) The First-Order Comprehensive Sensitivity Analysis Methodology (1^st-CASAM) for Scalar-Valued Responses: II. Illustrative Application to a Heat Transport Benchmark Model. American Journal of Computational Mathematics, 10, 290-310. doi: 10.4236/ajcm.2020.102016.