ABSTRACT
This chapter presents an application of the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) for nonlinear systems. A cylindrical test section for performing heat transfer experiments contains electrically heated rods and is filled with liquid lead–bismuth eutectic. Since the test section is insulated on its radial surface and since the length of the cylindrical test section is much greater than its radius, the temperature variation in the radial direction can be neglected in comparison to the temperature variations in the axial direction, for the purposes of this illustrative problem. The first- and second-order temperature sensitivities will be used in this section to illustrate their essential role for quantifying standard deviations and non-Gaussian features of the various response distributions. To quantify asymmetries in distribution, at least the third-order response correlations need to be computed, which require, in turn, the exact computation of the first- and second-order response sensitivities to model parameters.
